Mathematics Class VIII

Question 1 of 40

1. Question
1 point(s)
Factorise $y^2+3y+y+3 $
- $(y+3)\ (y+1) $
- $(y+1)\ (y+1) $
- $ (y+3)\ (y+3)$
- None of these
Correct

Incorrect

Hint

$y^2+3y+y+3=y(y+3)+1(y+3)=(y+1)\ (y+3)$
Question 2 of 40

2. Question
1 point(s)
Factorise $x^2+\dfrac{1}{x^2}+2-2x-\dfrac{2}{x} $
- $\left(x+\dfrac{1}{x}\right)\left(x+\dfrac{1}{x}-2\right) $
- $\left(x+\dfrac{1}{x}\right)\left(x-\dfrac{1}{x}+2\right) $
- $\left(x-\dfrac{1}{x}\right)\left(x+\dfrac{1}{x}-2\right) $
- $\left(x+\dfrac{1}{x}\right)\left(x+\dfrac{1}{x}+2\right) $
Correct

Incorrect

Hint

$\left(x+\dfrac{1}{x}\right)^2-2\left(x+\dfrac{1}{x}\right)\\ \\ \left(x+\dfrac{1}{x}\right)\left(x+\dfrac{1}{x}-2\right)$
Question 3 of 40

3. Question
1 point(s)
Factorise $\dfrac{9}{16}x^2+\dfrac{4}{9}y^2+4z^2-xy-\dfrac{8}{3}yz+3zx $
- $ \left(\dfrac{3x}{4}-\dfrac{2}{3}y+2z\right)^2$
- $\left(\dfrac{3x}{4}+\dfrac{2y}{3}+2z\right)^2 $
- $\left(\dfrac{3x}{4}+\dfrac{2y}{3}-2z\right)^2 $
- $ \left(\dfrac{3x}{4}-\dfrac{2y}{3}-2z\right)^2$
Correct

Incorrect

Hint

$\left(\dfrac{3x}{4}\right)^2+\left(\dfrac{-2y}{3}\right)^2+(2z)^2+2\times\dfrac{3x}{4}\times\dfrac{-2y}{3}+2\times\dfrac{-2y}{3}\times2z+2\times2z\times\dfrac{3x}{4}\\ \\ =\left(\dfrac{3x}{4} - \dfrac{2y}{3}+2z\right)^2$
Question 4 of 40

4. Question
1 point(s)
Factorise $x^2-xy-2xz-2yz $
- $(x-y)\ (x+2z) $
- $ (x+y)\ (x-2z) $
- $(x-y)\ (x-2z) $
- $(x+y)\ (x+2z) $
Correct

Incorrect

Hint

$x^2+xy-2xz-2yz=x(x+y)-2z(x+y)=(x-2z)(x+y)$
Question 5 of 40

5. Question
1 point(s)
Factorise $1-p^3 $
- $(1-p)\ (1+p+p^2) $
- $(1+p)\ (1-p-p^2) $
- $(1+p)\ (1+p^2) $
- $(1+p)\ (1-p^2) $
Correct

Incorrect

Hint

$1-p^3=1^3-p^3=(1-p)(1+p+p^2)$
Question 6 of 40

6. Question
1 point(s)
One of the factors of $x^2+\dfrac{1}{x^2}+2-2x\dfrac{-2}{x} $
- $x-\dfrac{1}{x} $
- $x+\dfrac{1}{x}-1 $
- $x+\dfrac{1}{x} $
- $x^2+\dfrac{1}{x^2} $
Correct

Incorrect

Hint

$x^2+\dfrac{1}{x^2}+2-2x\dfrac{-2}{x}\\ \\ =\left(x^2+\dfrac{1}{x^2}+2\right)-2\left(x+\dfrac{1}{x}\right)\\ \\ =\left(x+\dfrac{1}{x}\right)^2-2\left(x+\dfrac{1}{x}\right)\\ \\ =\left(x+\dfrac{1}{x}\right)\left(x+\dfrac{1}{x}-2\right)$
Question 7 of 40

7. Question
1 point(s)
If the factors of $a^2+b^2+2\ (ab+bc+ca)$ are $(a+b+m)$ and $(a+b+nc)$ then the value of $m+n$ is
- 0
- 2
- 4
- 6
Correct

Incorrect

Hint

$a^2+b^2+2ab+2bc+2ca+c^2-c^2\\ \\ =(a+b+c)^2-c^2=(a+b)\ (a+b+2c)$
Comparing,
$m=0,n=2\\ \\ m+n=0+2=2$
Question 8 of 40

8. Question
1 point(s)
The factors of $\sqrt3x^2+11x+6\sqrt3 $ is
- $(x-3\sqrt3)(\sqrt3x+2) $
- $(x-3\sqrt3)(\sqrt3x-2) $
- $(x+3\sqrt3)(\sqrt3x-2) $
- $(x+3\sqrt3)(\sqrt3x+2) $
Correct

Incorrect

Hint

$\sqrt3x^2+11x+6\sqrt3\\ \\ =\sqrt3x^2+9x+2x+6\sqrt3\\ \\ =\sqrt3x(x+3\sqrt3)+2(x+3\sqrt3)\\ \\ =(x+3\sqrt3)(\sqrt3x+2)$
Question 9 of 40

9. Question
1 point(s)
Factors of $x^4-(x-z)^4 $ are
- $(2x+z)\ (2x^3+z^3-2x^2) $
- $z\ (x+2z)\ (x^3+z^2-x^2) $
- $z\ (2x-z)\ (2x^2-2xz+z^2) $
- $z\ (x-2z)\ (2z^2-2xz+x^2) $
Correct

Incorrect

Hint

$\left(x^{2}\right)^{2}-\left\{(x-z)^{2}\right\}^{2}\\ \\ \left[x^{2}+(x-z)^{2}\right]\left[x^{2}-(x-z)^{2}\right]\\ \\ \left[x^{2}+(x-z)^{2}\right]\{x+(x-z)\}\{x-(x-z)\}\\ \\ (2 x-z) z\left(2 x^{2}+z^{2}-2 x z\right)$
Question 10 of 40

10. Question
1 point(s)
$\dfrac{a^2-b^2}{a(a-b)}-\dfrac{ab^2+a^2b}{ab^2} $ is equal to
- $\dfrac{(a+b)(b+a)}{ab} $
- $\dfrac{(a-b)(b-a)}{ab} $
- $\dfrac{(a+b)(a-b)}{ab} $
- $\dfrac{(a+b)(b-a)}{ab} $
Correct

Incorrect

Hint

$\dfrac{a^{2}-b^{2}}{a(a-b)}-\left[\dfrac{a b^{2}+a^{2} b}{a b^{2}}\right]\\ \\ \dfrac{(a-b)(a+b)}{a(a-b)}-\left[\dfrac{a b(b+a)}{(a b) b}\right]\\ \\ =\dfrac{a+b}{a}-\dfrac{(b+a)}{b}\\ \\ =\dfrac{(a+b) \times b-(b+a) \times a}{a b}\\ \\ =\dfrac{(a+b)(b-a)}{a b}$
Question 11 of 40

11. Question
1 point(s)
Factorise $36u^2+\dfrac{1}{25}v^2+25w^2\dfrac{-12uv}{5}-2vw+60wu $
- $\left(6u-\dfrac{v}{5}-5w\right)^2 $
- $\left(6u+\dfrac{v}{5}-5w\right)^2 $
- $\left(6u-\dfrac{v}{5}+5w\right)^2 $
- $\left(60+\dfrac{v}{5}+5w\right)^2 $
Correct

Incorrect

Hint

$(6 u)^{2}+\left(\frac{-v}{5}\right)^{2}+(5 w)^{2}+2 \times 6 u \times\left(\frac{-v}{5}\right)+2 \times\left(\frac{-v}{5}\right) \times 5 w+2 \times 6 u \times 5 w\\ \\ = \left(6 u - \frac{v}{5}+5 w\right)^{2}$
Question 12 of 40

12. Question
1 point(s)
The value of $52\ xyz\ (xy+yz+xz+y^2)\ (z+x) \div 104\ xy\ (xy+xz+yz+y^2)$ is
- $\dfrac{z(z+x)}{2} $
- $\dfrac{z(z-x)}{2} $
- $\dfrac{x(z-x)}{2} $
- $\dfrac{x(z+x)}{2} $
Correct

Incorrect

Hint

$\dfrac{52\ x y z\left(x y+y z+z x+y^{2}\right)(z+x)}{104\ x y\left(x y+x z+y z+y^{2}\right)}\\ \\ =\dfrac{1}{2} \times z \times(z+x)$
Question 13 of 40

13. Question
1 point(s)
The greatest common factor of $3m^2n^2+4n^2p^2+12\ m^2n^2p^2 $ is
- $n^2 $
- $m^2 $
- $p^2 $
- $mnp $
Correct

Incorrect

Hint

$3m^2n^2+4n^2p^2+12m^2n^2p^2$
The greatest common factor is $n^2$
Question 14 of 40

14. Question
1 point(s)
Factorise $(625\ b^4 – 800b^2+256)$
- $(5b+4)\ (5b+4)\ (5b-4)\ (5b-4) $
- $(5b-4)\ (5b-4)\ (5b-4)\ (5b-4) $
- $(b-1)\ (25b+16)\ (b-1)\ (25b+16) $
- $(5b^2+16)\ (5b-4)\ (5b+4) $
Correct

Incorrect

Hint

$(25 b^2)-(2\times16\times25 b^2)+16^2=(25b^2-16)^2\\ \\ = \left\{(5b)^2-4^2\right\}^2\\ \\ = \left\{(5b+4)\ (5b-4)\right\}^2$
Question 15 of 40

15. Question
1 point(s)
Factorise $64y^2-81$
- $ (8y+9)\ (8y-9)$
- $ (y-1)\ (64y+81) $
- $(y+1)\ (64y-81) $
- $(8y-9)\ (8y-9) $
Correct

Incorrect

Hint

$(8y)^2-9^2\\ \\ =(8y-9)\ (8y+9)$
Question 16 of 40

16. Question
1 point(s)
Find factors of $b^2+3ab-7b-21a$
- $ (3b+a)\ (-b-7)$
- $(3a-b)\ (b-7) $
- $(b+3a)\ (b-7) $
- $(3a+b)\ (-7b-1) $
Correct

Incorrect

Hint

$b^2+3ab-7b-21a\\ \\ =b(b+3a)-7(b+3a)\\ \\ =(b+3a)\ (b-7)$
Question 17 of 40

17. Question
1 point(s)
Factorise $81y^2 + 180y + 100$
- $ (y-1)\ (81y+100)$
- $(y+1)\ (81y+100) $
- $(9y+10)\ (9y+10) $
- $(9y+10)\ (9y-10) $
Correct

Incorrect

Hint

$81\ y^2+180y+100\\ \\ (9y)^2+10^2+2\times9y\times10\\ \\ =(9y+10)^2$
Question 18 of 40

18. Question
1 point(s)
The factors of $xy-6y-9x+54 $
- $(x-6)\ (y+9) $
- $ (-x-6)\ (-y-9) $
- $(-x-6)\ (y-9) $
- $ (x-6)\ (y-9)$
Correct

Incorrect

Hint

$xy - 6y-9x + 54\\ \\ =y(x-6) - 9\ (x-6)\\ \\ =(y-9)\ (x-6)$
Question 19 of 40

19. Question
1 point(s)
Factorise $(3y-2)^2+24y $
- $ (3y+2)\ (3y+2)$
- $(3y+2)\ (3y-2) $
- $(y+1)\ (9y+4) $
- $(y-1)\ (9y+4) $
Correct

Incorrect

Hint

$(3y-2)^2+24y\\ \\ =(3y)^2+2^2-2\times3y\times2+24y\\ \\ =9y^2+4-12y+24y\\ \\ =9y^2+4+12y\\ \\ =(3y+2)^2$
Question 20 of 40

20. Question
1 point(s)
Factorise $(64y^2+112y+49) $
- $ (y+1)\ (64y+49)$
- $ (8y+7)\ (8y+7)$
- $ (y-1)\ (64y+49)$
- $ (8y+7)\ (8y-7)$
Correct

Incorrect

Hint

$64y^2+112y+49\\ \\ (8y)^2+7^2+2\times8y\times7\\ \\ =(8y+7)^2 = (8y+7)\ (8y+7)$
Question 21 of 40

21. Question
1 point(s)
Factorise $16x^2-49 $
- $ (4x+7)\ (4x-7)$
- $(4x-7)\ (4x-7) $
- $ (x-1)\ (16x+49)$
- $(x+1)\ (16x-49) $
Correct

Incorrect

Hint

$16x^2-49=(4x)^2-7^2\\ \\ =(4x-7)\ (4x+7)$
Question 22 of 40

22. Question
1 point(s)
Factorise $(7b+3)^2 – 84b $
- $(7b-3)\ (7b-3) $
- $(b-1)\ (49b-9) $
- $(b+1)\ (49b-9) $
- $(7b+3)\ (7b-3) $
Correct

Incorrect

Hint

$(7b+3)^2 - 84b\\ \\ =49b^2+9+2\times7b\times3-84b\\ \\ =49b^2+9+42b-84b\\ \\ =49b^2+9-42b\\ \\ =(7b-3)^2$
Question 23 of 40

23. Question
1 point(s)
Factorise $(7x+6)^2 – 168x. $
- $(x-1)\ (49x-36) $
- $(7x+6)\ (7x-6) $
- $ (7x-6)\ (7x-6)$
- $(x+1)\ (49x-36) $
Correct

Incorrect

Hint

$(7x+6)^2 - 168x\\ \\ =49x^2+36+2\times7x \times 6-168x\\ \\ =49x^2+36+84x-168x\\ \\ =49x^2+36-84x\\ \\ =(7x-6)^2 = (7x-6)\ (7x-6)$
Question 24 of 40

24. Question
1 point(s)
Factorise $81y4-72y^2+16 $
- $ (3y+2)\ (3y+2)\ (3y-2)\ (3y-2)$
- $ (y-1)\ (9y+4)\ (y-1)\ (9y+4)$
- $(3y-2)\ (3y-2)\ (3y-2)\ (3y-2) $
- $(3y^2+4)\ (3y-2)\ (3y+2) $
Correct

Incorrect

Hint

$81y^4-72y^2+16\\ \\ =(9y^2)^2+4^2-2\times9y^2\times4\\ \\ =(9y^2-4)^2\\ \\ \left[(3y)^2-2^2\right]^2\\ \\ =(3y+2)^2(3y-2)^2\\ \\ =(3y+2)(3y+2)(3y-2)(3y-2)$
Question 25 of 40

25. Question
1 point(s)
Find the meaning values in the following factorisation.
$30ab + 12ab^3 =\underline{\quad}\underline{\quad}ab\ (\underline{\quad}\underline{\quad}+2b^2) $
- 6 and 5
- 5 and 6
- 8 and 3
- None of these
Correct

Incorrect

Hint

$30\ ab + 12ab^3= \underline6ab(\underline5 +2b^2)$
Question 26 of 40

26. Question
1 point(s)
Factorise $x^4-18x^2+81 $
- $ (x^2+9)\ (x-3)\ (x+3)$
- $ (x+3)\ (x+3)\ (x-3)\ (x-3)$
- $(x-1)\ (x+9)\ (x-1)\ (x+9) $
- $ (x-3)\ (x-3)\ (x-3)\ (x-3)$
Correct

Incorrect

Hint

$x^4-18x^2+81\\ \\ (x^2)^2 + 9^2-2\times x^2\times9\\ \\ =(x^2-9)^2\\ \\ =(x^2-3^2)^2=(x-3)^2\ (x+3)^2$
Question 27 of 40

27. Question
1 point(s)
Factorise $(3a-4)^2 + 48a $
- $ (3a+4)\ (3a+4)$
- $(a+1)\ (9a+16) $
- $(a-1)\ (9a+16) $
- $(3a+4)\ (3a-4) $
Correct

Incorrect

Hint

$(3a-4)^2 + 48a\\ \\ =9a^2+16-2\times3a\times4+48a\\ \\ =9a^2+16-24a+48a\\ \\ =9a^2+16+24a\\ \\ = (3a+4)^2$
Question 28 of 40

28. Question
1 point(s)
Find the missing values in the following factorisation.
$40\ x^3y^2z^2+12x^3yz^2=4x^3yz^2(\_\_y+\_\_) $
- 10 and 3
- 10 and 4
- 2 and 5
- 5 and 2
Correct

Incorrect

Hint

$40x^3y^2z^2+12x^3yz^2=\underline4x^3yz^2\left(10y + 3\right)\\ \\ (10y+3)$
Question 29 of 40

29. Question
1 point(s)
Find the factors of $ -7ab+4b-42a+24$
- $ (-7a+4)\ (b-6)$
- $ (-7a+4)\ (b+6)$
- $ (-7a+4)\ (-b+6)$
- $ (7a+4)\ (-b+6)$
Correct

Incorrect

Hint

$b(-7a+4) +6 (-7a+4)\\ \\ (b+6) (-7a+4)$
Question 30 of 40

30. Question
1 point(s)
Factorise $(3b-7)^2 + 84b $
- $(3b+7)\ (3b+7) $
- $ (b+1)\ (9b+49) $
- $(b-1)\ (9b+49) $
- $(3b+7)\ (3b-7) $
Correct

Incorrect

Hint

$(3b-7)^2+84b\\ \\ =9b^2+49-2\times3b\times7+84b\\ \\ =9b^2+49-42b+84b\\ \\ =9b^2+49+42b\\ \\ =(3b+7)^2$
Question 31 of 40

31. Question
1 point(s)
Find factors of $ 9b+ab-7a-63$
- $ (-a+9)\ (b-7)$
- $(-a+9)\ (-b-7) $
- $ (a+9)\ (b-7) $
- $(a+9)\ (-b-7) $
Correct

Incorrect

Hint

$b(a+9) -7\ (a+9)\\ \\ (b-7)\ (a+9)$
Question 32 of 40

32. Question
1 point(s)
Factorise $64x^2 – 25 $
- $(x-1)\ (64x+25) $
- $ (8x+5)\ (8x-5) $
- $ (8x-5)\ (8x-5)$
- $(x+1)\ (64x-25) $
Correct

Incorrect

Hint

$(8x)^2 - 5^2\\ \\ (8x-5)\ (8x+5)$
Question 33 of 40

33. Question
1 point(s)
Find factors of the polynomial $4x^2+4xy+y^2-4z^2 $
- $(2x+y-2z)\ (2x+y-2z) $
- $(2x-y+2z)\ (2x+y-2z) $
- $(2x+y+2z)\ (2x+y+2z) $
- $(2x+y+2z)\ (2x+y-2z) $
Correct

Incorrect

Hint

$(2x)^2 + 2\times2x \times y + y^2 - 4z^2\\ \\ (2x+y)^2-(2z)^2\\ \\ (2x+y+2z)\ (2x+y-2z)$
Question 34 of 40

34. Question
1 point(s)
Factorise $(16z^4-8z^2+1) $
- $ (2z-1)^2 (2z-1)^2$
- $(2z+1)^2 (2z-1)^2 $
- $ (z-1)^2 (4z+1)^2$
- $(2z^2+1)\ (2z-1)\ (2z+1) $
Correct

Incorrect

Hint

$(4z^2)^2 + 12 - 2\times 4z^2 \times 1\\ \\ (4z^2)^2 + 1^2 - 8z^2\\ \\ =(4z^2-1)^2\\ \\ =((2z)^2-1^2)^2\\ \\ = (2z-1)\ (2z+1)\ (2z-1)\ (2z+1)$
Question 35 of 40

35. Question
1 point(s)
Factorise $(2p+5)^2-40p $
- $ (p-1)\ (4p-25)$
- $(p+1)\ (4p-25) $
- $(2p+5)\ (2p-5) $
- $(2p-5)\ (2p-5) $
Correct

Incorrect

Hint

$(2p+5)^2 - 40p\\ \\ =4p^2+25+20p-40p\\ \\ =4p^2+25-20p\\ \\ =(2p-5)^2\\ \\ =(2p-5)\ (2p-5)$
Question 36 of 40

36. Question
1 point(s)
Factorise $9p^2-24p+16 $
- $(p+1)\ (9p-16) $
- $(p-1)\ (9p-16) $
- $ (3p+4)\ (3p-4)$
- $ (3p-4)^2$
Correct

Incorrect

Hint

$(3p)^2 + (-4)^2 -2 \times 3p \times 4\\ \\ = (3p-4)^2$
Question 37 of 40

37. Question
1 point(s)
Find factors of $5q^2-25pq+4q-20p $
- $ (-5q+p)\ (-5q+4)$
- $ (5p+q)\ (5q+4)$
- $(q-5p)\ (5q+4) $
- $(-5p+q)\ (4q-5) $
Correct

Incorrect

Hint

$5q(q-5p) +4 (q-5p)\\ \\ (5q+4)\ (q-5p)$
Question 38 of 40

38. Question
1 point(s)
Find factors of $3y^2+4y-15 $
- $(-y+3)\ (3y-5) $
- $ (y+3)\ (3y-5)$
- $(-y+3)\ (-3y-5) $
- $ (y-3)\ (3y-5)$
Correct

Incorrect

Hint

$3y^2+4y-15\\ \\ =3y^2+9y-5y-15 = 3y\ (y+3) -5(y+3)\\ \\ =(3y-5)\ (y+3)$
Question 39 of 40

39. Question
1 point(s)
Factorise $16y^2-88y+121 $
- $(4y-11)\ (4y-11) $
- $(4y+11)\ (4y-11) $
- $ (y-1)\ (16y-121)$
- $(y+1)\ (16y-121) $
Correct

Incorrect

Hint

$(4y)^2 + (-11)^2 -2 \times4y\times11\\ \\ =(4y-11)^2\\ \\ =(4y-11)\ (4y-11)$
Question 40 of 40

40. Question
1 point(s)
Find factors of $p^2-7p+10 $
- $(p-5)\ (p-2) $
- $(p-5)\ (-p-2) $
- $(p+5)\ (p-2) $
- $(-p-5)\ (-p-2) $
Correct

Incorrect

Hint

$P^2-7p+10\\ \\ P^2-5p-2p+10\\ \\ P(p-5) -2 (p-5)\\ \\ (p-2)\ (p-5)$