Factorization - ICSE STD 8 MATHS Questions

Q 1[1 Mark Question Answer]1 Mark

Factorize : $\frac{1}{4} z^6+9 a^2-3 a z^3$

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Q 2[1 Mark Question Answer]1 Mark

Factorize : $\frac{9 p^2}{q^2}+\frac{16 r^2}{m^2}+\frac{24 p r}{q m}$

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Q 3[1 Mark Question Answer]1 Mark

Factorize : $9 q^4 r^4-6 p^4 q^2 r^2+p^8$

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Q 4[1 Mark Question Answer]1 Mark

Factorize : $9-30 z+25 z^2$

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Q 5[1 Mark Question Answer]1 Mark

Factorize : $16+56 x+49 x^2$

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Q 6[2 Mark Question Answer]2 Marks

Using the identity $\left(a^2-b^2\right)=(a+b)(a-b)$, evaluate :
$\frac{7.3 \times 7.3-2.7 \times 2.7}{7.3-2.7}$

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Q 7[2 Mark Question Answer]2 Marks

Using the identity $\left(a^2-b^2\right)=(a+b)(a-b)$, evaluate :
$\left(6 \frac{4}{11}\right)^2-\left(4 \frac{7}{11}\right)^2$

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Q 8[2 Mark Question Answer]2 Marks

Using the identity $\left(a^2-b^2\right)=(a+b)(a-b)$, evaluate :
$\left(7 \frac{3}{4}\right)^2-\left(2 \frac{1}{4}\right)^2$

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Q 9[2 Mark Question Answer]2 Marks

Using the identity $\left(a^2-b^2\right)=(a+b)(a-b)$, evaluate :
$(0.8)^2-(0.2)^2$

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Q 10[2 Mark Question Answer]2 Marks

Using the identity $\left(a^2-b^2\right)=(a+b)(a-b)$, evaluate :
$(15.8)^2-(9.2)^2$

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Q 11[4 marks sum]4 Marks

Consider the following four algebraic expressions :
(A) $x^2+x-12$ $\quad$ (B) $x^2-9$ $\quad$ (C) $x^2-8 x+16$ $\quad$ (D) $x^2+6 x+9$
Q.1. Which of the following pairs of expressions do not have any common factor ?
(a) A and B $\quad$ (b) A and C $\quad$ (c) B and D $\quad$ (d) All of these
Q.2. ( $x-3$ ) is a factor of how many of the given expressions?
(a) None $\quad$ (b) One $\quad$ (c) Two $\quad$ (d) Three
Q.3. Expression A shares a common factor with which of the following expressions?
(a) $x^2-2 x-15$ $\quad$ (b) $x^2-9 x+20$ $\quad$ (c) $x^2+x-20$ $\quad$ (d) $x^2-16$
Q.4. Expression C shares a common factor with which of the following expressions ?
(a) $x^2+2 x+8$ $\quad$ (b) $x^2-7 x+12$ $\quad$ (c) $x^2-x-20$ $\quad$ (d) $x^2+3 x-4$

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Q 12MCQ1 Mark

$a^2-a c+a b-b c=$ ?