Factorisation - ICSE STD 9 MATHEMATICS Questions

An expression is factorised as $\left(2 x^3+2 x^2+x\right)\left(x^2-2 x+2\right)$. Which of the following terms will appear in the simplest form of the above expression?

A
$-2 x^3$
B
$3 x^3$
C
$6 x^3$
✓
$x^3$

Answer: D.

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Q 12MCQ1 Mark

If $x=\frac{a+b+c}{3}$, then $(x-a)^3+(x-b)^3+(x-c)^3$ can be factorised as :

A
$(x-a)(x-b)(x-c)$
B
$\frac{(x-a)(x-b)(x-c)}{3}$
✓
$3(x-a)(x-b)(x-c)$
D
none of these

Answer: C.

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Q 13MCQ1 Mark

$x^4+7 x^2+16$ can be factorised as :

✓
$\left(x^2+x+4\right)\left(x^2-x+4\right)$
B
$\left(x^2+x-4\right)\left(x^2-x+4\right)$
C
$\left(x^2-x-4\right)\left(x^2+x+4\right)$
D
none of these

Answer: A.

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Q 14MCQ1 Mark

One of the factors of $\left(x^2-4 x\right)\left(x^2-4 x-1\right)-20$ is :

A
$x-1$
✓
$x-2$
C
$x-4$
D
$x+5$

Answer: B.

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Q 15MCQ1 Mark

Assertion (A) : $a^3-2 \sqrt{2} b^3$ can be factorised as $(a-2 \sqrt{2})\left(a^2+\sqrt{2} a b+2 b^2\right)$
Reason (R) : $x^3-y^3=(x-y)\left(x^2+x y+y^2\right)$.

A
A is true, R is false
✓
A is false, R is true
C
Both A and R are true
D
Both A and R are false.

Answer: B.

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