Question

Factorise a^2x^3+2abx^2+b^2x

Answer 1

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Answer 2

Factors of $\bf \: {a}^{2} {x}^{3} + 2abx^{2} + {b}^{2}x$ are $\bf \red{x(ax + b)^{2}}$.

Given:

• ${a}^{2} {x}^{3} + 2ab {x}^{2} + {b}^{2} x$

To find:

• Factorise the polynomial.

Solution:

Step 1:

Take x common from all terms.

$\bf {a}^{2} {x}^{3} + 2ab {x}^{2} + {b}^{2} x = x({a}^{2} {x}^{2} + 2ab x+ {b}^{2} )$

Step 2:

Find the factors of polynomials.

Split the middle term.

${a}^{2} {x}^{3} + 2ab {x}^{2} + {b}^{2} x = x({a}^{2} {x}^{2} + ab x+abx+ {b}^{2} )$

Take common from the first two terms and the last two terms.

${a}^{2} {x}^{3} + 2ab {x}^{2} + {b}^{2} x = x[ax(ax + b) + b(ax + b)]$

Take common (ax+b) from both terms.

${a}^{2} {x}^{3} + 2ab {x}^{2} + {b}^{2} x = x(ax + b)(ax + b)$

or

$\bf {a}^{2} {x}^{3} + 2ab {x}^{2} + {b}^{2} x = x(ax + b)^{2}$

Thus,

Factors are $\bf \: {a}^{2} {x}^{3} + 2abx^{2} + {b}^{2}x = x(ax + b)^{2}$

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