Factorise the following polynomial: $9 x^{2} + 30 x + 25$

(x + 5) (x + 5)

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(3 x + 5) (3 x - 5)

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(3 x + 5) (3 x + 5)

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(9 x + 5) (5 x + 5)

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Solution

The correct option is B $(3 x + 5) (3 x + 5)$
We know that $(a x + b)^{2} = (a x + b) (a x + b)$
$=$ $a^{2} x^{2} + 2 a b x + b^{2}$
Now compare the coefficients, we get
$a^{2} = 9, 2 a b = 30, b^{2} = 25$
So, $a = 3, b = 5, a b = 15$
Therefore, factors of $9 x^{2} + 30 x + 25$ are $(3 x + 5) (3 x + 5)$

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