Factorize the following
$x^{2} + 13 x + 30$

(x + 3) (x + 10)

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(x - 3) (x + 10)

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(x + 3) (x - 10)

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None of these

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Solution

The correct option is A $(x + 3) (x + 10)$
In the given polynomial $x^{2} + 13 x + 30$ ,

The first term is $x^{2}$ and its coefficient is $1$ .

The middle term is $13 x$ and its coefficient is $13$ .

The last term is a constant term $30$ .

Multiply the coefficient of the first term by the constant $1 \times 13 = 13$ .

We now find the factor of $30$ whose sum equals the coefficient of the middle term, which is $13$ and then factorize the polynomial $x^{2} + 13 x + 30$ as shown below:
$x^{2} + 13 x + 30$

$= x^{2} + 10 x + 3 x + 30$

$= x (x + 10) + 3 (x + 10)$

$= (x + 3) (x + 10)$

Hence, $x^{2} + 13 x + 30 = (x + 3) (x + 10)$ .

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Similar questions

The factors of x⁴ + x² + 25 are

(a) (x² + 3x + 5) (x² − 3x + 5)

(b) (x²+ 3x + 5) (x² + 3x − 5)

(c) (x² + x +5) (x² − x + 5)

(d) none of these

8 x^{2} - 13 x - 5

x^{2} - 3 x + 10

{3 x}^{2} - x - 10.

{3 x}^{2} - x - 10.

x^{2} + 3 x - 5

x^{4} + 4 x^{3} + x - 10

x = 10

x^{2} - 3 (x - 10)

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