Factor by Grouping x^2-5xs-24s^2

$x^{2} - 5 x s - 24 s^{2}$

Step 1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = - 24 \cdot 1 = - 24$ and whose sum is $b = - 5$ .

Reorder terms.

$- 24 s^{2} + x^{2} - 5 s x$

Reorder $x^{2}$ and $- 5 s x$ .

$- 24 s^{2} - 5 s x + x^{2}$

Factor $- 5$ out of $- 5 s x$ .

$- 24 s^{2} - 5 (s x) + x^{2}$

Rewrite $- 5$ as $3$ plus $- 8$

$- 24 s^{2} + (3 - 8) (s x) + x^{2}$

Apply the distributive property.

$- 24 s^{2} + 3 (s x) - 8 (s x) + x^{2}$

Remove unnecessary parentheses.

$- 24 s^{2} + 3 s x - 8 (s x) + x^{2}$

Remove unnecessary parentheses.

$- 24 s^{2} + 3 s x - 8 s x + x^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(- 24 s^{2} + 3 s x) - 8 s x + x^{2}$

Factor out the greatest common factor (GCF) from each group.

$3 s (- 8 s + x) + x (- 8 s + x)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $- 8 s + x$ .

$(- 8 s + x) (3 s + x)$

Factor by Grouping x^2-5xs-24s^2

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