Factor 5t^2-24t-5

$5 t^{2} - 24 t - 5$

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 $a \cdot c = 5 \cdot - 5 = - 25$ and whose sum is $b = - 24$ .

Factor $- 24$ out of $- 24 t$ .

$5 t^{2} - 24 (t) - 5$

Rewrite $- 24$ as $1$ plus $- 25$

$5 t^{2} + (1 - 25) t - 5$

Apply the distributive property.

$5 t^{2} + 1 t - 25 t - 5$

Multiply $t$ by $1$ .

$5 t^{2} + t - 25 t - 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 t^{2} + t) - 25 t - 5$

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

$t (5 t + 1) - 5 (5 t + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 t + 1$ .

$(5 t + 1) (t - 5)$

Factor 5t^2-24t-5

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