Factor 25p^2-74p-3

$25 p^{2} - 74 p - 3$

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 $a \cdot c = 25 \cdot - 3 = - 75$ and whose sum is $b = - 74$ .

Factor $- 74$ out of $- 74 p$ .

$25 p^{2} - 74 (p) - 3$

Rewrite $- 74$ as $1$ plus $- 75$

$25 p^{2} + (1 - 75) p - 3$

Apply the distributive property.

$25 p^{2} + 1 p - 75 p - 3$

Multiply $p$ by $1$ .

$25 p^{2} + p - 75 p - 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(25 p^{2} + p) - 75 p - 3$

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

$p (25 p + 1) - 3 (25 p + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $25 p + 1$ .

$(25 p + 1) (p - 3)$

Factor 25p^2-74p-3

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