Factor 5t^2+28t+32

$5 t^{2} + 28 t + 32$

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 $a \cdot c = 5 \cdot 32 = 160$ and whose sum is $b = 28$ .

Factor $28$ out of $28 t$ .

$5 t^{2} + 28 (t) + 32$

Rewrite $28$ as $8$ plus $20$

$5 t^{2} + (8 + 20) t + 32$

Apply the distributive property.

$5 t^{2} + 8 t + 20 t + 32$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 t^{2} + 8 t) + 20 t + 32$

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

$t (5 t + 8) + 4 (5 t + 8)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 t + 8$ .

$(5 t + 8) (t + 4)$

Factor 5t^2+28t+32

Related Questions

Support LCMGCF.com by disabling your adblocker.