Factor 4t^2-11t+7

$4 t^{2} - 11 t + 7$

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 $a \cdot c = 4 \cdot 7 = 28$ and whose sum is $b = - 11$ .

Factor $- 11$ out of $- 11 t$ .

$4 t^{2} - 11 (t) + 7$

Rewrite $- 11$ as $- 4$ plus $- 7$

$4 t^{2} + (- 4 - 7) t + 7$

Apply the distributive property.

$4 t^{2} - 4 t - 7 t + 7$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 t^{2} - 4 t) - 7 t + 7$

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

$4 t (t - 1) - 7 (t - 1)$

Step 3

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

$(t - 1) (4 t - 7)$

Factor 4t^2-11t+7

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