Factor 4a^2-21a+5

$4 a^{2} - 21 a + 5$

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 $a \cdot c = 4 \cdot 5 = 20$ and whose sum is $b = - 21$ .

Factor $- 21$ out of $- 21 a$ .

$4 a^{2} - 21 (a) + 5$

Rewrite $- 21$ as $- 1$ plus $- 20$

$4 a^{2} + (- 1 - 20) a + 5$

Apply the distributive property.

$4 a^{2} - 1 a - 20 a + 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 a^{2} - 1 a) - 20 a + 5$

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

$a (4 a - 1) - 5 (4 a - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 a - 1$ .

$(4 a - 1) (a - 5)$

Factor 4a^2-21a+5

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