Algebra Examples

$5 x^{2} + 21 x + 4$

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

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Step 1.1

Factor $21$ out of $21 x$ .

$5 x^{2} + 21 (x) + 4$

Step 1.2

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

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

Step 1.3

Apply the distributive property.

$5 x^{2} + 1 x + 20 x + 4$

Step 1.4

Multiply $x$ by $1$ .

$5 x^{2} + x + 20 x + 4$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$(5 x^{2} + x) + 20 x + 4$

Step 2.2

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

$x (5 x + 1) + 4 (5 x + 1)$

Step 3

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

$(5 x + 1) (x + 4)$