Algebra Examples

3 y^{2} + 7 y + 2

$3 y^{2} + 7 y + 2$

Step 1

For a polynomial of the form

a x^{2} + b x + c

$a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is

a \cdot c = 3 \cdot 2 = 6

$a \cdot c = 3 \cdot 2 = 6$ and whose sum is

b = 7

$b = 7$ .

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Step 1.1

Factor

7

$7$ out of

7 y

$7 y$ .

3 y^{2} + 7 (y) + 2

$3 y^{2} + 7 (y) + 2$

Step 1.2

Rewrite

7

$7$ as

1

$1$ plus

6

$6$

3 y^{2} + (1 + 6) y + 2

$3 y^{2} + (1 + 6) y + 2$

Step 1.3

Apply the distributive property.

3 y^{2} + 1 y + 6 y + 2

$3 y^{2} + 1 y + 6 y + 2$

Step 1.4

Multiply

y

$y$ by

1

$1$ .

3 y^{2} + y + 6 y + 2

$3 y^{2} + y + 6 y + 2$

3 y^{2} + y + 6 y + 2

$3 y^{2} + y + 6 y + 2$

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.

(3 y^{2} + y) + 6 y + 2

$(3 y^{2} + y) + 6 y + 2$

Step 2.2

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

y (3 y + 1) + 2 (3 y + 1)

$y (3 y + 1) + 2 (3 y + 1)$

y (3 y + 1) + 2 (3 y + 1)

$y (3 y + 1) + 2 (3 y + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

3 y + 1

$3 y + 1$ .

(3 y + 1) (y + 2)

$(3 y + 1) (y + 2)$

3 y^{2} + 7 y + 2

$3 y^{2} + 7 y + 2$

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