Finite Math Examples

$3 {(x + 8)}^{2} + 19 (x + 8) + 30$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(x + 8)}^{2}$ as $(x + 8) (x + 8)$ .

$3 ((x + 8) (x + 8)) + 19 (x + 8) + 30$

Step 1.2

Expand $(x + 8) (x + 8)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$3 (x (x + 8) + 8 (x + 8)) + 19 (x + 8) + 30$

Step 1.2.2

Apply the distributive property.

$3 (x \cdot x + x \cdot 8 + 8 (x + 8)) + 19 (x + 8) + 30$

Step 1.2.3

Apply the distributive property.

$3 (x \cdot x + x \cdot 8 + 8 x + 8 \cdot 8) + 19 (x + 8) + 30$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

$3 (x^{2} + x \cdot 8 + 8 x + 8 \cdot 8) + 19 (x + 8) + 30$

Step 1.3.1.2

Move $8$ to the left of $x$ .

$3 (x^{2} + 8 \cdot x + 8 x + 8 \cdot 8) + 19 (x + 8) + 30$

Step 1.3.1.3

Multiply $8$ by $8$ .

$3 (x^{2} + 8 x + 8 x + 64) + 19 (x + 8) + 30$

Step 1.3.2

Add $8 x$ and $8 x$ .

$3 (x^{2} + 16 x + 64) + 19 (x + 8) + 30$

Step 1.4

Apply the distributive property.

$3 x^{2} + 3 (16 x) + 3 \cdot 64 + 19 (x + 8) + 30$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $16$ by $3$ .

$3 x^{2} + 48 x + 3 \cdot 64 + 19 (x + 8) + 30$

Step 1.5.2

Multiply $3$ by $64$ .

$3 x^{2} + 48 x + 192 + 19 (x + 8) + 30$

Step 1.6

Apply the distributive property.

$3 x^{2} + 48 x + 192 + 19 x + 19 \cdot 8 + 30$

Step 1.7

Multiply $19$ by $8$ .

$3 x^{2} + 48 x + 192 + 19 x + 152 + 30$

Step 2

Simplify by adding terms.

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Step 2.1

Add $48 x$ and $19 x$ .

$3 x^{2} + 67 x + 192 + 152 + 30$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $192$ and $152$ .

$3 x^{2} + 67 x + 344 + 30$

Step 2.2.2

Add $344$ and $30$ .

$3 x^{2} + 67 x + 374$

Step 3

Factor by grouping.

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Step 3.1

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 $a \cdot c = 3 \cdot 374 = 1122$ and whose sum is $b = 67$ .

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Step 3.1.1

Factor $67$ out of $67 x$ .

$3 x^{2} + 67 (x) + 374$

Step 3.1.2

Rewrite $67$ as $33$ plus $34$

$3 x^{2} + (33 + 34) x + 374$

Step 3.1.3

Apply the distributive property.

$3 x^{2} + 33 x + 34 x + 374$

Step 3.2

Factor out the greatest common factor from each group.

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Step 3.2.1

Group the first two terms and the last two terms.

$(3 x^{2} + 33 x) + 34 x + 374$

Step 3.2.2

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

$3 x (x + 11) + 34 (x + 11)$

Step 3.3

Factor the polynomial by factoring out the greatest common factor, $x + 11$ .

$(x + 11) (3 x + 34)$