Math  /  Algebra

QuestionFactor using the GCF 1) 12x3+8x12 x^{3}+8 x (guided practice)
1. Factor each term and mark the common factors.
2. Multiply the common factors to find the GCF.
3. Rewrite each term as the product of the GCF and other factors.
4. Rewrite the expression using the factors from the previous step.
5. Use the distributive property: ab+ac=a(b+c)a b+a c=a(b+c).

Studdy Solution

STEP 1

1. We are given a polynomial expression: 12x3+8x12x^3 + 8x.
2. We need to factor this expression using the Greatest Common Factor (GCF).
3. The steps provided will guide us through the process of factoring.

STEP 2

1. Factor each term and identify the common factors.
2. Determine the GCF by multiplying the common factors.
3. Rewrite each term as a product of the GCF and other factors.
4. Rewrite the entire expression using these factors.
5. Apply the distributive property to express the factored form.

STEP 3

Factor each term in the expression 12x3+8x12x^3 + 8x.
- For 12x312x^3, the factors are 2×2×3×x×x×x2 \times 2 \times 3 \times x \times x \times x. - For 8x8x, the factors are 2×2×2×x2 \times 2 \times 2 \times x.
Identify the common factors: 2×2×x2 \times 2 \times x.

STEP 4

Multiply the common factors to find the GCF:
GCF=2×2×x=4x \text{GCF} = 2 \times 2 \times x = 4x

STEP 5

Rewrite each term as the product of the GCF and other factors:
- For 12x312x^3, express it as 4x×(3x2)4x \times (3x^2). - For 8x8x, express it as 4x×24x \times 2.

STEP 6

Rewrite the entire expression using the factors from the previous step:
12x3+8x=4x×(3x2)+4x×2 12x^3 + 8x = 4x \times (3x^2) + 4x \times 2

STEP 7

Apply the distributive property to factor the expression:
4x×(3x2+2) 4x \times (3x^2 + 2)
The expression is now factored using the GCF.

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