Math / Algebra

QuestionFactor by grouping. 4) $5 x^{3}-10 x^{2}-3 x+6$ (guided practice)
1. Factor each term and mark the common factors. There are common factors for the group including the first two terms and separate common factors for the group including the last two terms.
2. Multiply the common factors in each group to find the GCFs.
3. Factor the GCF out of the first two terms and the GCF out of the second two terms.
4. Use the distributive property to factor out the common binomial factor and multiply the combination of the GCFs by that binomial factor.

Studdy Solution

STEP 1

1. We are given a polynomial expression $5x^3 - 10x^2 - 3x + 6$ .
2. The goal is to factor the expression by grouping terms.
3. We will follow the guided practice steps provided.

STEP 2

1. Group the terms and identify common factors within each group.
2. Determine the greatest common factor (GCF) for each group.
3. Factor out the GCF from each group.
4. Use the distributive property to factor out the common binomial factor.

STEP 3

Group the terms in the polynomial:
$(5x^3 - 10x^2) + (-3x + 6)$
Identify common factors in each group. For the first group $5x^3 - 10x^2$ , the common factor is $5x^2$ . For the second group $-3x + 6$ , the common factor is $-3$ .

STEP 4

Determine the GCF for each group:
- For $5x^3 - 10x^2$ , the GCF is $5x^2$ . - For $-3x + 6$ , the GCF is $-3$ .

STEP 5

Factor out the GCF from each group:
$5x^2(x - 2) - 3(x - 2)$
Notice that both terms now contain the common binomial factor $(x - 2)$ .

STEP 6

Use the distributive property to factor out the common binomial factor $(x - 2)$ :
$(5x^2 - 3)(x - 2)$
The expression is now fully factored by grouping.

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Studdy Solution

STEP 1

1. We are given a polynomial expression $5x^3 - 10x^2 - 3x + 6$ .
2. The goal is to factor the expression by grouping terms.
3. We will follow the guided practice steps provided.

STEP 2

1. Group the terms and identify common factors within each group.
2. Determine the greatest common factor (GCF) for each group.
3. Factor out the GCF from each group.
4. Use the distributive property to factor out the common binomial factor.

STEP 3

Group the terms in the polynomial:
$(5x^3 - 10x^2) + (-3x + 6)$
Identify common factors in each group. For the first group $5x^3 - 10x^2$ , the common factor is $5x^2$ . For the second group $-3x + 6$ , the common factor is $-3$ .

STEP 4

Determine the GCF for each group:
- For $5x^3 - 10x^2$ , the GCF is $5x^2$ . - For $-3x + 6$ , the GCF is $-3$ .

STEP 5

Factor out the GCF from each group:
$5x^2(x - 2) - 3(x - 2)$
Notice that both terms now contain the common binomial factor $(x - 2)$ .

STEP 6

Use the distributive property to factor out the common binomial factor $(x - 2)$ :
$(5x^2 - 3)(x - 2)$
The expression is now fully factored by grouping.

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Studdy Solution

STEP 1

1. We are given a polynomial expression 5x3−10x2−3x+65x^3 - 10x^2 - 3x + 65x3−10x2−3x+6.2. The goal is to factor the expression by grouping terms.3. We will follow the guided practice steps provided.

STEP 2

1. Group the terms and identify common factors within each group.2. Determine the greatest common factor (GCF) for each group.3. Factor out the GCF from each group.4. Use the distributive property to factor out the common binomial factor.

STEP 3

STEP 4

Determine the GCF for each group:- For 5x3−10x25x^3 - 10x^25x3−10x2, the GCF is 5x25x^25x2. - For −3x+6-3x + 6−3x+6, the GCF is −3-3−3.

STEP 5

Factor out the GCF from each group:5x2(x−2)−3(x−2) 5x^2(x - 2) - 3(x - 2) 5x2(x−2)−3(x−2)Notice that both terms now contain the common binomial factor (x−2)(x - 2)(x−2).

STEP 6

Use the distributive property to factor out the common binomial factor (x−2)(x - 2)(x−2):(5x2−3)(x−2) (5x^2 - 3)(x - 2) (5x2−3)(x−2)The expression is now fully factored by grouping.

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1. We are given a polynomial expression $5x^3 - 10x^2 - 3x + 6$ .
2. The goal is to factor the expression by grouping terms.
3. We will follow the guided practice steps provided.

1. Group the terms and identify common factors within each group.
2. Determine the greatest common factor (GCF) for each group.
3. Factor out the GCF from each group.
4. Use the distributive property to factor out the common binomial factor.

Determine the GCF for each group:
- For $5x^3 - 10x^2$ , the GCF is $5x^2$ . - For $-3x + 6$ , the GCF is $-3$ .

Factor out the GCF from each group:
$5x^2(x - 2) - 3(x - 2)$
Notice that both terms now contain the common binomial factor $(x - 2)$ .

Use the distributive property to factor out the common binomial factor $(x - 2)$ :
$(5x^2 - 3)(x - 2)$
The expression is now fully factored by grouping.