Math / Algebra

QuestionFactor out the greatest common factor from the expression $8b^2 - 4b + 20$ .

Studdy Solution

STEP 1

1. We are asked to factor the greatest common factor (GCF) from the expression.
2. The expression is a polynomial with three terms: $8b^2$ , $-4b$ , and $20$ .
3. The GCF is the largest expression that divides each term of the polynomial without leaving a remainder.

STEP 2

1. Identify the greatest common factor of the coefficients in the expression.
2. Factor out the greatest common factor from the expression.

STEP 3

Identify the coefficients of each term in the expression: $8b^2$ , $-4b$ , and $20$ . The coefficients are $8$ , $-4$ , and $20$ .

STEP 4

Find the greatest common factor of the coefficients $8$ , $-4$ , and $20$ .
- The factors of $8$ are $1, 2, 4, 8$ . - The factors of $-4$ are $1, 2, 4$ . - The factors of $20$ are $1, 2, 4, 5, 10, 20$ .
The greatest common factor is $4$ .

STEP 5

Factor out the greatest common factor $4$ from each term in the expression:
$8b^2 - 4b + 20 = 4(2b^2 - b + 5)$
The expression with the greatest common factor factored out is:
$\boxed{4(2b^2 - b + 5)}$

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QuestionFactor out the greatest common factor from the expression $8b^2 - 4b + 20$ .

Studdy Solution

STEP 1

1. We are asked to factor the greatest common factor (GCF) from the expression.
2. The expression is a polynomial with three terms: $8b^2$ , $-4b$ , and $20$ .
3. The GCF is the largest expression that divides each term of the polynomial without leaving a remainder.

STEP 2

1. Identify the greatest common factor of the coefficients in the expression.
2. Factor out the greatest common factor from the expression.

STEP 3

Identify the coefficients of each term in the expression: $8b^2$ , $-4b$ , and $20$ . The coefficients are $8$ , $-4$ , and $20$ .

STEP 4

Find the greatest common factor of the coefficients $8$ , $-4$ , and $20$ .
- The factors of $8$ are $1, 2, 4, 8$ . - The factors of $-4$ are $1, 2, 4$ . - The factors of $20$ are $1, 2, 4, 5, 10, 20$ .
The greatest common factor is $4$ .

STEP 5

Factor out the greatest common factor $4$ from each term in the expression:
$8b^2 - 4b + 20 = 4(2b^2 - b + 5)$
The expression with the greatest common factor factored out is:
$\boxed{4(2b^2 - b + 5)}$

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QuestionFactor out the greatest common factor from the expression 8b2−4b+208b^2 - 4b + 208b2−4b+20.

Studdy Solution

STEP 1

1. We are asked to factor the greatest common factor (GCF) from the expression.2. The expression is a polynomial with three terms: 8b28b^28b2, −4b-4b−4b, and 202020.3. The GCF is the largest expression that divides each term of the polynomial without leaving a remainder.

STEP 2

1. Identify the greatest common factor of the coefficients in the expression.2. Factor out the greatest common factor from the expression.

STEP 3

Identify the coefficients of each term in the expression: 8b28b^28b2, −4b-4b−4b, and 202020. The coefficients are 888, −4-4−4, and 202020.

STEP 4

Find the greatest common factor of the coefficients 888, −4-4−4, and 202020.- The factors of 888 are 1,2,4,81, 2, 4, 81,2,4,8. - The factors of −4-4−4 are 1,2,41, 2, 41,2,4. - The factors of 202020 are 1,2,4,5,10,201, 2, 4, 5, 10, 201,2,4,5,10,20.The greatest common factor is 444.

STEP 5

Factor out the greatest common factor 444 from each term in the expression:8b2−4b+20=4(2b2−b+5) 8b^2 - 4b + 20 = 4(2b^2 - b + 5) 8b2−4b+20=4(2b2−b+5) The expression with the greatest common factor factored out is:4(2b2−b+5) \boxed{4(2b^2 - b + 5)} 4(2b2−b+5)​

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QuestionFactor out the greatest common factor from the expression $8b^2 - 4b + 20$ .

1. We are asked to factor the greatest common factor (GCF) from the expression.
2. The expression is a polynomial with three terms: $8b^2$ , $-4b$ , and $20$ .
3. The GCF is the largest expression that divides each term of the polynomial without leaving a remainder.

1. Identify the greatest common factor of the coefficients in the expression.
2. Factor out the greatest common factor from the expression.

Identify the coefficients of each term in the expression: $8b^2$ , $-4b$ , and $20$ . The coefficients are $8$ , $-4$ , and $20$ .

Find the greatest common factor of the coefficients $8$ , $-4$ , and $20$ .
- The factors of $8$ are $1, 2, 4, 8$ . - The factors of $-4$ are $1, 2, 4$ . - The factors of $20$ are $1, 2, 4, 5, 10, 20$ .
The greatest common factor is $4$ .

Factor out the greatest common factor $4$ from each term in the expression:
$8b^2 - 4b + 20 = 4(2b^2 - b + 5)$
The expression with the greatest common factor factored out is:
$\boxed{4(2b^2 - b + 5)}$