Math / Algebra

QuestionFactor completely, or state that the polynomial is prime. $2 x^{2}-8$
Select the correct choice below and, if necessary, fill in the answer box within your choice. A. $2 x^{2}-8=$ $\square$ B. The polynomial is prime.

Studdy Solution

STEP 1

1. We are given a polynomial $2x^2 - 8$ .
2. We need to determine if it can be factored completely or if it is prime.
3. A polynomial is prime if it cannot be factored into polynomials of lower degree with integer coefficients.

STEP 2

1. Identify and factor out the greatest common factor (GCF) from the polynomial.
2. Check if the resulting expression can be factored further.

STEP 3

Identify the greatest common factor (GCF) of the terms in the polynomial $2x^2 - 8$ .
The GCF of $2x^2$ and $-8$ is $2$ .

STEP 4

Factor out the GCF from the polynomial:
$2x^2 - 8 = 2(x^2 - 4)$

STEP 5

Examine the expression inside the parentheses, $x^2 - 4$ , to see if it can be factored further.
Notice that $x^2 - 4$ is a difference of squares, which can be factored as:
$x^2 - 4 = (x - 2)(x + 2)$

STEP 6

Substitute the factored form of $x^2 - 4$ back into the expression:
$2(x^2 - 4) = 2(x - 2)(x + 2)$
The polynomial is completely factored as:
$2(x - 2)(x + 2)$
The correct choice is:
A. $2x^2 - 8 = 2(x - 2)(x + 2)$

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QuestionFactor completely, or state that the polynomial is prime. $2 x^{2}-8$
Select the correct choice below and, if necessary, fill in the answer box within your choice. A. $2 x^{2}-8=$ $\square$ B. The polynomial is prime.

Studdy Solution

STEP 1

1. We are given a polynomial $2x^2 - 8$ .
2. We need to determine if it can be factored completely or if it is prime.
3. A polynomial is prime if it cannot be factored into polynomials of lower degree with integer coefficients.

STEP 2

1. Identify and factor out the greatest common factor (GCF) from the polynomial.
2. Check if the resulting expression can be factored further.

STEP 3

Identify the greatest common factor (GCF) of the terms in the polynomial $2x^2 - 8$ .
The GCF of $2x^2$ and $-8$ is $2$ .

STEP 4

Factor out the GCF from the polynomial:
$2x^2 - 8 = 2(x^2 - 4)$

STEP 5

Examine the expression inside the parentheses, $x^2 - 4$ , to see if it can be factored further.
Notice that $x^2 - 4$ is a difference of squares, which can be factored as:
$x^2 - 4 = (x - 2)(x + 2)$

STEP 6

Substitute the factored form of $x^2 - 4$ back into the expression:
$2(x^2 - 4) = 2(x - 2)(x + 2)$
The polynomial is completely factored as:
$2(x - 2)(x + 2)$
The correct choice is:
A. $2x^2 - 8 = 2(x - 2)(x + 2)$

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QuestionFactor completely, or state that the polynomial is prime. 2x2−82 x^{2}-82x2−8Select the correct choice below and, if necessary, fill in the answer box within your choice. A. 2x2−8=2 x^{2}-8=2x2−8= □\square□ B. The polynomial is prime.

Studdy Solution

STEP 1

1. We are given a polynomial 2x2−82x^2 - 82x2−8.2. We need to determine if it can be factored completely or if it is prime.3. A polynomial is prime if it cannot be factored into polynomials of lower degree with integer coefficients.

STEP 2

1. Identify and factor out the greatest common factor (GCF) from the polynomial.2. Check if the resulting expression can be factored further.

STEP 3

Identify the greatest common factor (GCF) of the terms in the polynomial 2x2−82x^2 - 82x2−8.The GCF of 2x22x^22x2 and −8-8−8 is 222.

STEP 4

Factor out the GCF from the polynomial:2x2−8=2(x2−4) 2x^2 - 8 = 2(x^2 - 4) 2x2−8=2(x2−4)

STEP 5

Examine the expression inside the parentheses, x2−4x^2 - 4x2−4, to see if it can be factored further.Notice that x2−4x^2 - 4x2−4 is a difference of squares, which can be factored as:x2−4=(x−2)(x+2) x^2 - 4 = (x - 2)(x + 2) x2−4=(x−2)(x+2)

STEP 6

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QuestionFactor completely, or state that the polynomial is prime. $2 x^{2}-8$
Select the correct choice below and, if necessary, fill in the answer box within your choice. A. $2 x^{2}-8=$ $\square$ B. The polynomial is prime.

1. We are given a polynomial $2x^2 - 8$ .
2. We need to determine if it can be factored completely or if it is prime.
3. A polynomial is prime if it cannot be factored into polynomials of lower degree with integer coefficients.

1. Identify and factor out the greatest common factor (GCF) from the polynomial.
2. Check if the resulting expression can be factored further.

Identify the greatest common factor (GCF) of the terms in the polynomial $2x^2 - 8$ .
The GCF of $2x^2$ and $-8$ is $2$ .

Factor out the GCF from the polynomial:
$2x^2 - 8 = 2(x^2 - 4)$

Examine the expression inside the parentheses, $x^2 - 4$ , to see if it can be factored further.
Notice that $x^2 - 4$ is a difference of squares, which can be factored as:
$x^2 - 4 = (x - 2)(x + 2)$