Math / Algebra

QuestionFactor by grouping. $x^{2}+6 x-9 x-54$ $(x+6)(x-3)$ $(x-6)(x-9)$ $2(3 x-27)$ $(x+6)(x-9)$

Studdy Solution

STEP 1

1. The expression $x^{2} + 6x - 9x - 54$ is a polynomial that can be factored by grouping.
2. Factoring by grouping involves rearranging and grouping terms to factor out common factors.

STEP 2

1. Group the terms in pairs.
2. Factor out the greatest common factor from each pair.
3. Identify and factor out the common binomial factor.

STEP 3

Group the terms in pairs:
$(x^{2} + 6x) + (-9x - 54)$

STEP 4

Factor out the greatest common factor from each pair:
From the first pair $x^{2} + 6x$ , factor out $x$ :
$x(x + 6)$
From the second pair $-9x - 54$ , factor out $-9$ :
$-9(x + 6)$

STEP 5

Notice that both terms have a common binomial factor $(x + 6)$ . Factor out the common binomial:
$x(x + 6) - 9(x + 6) = (x - 9)(x + 6)$
This is the factored form of the polynomial.
The correct factorization of the expression $x^{2} + 6x - 9x - 54$ is:
$(x + 6)(x - 9)$

Was this helpful?

QuestionFactor by grouping. $x^{2}+6 x-9 x-54$ $(x+6)(x-3)$ $(x-6)(x-9)$ $2(3 x-27)$ $(x+6)(x-9)$

Studdy Solution

STEP 1

1. The expression $x^{2} + 6x - 9x - 54$ is a polynomial that can be factored by grouping.
2. Factoring by grouping involves rearranging and grouping terms to factor out common factors.

STEP 2

1. Group the terms in pairs.
2. Factor out the greatest common factor from each pair.
3. Identify and factor out the common binomial factor.

STEP 3

Group the terms in pairs:
$(x^{2} + 6x) + (-9x - 54)$

STEP 4

Factor out the greatest common factor from each pair:
From the first pair $x^{2} + 6x$ , factor out $x$ :
$x(x + 6)$
From the second pair $-9x - 54$ , factor out $-9$ :
$-9(x + 6)$

STEP 5

Notice that both terms have a common binomial factor $(x + 6)$ . Factor out the common binomial:
$x(x + 6) - 9(x + 6) = (x - 9)(x + 6)$
This is the factored form of the polynomial.
The correct factorization of the expression $x^{2} + 6x - 9x - 54$ is:
$(x + 6)(x - 9)$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFactor by grouping. x2+6x−9x−54x^{2}+6 x-9 x-54x2+6x−9x−54 (x+6)(x−3)(x+6)(x-3)(x+6)(x−3) (x−6)(x−9)(x-6)(x-9)(x−6)(x−9) 2(3x−27)2(3 x-27)2(3x−27) (x+6)(x−9)(x+6)(x-9)(x+6)(x−9)

Studdy Solution

STEP 1

1. The expression x2+6x−9x−54x^{2} + 6x - 9x - 54x2+6x−9x−54 is a polynomial that can be factored by grouping.2. Factoring by grouping involves rearranging and grouping terms to factor out common factors.

STEP 2

1. Group the terms in pairs.2. Factor out the greatest common factor from each pair.3. Identify and factor out the common binomial factor.

STEP 3

Group the terms in pairs:(x2+6x)+(−9x−54) (x^{2} + 6x) + (-9x - 54) (x2+6x)+(−9x−54)

STEP 4

Factor out the greatest common factor from each pair:From the first pair x2+6xx^{2} + 6xx2+6x, factor out xxx:x(x+6) x(x + 6) x(x+6)From the second pair −9x−54-9x - 54−9x−54, factor out −9-9−9:−9(x+6) -9(x + 6) −9(x+6)

STEP 5

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFactor by grouping. $x^{2}+6 x-9 x-54$ $(x+6)(x-3)$ $(x-6)(x-9)$ $2(3 x-27)$ $(x+6)(x-9)$

1. The expression $x^{2} + 6x - 9x - 54$ is a polynomial that can be factored by grouping.
2. Factoring by grouping involves rearranging and grouping terms to factor out common factors.

1. Group the terms in pairs.
2. Factor out the greatest common factor from each pair.
3. Identify and factor out the common binomial factor.

Group the terms in pairs:
$(x^{2} + 6x) + (-9x - 54)$

Factor out the greatest common factor from each pair:
From the first pair $x^{2} + 6x$ , factor out $x$ :
$x(x + 6)$
From the second pair $-9x - 54$ , factor out $-9$ :
$-9(x + 6)$