QuestionFactor completely: $7x^{2} + 35x + 42 =$

Studdy Solution

STEP 1

Assumptions1. The given expression is a quadratic expression in the form of $ax^{} + bx + c$ . The expression can be factored completely.

STEP 2

The given expression is $7x^{2} +35x +42$ We can start by factoring out the greatest common factor (GCF) from each term. The GCF of7,35, and42 is7.
$7x^{2} +35x +42 =7(x^{2} +5x +6)$

STEP 3

Now, we have a quadratic expression inside the parentheses in the form of $ax^{2} + bx + c$ where a =1, b =5, and c =6.
We can factor this quadratic expression by finding two numbers that multiply to c (6) and add up to b (5).

STEP 4

The two numbers that satisfy these conditions are2 and3, because2 *3 =6 and2 +3 =.
So, we can write the quadratic expression as $x^{2} +x +6 = (x +2)(x +3)$

STEP 5

Substitute this back into the expression we obtained in2 $7(x^{2} +5x +) =7(x +2)(x +3)$ So, the factored form of the given expression is $7(x +2)(x +3)$

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QuestionFactor completely: $7x^{2} + 35x + 42 =$

Studdy Solution

STEP 1

Assumptions1. The given expression is a quadratic expression in the form of $ax^{} + bx + c$ . The expression can be factored completely.

STEP 2

The given expression is $7x^{2} +35x +42$ We can start by factoring out the greatest common factor (GCF) from each term. The GCF of7,35, and42 is7.
$7x^{2} +35x +42 =7(x^{2} +5x +6)$

STEP 3

Now, we have a quadratic expression inside the parentheses in the form of $ax^{2} + bx + c$ where a =1, b =5, and c =6.
We can factor this quadratic expression by finding two numbers that multiply to c (6) and add up to b (5).

STEP 4

The two numbers that satisfy these conditions are2 and3, because2 *3 =6 and2 +3 =.
So, we can write the quadratic expression as $x^{2} +x +6 = (x +2)(x +3)$

STEP 5

Substitute this back into the expression we obtained in2 $7(x^{2} +5x +) =7(x +2)(x +3)$ So, the factored form of the given expression is $7(x +2)(x +3)$

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QuestionFactor completely: 7x2+35x+42=7x^{2} + 35x + 42 = 7x2+35x+42=

Studdy Solution

STEP 1

Assumptions1. The given expression is a quadratic expression in the form of ax+bx+cax^{} + bx + cax+bx+c. The expression can be factored completely.

STEP 2

The given expression is 7x2+35x+427x^{2} +35x +427x2+35x+42We can start by factoring out the greatest common factor (GCF) from each term. The GCF of7,35, and42 is7.7x2+35x+42=7(x2+5x+6)7x^{2} +35x +42 =7(x^{2} +5x +6)7x2+35x+42=7(x2+5x+6)

STEP 3

Now, we have a quadratic expression inside the parentheses in the form of ax2+bx+cax^{2} + bx + cax2+bx+c where a =1, b =5, and c =6.We can factor this quadratic expression by finding two numbers that multiply to c (6) and add up to b (5).

STEP 4

The two numbers that satisfy these conditions are2 and3, because2 *3 =6 and2 +3 =.So, we can write the quadratic expression asx2+x+6=(x+2)(x+3)x^{2} +x +6 = (x +2)(x +3)x2+x+6=(x+2)(x+3)

STEP 5

Substitute this back into the expression we obtained in27(x2+5x+)=7(x+2)(x+3)7(x^{2} +5x +) =7(x +2)(x +3)7(x2+5x+)=7(x+2)(x+3)So, the factored form of the given expression is 7(x+2)(x+3)7(x +2)(x +3)7(x+2)(x+3)

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QuestionFactor completely: $7x^{2} + 35x + 42 =$

Assumptions1. The given expression is a quadratic expression in the form of $ax^{} + bx + c$ . The expression can be factored completely.

The given expression is $7x^{2} +35x +42$ We can start by factoring out the greatest common factor (GCF) from each term. The GCF of7,35, and42 is7.
$7x^{2} +35x +42 =7(x^{2} +5x +6)$

Now, we have a quadratic expression inside the parentheses in the form of $ax^{2} + bx + c$ where a =1, b =5, and c =6.
We can factor this quadratic expression by finding two numbers that multiply to c (6) and add up to b (5).

The two numbers that satisfy these conditions are2 and3, because2 *3 =6 and2 +3 =.
So, we can write the quadratic expression as $x^{2} +x +6 = (x +2)(x +3)$

Substitute this back into the expression we obtained in2 $7(x^{2} +5x +) =7(x +2)(x +3)$ So, the factored form of the given expression is $7(x +2)(x +3)$