Solve the following quadratic equations using the factorization method: a) x2 + 8x + 12 = 0 b) x2 - 6x + 5…

Question

Solve the following quadratic equations using the factorization method: a) x2 + 8x + 12 = 0 b) x2 - 6x + 5 = 0

ScanSolve AI Tutor · Accepted Answer

Here are the solutions using the factorization method: a) x² + 8x + 12 = 0 Step 1: Find two numbers that multiply to 12 (the constant term) and add up to 8 (the coefficient of the x term). The numbers are 6 and 2. Step 2: Rewrite the middle term using these two numbers. x² + 6x + 2x + 12 = 0 Step 3: Group the terms and factor out the common factors from each group. x(x+6) + 2(x+6) = 0 Step 4: Factor out the common binomial factor (x+6). (x+6)(x+2) = 0 Step 5: Set each factor equal to zero and solve for x. x+6 = 0 or x+2 = 0; x = −6 or x = −2; The solutions are x = −6, x = −2. b) x² − 6x + 5 = 0 Step 1: Find two numbers that multiply to 5 (the constant term) and add up to −6 (the coefficient of the x term). The numbers are −1 and −5. Step 2: Rewrite the middle term using these two numbers. x² − 1x − 5x + 5 = 0 Step 3: Group the terms and factor out the common factors from each group. x(x−1) − 5(x−1) = 0 Step 4: Factor out the common binomial factor (x−1). (x−1)(x−5) = 0 Step 5: Set each factor equal to zero and solve for x. x−1 = 0 or x−5 = 0; x = 1 or x = 5; The solutions are x = 1, x = 5.

Solve the following quadratic equations using the factorization method: a) x2 + 8x + 12 = 0 b) x2 − 6x + 5 = 0

Answers

Step-by-step solution

Part a· 5 steps

Find two numbers that multiply to 12 (the constant term) and add up to 8 (the coefficient of the $x$ term).

Rewrite the middle term using these two numbers.

Group the terms and factor out the common factors from each group.

Factor out the common binomial factor $(x+6)$ .

Set each factor equal to zero and solve for $x$ .

Part b· 5 steps
$x = 1, x = 5$

Find two numbers that multiply to 5 (the constant term) and add up to -6 (the coefficient of the $x$ term).

Rewrite the middle term using these two numbers.

Group the terms and factor out the common factors from each group.

Factor out the common binomial factor $(x-1)$ .

Set each factor equal to zero and solve for $x$ .

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More Mathematics Questions

Solve the following quadratic equations using the factorization method: a) x2 + 8x + 12 = 0 b) x2 − 6x + 5 = 0

Answers

Step-by-step solution

Part a· 5 steps

Find two numbers that multiply to 12 (the constant term) and add up to 8 (the coefficient of the xxx term).

Rewrite the middle term using these two numbers.

Group the terms and factor out the common factors from each group.

Factor out the common binomial factor (x+6)(x+6)(x+6).

Set each factor equal to zero and solve for xxx.

Part b· 5 stepsx=1,x=5x = 1, x = 5x=1,x=5

Find two numbers that multiply to 5 (the constant term) and add up to -6 (the coefficient of the xxx term).

Rewrite the middle term using these two numbers.

Group the terms and factor out the common factors from each group.

Factor out the common binomial factor (x−1)(x-1)(x−1).

Set each factor equal to zero and solve for xxx.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Find two numbers that multiply to 12 (the constant term) and add up to 8 (the coefficient of the $x$ term).

Factor out the common binomial factor $(x+6)$ .

Set each factor equal to zero and solve for $x$ .

Part b· 5 steps
$x = 1, x = 5$

Find two numbers that multiply to 5 (the constant term) and add up to -6 (the coefficient of the $x$ term).

Factor out the common binomial factor $(x-1)$ .

Set each factor equal to zero and solve for $x$ .