Question

1. $x^2 - 7x - 8$

factored form:
solution(s):

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-8\) (the constant term) and add up to \(-7\) (the coefficient of \(x\)). The numbers are \(-8\) and \(1\) because \(-8\times1 = -8\) and \(-8 + 1=-7\).

Step2: Factor the quadratic

Using these two numbers, we can factor the quadratic \(x^{2}-7x - 8\) as \((x - 8)(x+1)\).

Step3: Find the solutions

To find the solutions, we set each factor equal to zero:

• For \(x - 8=0\), we get \(x = 8\).
• For \(x + 1=0\), we get \(x=-1\).

Factored Form:

\((x - 8)(x + 1)\)

Solution(s):

\(x = 8\) or \(x=-1\)

Answer:

Step1: Find two numbers

We need two numbers that multiply to \(-8\) (the constant term) and add up to \(-7\) (the coefficient of \(x\)). The numbers are \(-8\) and \(1\) because \(-8\times1 = -8\) and \(-8 + 1=-7\).

Step2: Factor the quadratic

Using these two numbers, we can factor the quadratic \(x^{2}-7x - 8\) as \((x - 8)(x+1)\).

Step3: Find the solutions

To find the solutions, we set each factor equal to zero:

• For \(x - 8=0\), we get \(x = 8\).
• For \(x + 1=0\), we get \(x=-1\).

Factored Form:

\((x - 8)(x + 1)\)

Solution(s):

\(x = 8\) or \(x=-1\)