9.2 Solving Quadratic Equations by Factoring

One solution of a quadratic equation is 8. What do you know about the quadratic​ equation? What are two ways you would know if a quadratic equation could have this​ solution?

• The expression x−8

  must be a factor. To know​ this, divide both sides by 8 and solve for x to check if the solution is​ 0, or factor the equation to see if

  x−8 is a factor.

• The expression x−8

  must be a factor. To know​ this, substitute 8 into the quadratic equation and see if it​ checks, or factor the equation to see if

  x−8 is a factor.

• The expression x+8

  must be a factor. To know​ this, substitute 8 into the quadratic equation and see if it​ checks, or factor the equation to see if

  x+8 is a factor.

• The expression

  x+8 must be a factor. To know​ this, divide both sides by 8 and solve for x to check if the solution is​ 0, or factor the equation to see if

  x+8 is a factor.

Describe the error. Choose the correct answer below.

• The student did not take the square root of both sides first.

• The student did not solve the two equations for x correctly.

• The student did not factor correctly.

• The student did not get 0 on one side of the equation.

What is the solution set to (x+5)(x-7)?

Enter answer in {n,n} format.

Use the​ zero-product property to solve the following equation. Write your solutions as a set in roster form. {n,n}

The total area of the figure to the right is

342cm^2.

Use this fact to write a quadratic equation involving x.

Write the factored form of the quadratic function.

f(x)=________