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### Transcript of Solving Quadratic Equations …by Factoring. Solving Quadratic Equations by Factoring Get ZERO on...

…by Factoring

• Get ZERO on one side by itself.

• Factor. Consider Common Factors FIRST!

• Set each factor = 0.

• Solve each part.

Solve by factoring.

Answer: The solution set is {0, –4}.

Original equation

Factor the binomial.

Solve the second equation.

Zero Product Propertyor

Check Substitute 0 and –4 in for x in the original equation.

Solve by factoring.

Original equation

Subtract 5x and 2 from each side.

Factor the trinomial.

Zero Product Propertyor

Solve each equation.

Answer: The solution set is Check each solution.

Solve each equation by factoring.

a.

b.

Answer: The solution set is {3}.

Solve by factoring.

Original equation

Factor.

Zero Product Propertyor

Solve each equation.

CheckThe graph of the related function, intersects the x-axis only once. Since the zero of the function is 3, the solution of the related equation is 3.

Solve by factoring.

Multiple-Choice Test Item What is the positive solution of the equation ?A –3 B 5 C 6 D 7

You are asked to find the positive solution of the given quadratic equation. This implies that the equation also has a solution that is not positive. Since a quadratic equation can either have one, two, or no solutions, we should expect this equation to have two solutions.

Solve the Test Item

Both solutions, –3 and 7, are listed among the answer choices. However, the question asks for the positive solution, 7.

Original equation

Factor.

Divide each side by 2.

Factor.

or Zero Product Property

Solve each equation.

Multiple-Choice Test Item What is the positive solution of the equation ?A 5 B –5 C 2 D 6

Write a quadratic equation with and 6 as its

roots. Write the equation in the form

where a, b, and c are integers.

Write the pattern.

Simplify.

Replace p with and q with 6.

Use FOIL.

Multiply each side by 3 so that b is an integer.

and integral coefficients is

You can check this result by graphing the

related function.

Write a quadratic equation with and 5 as its

roots. Write the equation in the form

where a, b, and c are integers.