9.4 Solving Trinomials9.4 Solving Trinomials

StepsSteps

Move all terms to one side of the = Move all terms to one side of the = FactorFactorSet each factor equal to zeroSet each factor equal to zeroSolve each factorSolve each factorCheck all answersCheck all answers

Solve

Original equation

Rewrite so one side equals 0.

Factor the left side.

or Zero Product Property

Solve each equation.

Answer: The solution set is

Solve

Answer:

Model Rockets Ms. Nguyen’s science class built an air-launched model rocket for a competition. When they test-launched their rocket outside the classroom, the rocket landed in a nearby tree. If the launch pad was 2 feet above the ground, the initial velocity of the rocket was 64 feet per second, and the rocket landed 30 feet above the ground, how long was the rocket in flight? Use the equation

Vertical motion model

Subtract 30 from each side.

Factor out –4.

Divide each side by –4.

Factor

or Zero Product PropertySolve each equation.

The solutions are and seconds. The first time

represents how long it takes the rocket to reach a height of

30 feet on its way up. The second time represents how

long it will take for the rocket to reach the height of 30 feet

again on its way down. Thus the rocket will be in flight for

3.5 seconds before coming down again.

Answer: 3.5 seconds

When Mario jumps over a hurdle, his feet leave the ground traveling at an initial upward velocity of 12 feet per second. Find the time t in seconds it takes for Mario’s feet to reach the ground again. Use the equation

Answer: second

Solve Check your solutions.

Original equation

Rewrite the equation so that one side equals 0.

Factor.

or Zero Product Property

Solve each equation.

Answer: The solution is

Check Substitute –5 and 3 for x in the original equation.

Solve Check your solutions.

Answer:

Architecture Marion has a small art studio measuring 10 feet by 12 feet in her backyard. She wants to build a new studio that has three times the area of the old studio by increasing the length and width by the same amount. What will be the dimensions of the new studio?

Explore Begin by making a diagram like the one shown to the right, labeling the appropriate dimensions.

Plan Let the amount added to each dimension of the studio.The new length times the new width equals the new area.

old area

Solve Write the equation.

Multiply.

Subtract 360 from each side.

Factor.

Solve each equation.

Zero Product Property

or

Examine The solution set is Only 8 is a valid solution, since dimensions cannot be negative.

Answer: The length of the new studio should beor 20 feet and the new width should be or 18 feet.

Photography Adina has a photograph. She wants to enlarge the photograph by increasing the length and width by the same amount. What dimensions of the enlarged photograph will be twice the area of the original photograph?

Answer:

Practice ProblemsPractice Problems

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Problems 14-27, 35-46