5 8 Rational Zero Theorem FIND ALL RATIONAL

FIND ALL RATIONAL ROOTS: 1. Use calculator to decide which roots to test. 2.

EXAMPLES FIND ALL ZEROS OF THE POLYNOMIAL 1. f(x) = x 3 – x

EXAMPLES FIND ALL ZEROS OF THE POLYNOMIAL 2. f(x) = 15 x 4 –

EXAMPLE 3 FIND ALL ZEROS OF THE POLYNOMIAL

EXAMPLE 4 Some ice sculptures are made by filling a mold with water and

EXAMPLE 5 The volume of a rectangular solid is 1120 cubic feet. The width

EXAMPLE 6 You are building a solid concrete wheelchair ramp. The width of the

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5. 8 Rational Zero Theorem

FIND ALL RATIONAL ROOTS: 1. Use calculator to decide which roots to test. 2. Use synthetic division to find the unknown factor (Correct if remainder = 0) 3. Repeat step 2 with this new factor until you have a quadratic. 4. Solve the quadratic by factoring or the quadratic formula.

EXAMPLES FIND ALL ZEROS OF THE POLYNOMIAL 1. f(x) = x 3 – x 2 – 6 x + 8

EXAMPLES FIND ALL ZEROS OF THE POLYNOMIAL 2. f(x) = 15 x 4 – 68 x 3 – 7 x 2 + 24 x – 4

EXAMPLE 3 FIND ALL ZEROS OF THE POLYNOMIAL

EXAMPLE 4 Some ice sculptures are made by filling a mold with water and then freezing it. You are making such an ice sculpture for a school dance. It is to be shaped like a pyramid with a height that is 1 foot greater than the length of each side of its square base. The volume of the ice sculpture is 4 cubic feet. Write a polynomial equation in standard form that represents the volume of the mold and use it to find the dimensions of the mold.

EXAMPLE 5 The volume of a rectangular solid is 1120 cubic feet. The width is 2 feet less than the height, and the length is 4 feet more than the height. Write a polynomial equation in standard form that represents the volume of the solid and use it to find the dimensions of the solid.

EXAMPLE 6 You are building a solid concrete wheelchair ramp. The width of the ramp is three times the height, and the length is 5 feet more that 10 times the height. If 150 cubic feet of concrete is used, what are the dimensions of the ramp?