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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
10. Roots and Zeros
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Exercise 40 Page 77

If a is a zero of f(x)=0, then (x-a) is a factor of f(x).

f(x)=x^3+2x^2-23x-60

Practice makes perfect

We want to write a polynomial function with integral coefficients so that f(x)=0 has the given zeros. -4, -3, 5Recall that if a is a zero of f(x)=0, then (x-a) is a factor of f(x).

Root Factor
-4 x-(-4)
-3 x-(-3)
5 x-5
Polynomial f(x)= [x-(-4)] [x-(-3)] (x-5)

Let's simplify the polynomial by applying the Distributive Property. For simplicity, we will start by multiplying the first two factors and then we will multiply the result by the last factor.

f(x)=(x-(-4))(x-(-3))(x-5)
NegNeg

- (- a)=a

f(x)=(x+4)(x+3)(x-5)
Distr

Distribute (x+3)

f(x)=(x(x+3)+4(x+3))(x-5)
â–¼
Distribute x & 4
Distr

Distribute x

f(x)=(x^2+3x+4(x+3))(x-5)
Distr

Distribute 4

f(x)=(x^2+3x+4x+12)(x-5)
AddTerms

Add terms

f(x)=(x^2+7x+12)(x-5)
Distr

Distribute (x-5)

f(x)=x^2(x-5)+7x(x-5)+12(x-5)
â–¼
Distribute x^2 & 7x & 12
Distr

Distribute x^2

f(x)=x^3-5x^2+7x(x-5)+12(x-5)
Distr

Distribute 7x

f(x)=x^3-5x^2+7x^2-35x+12(x-5)
Distr

Distribute 12

f(x)=x^3-5x^2+7x^2-35x+12x-60
AddTerms

Add terms

f(x)=x^3+2x^2-23x-60
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Exercises 2 (Page 77)
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