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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 39 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^2-13x-10

Practice makes perfect

We want to write a polynomial function with integral coefficients so that f(x)=0 has the given zeros. 5, -2, -1Recall that if a is a zero of f(x)=0, then (x-a) is a factor of f(x).

Root Factor
5 x-5
-2 x-(-2)
-1 x-(-1)
Polynomial f(x)= (x-5) [x-(-2)] [x-(-1)]

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-5)(x-(-2))(x-(-1))
NegNeg

- (- a)=a

f(x)=(x-5)(x+2)(x+1)
Distr

Distribute (x+2)

f(x)=(x(x+2)-5(x+2))(x+1)
â–¼
Distribute x & -5
Distr

Distribute x

f(x)=(x^2+2x-5(x+2))(x+1)
Distr

Distribute - 5

f(x)=(x^2+2x-5x-10)(x+1)
SubTerm

Subtract term

f(x)=(x^2-3x-10)(x+1)
Distr

Distribute (x+1)

f(x)=x^2(x+1)-3x(x+1)-10(x+1)
â–¼
Distribute x^2 & -3x & -10
Distr

Distribute x^2

f(x)=x^3+x^2-3x(x+1)-10(x+1)
Distr

Distribute -3x

f(x)=x^3+x^2-3x^2-3x-10(x+1)
Distr

Distribute -10

f(x)=x^3+x^2-3x^2-3x-10x-10
SubTerms

Subtract terms

f(x)=x^3-2x^2-13x-10
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Exercises 2 (Page 77)
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