Unit 2, Lesson 13
Polynomial Division (Part 2)
Algebra 2
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Let the function \(P\) be defined by \(P(x) = x^3 + 7x^2 - 26x - 72\) where \((x+9)\) is a factor. To rewrite the function as the product of two factors, long division was used but an error was made:
\(\displaystyle \require{enclose} \begin{array}{r} x^2+16x+118\phantom{000} \\ x+9 \enclose{longdiv}{x^3+7x^2-26x-72} \phantom{000}\\ \underline{-x^3+9x^2} \phantom{-26x-720000} \\ 16x^2-26x \phantom{-720000}\\ \underline{-16x^2+144x} \phantom{-20000} \\ 118x-72 \phantom{00} \\ \underline{-118x+1062} \\ 990 \end{array}\)
How can we tell by looking at the remainder that an error was made somewhere?
The graph of a polynomial function \(f\) is shown. Which statement is true about the end behavior of the polynomial function?
\(P(x)=5(x-2)(x-3)(x+7)\)
\(P(x)=\text-5(x-2)(x-3)(x+7)\)
-210
-42
21
42
210
As \(x\) gets larger and larger in the either the positive or the negative direction, \(f\) gets larger and larger in the positive direction.
As \(x\) gets larger and larger in the positive direction, \(f\) gets larger and larger in the positive direction. As \(x\) gets larger and larger in the negative direction, \(f\) gets larger and larger in the negative direction.
As \(x\) gets larger and larger in the positive direction, \(f\) gets larger and larger in the negative direction. As \(x\) gets larger and larger in the negative direction, \(f\) gets larger and larger in the positive direction.
As \(x\) gets larger and larger in the either the positive or negative direction, \(f\) gets larger and larger in the negative direction.