Concepts
To solve a polynomial inequality, we factor the polynomial into irreducible factors and find all the real _______ of the polynomial. Then we find all the real _________ of the real ________ and use test points in each interval to find the sign of the polynomial on that interval. Let
Fill in the diagram below to find the intervals on which
From the diagram above we see that
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Algebra and Trigonometry (MindTap Course List)
- To solve a polynomial inequality, we factor the polynomial into irreducible factors and find all the real _______of the polynomial. Then we find the intervals determined by the real____ and use test points in each interval to find the sign of the polynomial on that interval. Let P(x)=x(x+2)(x1) Fill in the diagram below to find the intervals on which P(x)0. From the diagram above we see that P(x)0 on the intervals _____ and _____ .arrow_forwardPractice: Determine how many zeros each polynomial function has. Two zeros of P(x)=3x2(x714x+3) are 0 How many other zeros are there?arrow_forward(a) Give the general form of polynomial function P of degree n. (b) What does it mean to say that c is a zero of P? Give two equivalent conditions that tell us that c is a zero of P.arrow_forward
- Fill in the blanks. If (x+5)3 occurs as a factor of a polynomial function, then the ________ of the zero x=5 is 3.arrow_forwardFill in the blanks. The graph of a nth degree polynomial function can have at most ________ turning points.arrow_forwardFill in the blanks. When x=a is a zero of a polynomial function f, the three statements below are true. (a) x=ais a of the polynomial equation f(x)=0. (b) is a factor of the polynomial f(x). (c) (a,0)is an of the graph of f.arrow_forward
- Building Envelope The building code in a certain town requires that a house be at least 10 ft from the boundaries of the lot. The buildable area or building envelope for the rectangular lot shown in the following figure is given by A=(x20)(y20) a Explain how the expression for A is obtained. b Expand to express A as a polynomial in x and y. c A contractor has a choice of purchasing one of two rectangular lots, each having the same area. One lot measures 100 ft by 400 ft; the other measures 200 ft by 200 ft. Which lot has the larger building envelope?arrow_forwardThe polynomial P(x)=5x2(x4)3(x+7) has degree ___________. It has zeros 0, 4, and ______________. The zero has multiplicity _________arrow_forward
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