Polynomials

Elena is making an open-tip box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 inches long, and then folding up the sides. If the side lengths of her square cutouts are x inches, then the volume of the box is given by: V(x)=x(11-2x)(17-2x). Elena graphs the volume of the box along with the function B(x)=140. ( https://www.desmos.com/calculator/66nqdcvogm ) a) What is a reasonable domain for V(x)? b) Approximatley which value of x will giver her a box with the greatest volume? c)For approximatley what value of x is the volume of the box increasing? d) What do the points of intersection of two graphs represent?

a) 0-5.5 b) 2.5 c) The volume is increasing from 0-25 d) The graph's point of intersection represents the volume's arrival at 140.

Let g(x) = -2(3x+2)(x-1)(x-4)² be a polynomial function. a) Sketch a graph of the polynomial. b) State all the relative maximums and minimums. c) State the horizontal and vertical intercepts. d) State the end behavior.

a) https://www.desmos.com/calculator/mlyaiov497 b) MAXIMUM: 4 MINIMUM: -2 c) HORIZONTAL: -2/3, 1, 4 (bounce) VERTICAL: -5/2 d) End Behavior: this function has a degree of -4, so both ends of the polynomial will point down.

The polynomial p is a function of x. The graph of p has four zeroes at -4, -²/₃,0, and 9. Select ALL the expressions that could represent p: a. 3x(x-4) (x+ ²/₃)(x-9) b. -x(x+4)(x+²/₃)(x-9) c. -3x(x+4)(3x+2)(x-9) d. 3x(x+4)(2x+3)(x-9) e. -3x(x+4)(3x+2)(x-9)²

c. -3x(x+4)(3x+2)(x-9) d. 3x(x+4)(2x+3)(x-9) e. -3x(x+4)(3x+2)(x-9)²

Write a polynomial function for the graph: https://www.desmos.com/calculator/0yurhondlv

-¹/₁₂ (x+3)(x+2)²(x-1)³

Which expression is equivalent to 2(3x+4)(x-1)(x-3): A. 6x³-16x²-14x+24 B. 6x²-4x²-34x-24 C. 3x³+8x²-7x+12 D. 6x²+20x²-2x-24

A. 6x³-16x²-14x+24