Question

1. use synthetic division to divide (x^{3}+4x^{2}+15x - 14) by (x - 2).
2. use long - division to divide (6x^{4}+7x^{3}+4x^{2}+3x + 1) by (2x+1).
3. use the identities to rewrite the factors (144x^{2}-49).
4. use the identities to rewrite as the factors (x^{3}-64y^{3}).
5. is (x - 2) a factor of the polynomial (p(x)=x^{4}-5x^{3}+5x^{2}-x - 107) explain.

a. yes, because (p(2)=0).
b. yes, because (p(-2)=0).
c. no, because (p(-2)
eq0).
d. no, because (p(2)
eq0).

1. use polynomial identities to find the factors of (64x^{3}+125y^{3}).

a. ((4x + 5y)(16x^{2}-20xy + 25y^{2}))
b. ((4x^{2}-5y^{2})(16x^{4}-20x^{2}y^{2}+25y^{4}))
c. ((4x^{3}+5y^{3})(16x^{6}-20x^{3}y^{3}+25y^{6}))
d. ((4x - 5y)(16x^{2}+20xy + 25y^{2}))

1. what is the remainder when (f(x)=2x^{4}-x^{3}-8x - 1) is divided by (x - 2)?

a. 25
b. 7
c. - 5
d. 3

1. a rectangle has a length of ((2x + 3)) feet, a width of ((2x + 1)) feet. write an expression that shows the area of the rectangle. make sure the expression is given in simplest form.
2. what is the total area, in square feet of the figure?

a. (9x + 7)
b. (10x+8)
c. (5x^{2}+2x + 1)
d. (5x^{2}+6x + 1)

1. graph the following polynomial, using the roots, y - intercept, and correct end behavior. (f(x)=(x + 2)(x - 3)(x - 1))

Explanation:

Step1: Analyze problem 19

We need to find the area of the figure by splitting it into two rectangles.

Step2: Calculate area of first rectangle

The first rectangle has length $(2x + 1)$ and width $(2x+1)$. Using the area formula $A = lw$, its area $A_1=(2x + 1)(2x + 1)=4x^{2}+4x + 1$.

Step3: Calculate area of second rectangle

The second rectangle has length $(x + 2)$ and width $x$. Using the area formula $A=lw$, its area $A_2=(x + 2)x=x^{2}+2x$.

Step4: Find total area

The total area $A=A_1+A_2=(4x^{2}+4x + 1)+(x^{2}+2x)=5x^{2}+6x + 1$.

Answer:

D. $5x^{2}+6x + 1$