Division of Polynomials

Divide

The quotient is 10 and 16 The remainder is 28, 10, and 22

Complete the division. The quotient is 3x2 +

-2 and -5

If (3x2 + 22x + 7) ÷(x + 7) = 3x + 1, then (x + 7)(

3x+1 3x^2+22x+7

The area, A, of a rectangle is 120x2 + 78x - 90, and the length, l, of the rectangle is 12x + 15. Which of the following gives the width, w, of the rectangle?

C

The volume of a rectangular prism is given by the expression10x3 + 46x2 - 21x - 27. The area of the base of the prism is given by the expression 2x2 + 8x - 9. Which of the following expressions represents the height of the prism? (V = Bh)

C

Identify the quotient and the remainder. (24x3 − 14x2 + 20x + 6) ÷ (4x2 − 3x + 5) = Q + R4x2 − 3x + 5

Q=6x+1 R=-7x+1

Casey is dividing x3 - 2x2 - 10x + 21 by x2 + x - 7 using a division table. His work is shown here. What is the value of A?

A

Isiah is dividing 2x3 - x2 + 2x + 5 by x + 1 using a division table. His work is shown here. What is the value of A?

B

The polynomial −2x3 − x2 + 13x in the last line is the result of

B

Find the remainder when (x3 - 2) is divided by (x - 1).What is the remainder?

D

Use the following long division. The term 3x2 in the quotient is the result of dividing 3x4 by

X^2

Whole numbers are closed under addition because the sum of two whole numbers is always a whole number. Explain how the process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition.

The quotient will be a polynomial (with or without a remainder). Multiplying this polynomial by the polynomial divisor, we get a polynomial in which the exponents and coefficients have changed. Thus polynomials are closed under multiplication.