Division of Polynomials Assignment (Algebra II)

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? 9x + 4 10x - 19 10x - 6 8x - 6

10x - 6

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

6x+1 -7x+1

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.

A polynomial is a finite sum of terms in which all variables have whole number exponents and no variable appears in a denominator. When adding polynomials, the variables and their exponents do not change. Only their coefficients will possibly change. This guarantees that the sum has variables and exponents which are already classified as belonging to polynomials. Polynomials are closed under addition. When multiplying polynomials, the variables' exponents are added, according to the rules of exponents. Remember that the exponents in polynomials are whole numbers. The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Consequently, polynomials are closed under multiplication.

Find the remainder when (x3 - 2) is divided by (x - 1). What is the remainder? -x2 - 2 x2 - 2 -2 -1

-1

Complete the division. The quotient is 3x2 + x + .

-2 and 5

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) 8x - 3 3x - 5 5x + 3 42x + 3

C.) 5x + 3

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

x^2

Complete the sentence below. If (3x2 + 22x + 7) ÷(x + 7) = 3x + 1, then (x + 7)(___) = ___ . The check of the polynomial division problem shows that the product of two polynomials is a polynomial. This supports the fact that the property is satisfied for polynomial multiplication.

3x+1 3x²+22x+7 closure

The polynomial −2x3 − x2 + 13x in the last line is the result of dividing x2 + 3x + 1 by 3x2 and bringing down 13x. subtracting 3x4 + 9x3 + 3x2 from the dividend and bringing down 13x multiplying 3x2 by x2 + 3x + 1.

B.) subtracting 3x4 + 9x3 + 3x2 from thedividend and bringing down 13x .

Divide The quotient is ___ x+ ___ The remainder is ___ x^2+ ___ x+ ___

The quotient is 10x+16 The remainder is 28x^2+10x+22