Page 634 - Algebra 1

SOLUTION
x-4 2x2 -7x-9
(2x2 - 9 - 7x) ÷ (-4 + x)
x-4 2x2 -7x-9 2x
Write in long-division form with expressions in standard form.
Divide the first term of the dividend by the first term of the divisor to find the first term of the quotient.
Multiply the first term of the quotient by the binomial divisor. Write the product under the dividend. Align like terms.
Subtract the product from the dividend. Then bring down the next term in the dividend.
Repeat the steps to find each term of the quotient.
_5
x - 4 .
2x
x-4 2x2 -7x-9 2
2x -8x ____
2x
x-4 2x2 -7x-9 -(2x2 - 8x)
______ x-9
2x + 1
x-4 2x2 -7x-9 -(2x2 - 8x)
______ x-9
-(x - 4) ____
-5 The quotient is 2x + 1 -
Example
5
Dividing a Polynomial with a Zero Coefficient
Divide (-2x + 5 + 3x3) ÷ (-3 + x). SOLUTION
(-2x + 5 + 3x3) ÷ (-3 + x) (3x3 - 2x + 5) ÷ (x - 3)
x - 3 3x3 + 0x2 - 2x + 5
Write each polynomial in standard form. Write in long division form. Use 0x2 as a
placeholder for the x2-term. 3x3 ÷x=3x2
Mulitply 3x2(x - 3). Then subtract. Bring down -2x. 9x2 ÷ x = 9x Multiply 9x(x - 3). Then subtract. Bring down 5. 25x ÷ x = 25 Multiply 25(x - 3). Then subtract. The remainder is 80.
3x2 +9x+25
x-3 3x3 +0x2 -2x+5 -(3x3 - 9x2)
______
9x2 - 2x
-(9x2 - 27x) ______
25x + 5 -(25x - 75)
______
Thequotientis3x2 +9x+25+_80 . x-3
80
Lesson 93 619