Page 633 - Algebra 1

Divide using long division.
(-25x+3x2 +8)÷(x-8)
SOLUTION
(-25x + 3x2 + 8) ÷ (x - 8)
x-8 (3x2 -25x+8) 3x
Dividing a Polynomial Using Long Division
Example
3
Caution
Be sure to put the divisor and dividend in descending order before dividing.
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.
0
The quotient is (3x - 1) remainder 0.
Check Multiplythequotientandthedivisor. (3x - 1)(x - 8)
=3x2 -24x-x+8 =3x2 -25x+8
The divisor is not always a factor of the dividend. When it is not, the remainder will not be 0. The remainder can be written as a rational expression using the divisor as the denominator.
Long Division with a Remainder
Divide using long division. (2x2 - 9 - 7x) ÷ (-4 + x)
x-8 3x2 -25x+8x
3x
x-8 3x2 -25x+8 2
3x -24x _____
3x
x-8 3x2 -25x+8 -(3x2 - 24x)
______ -x + 8
3x - 1
x-8 3x2 -25x+8 -3x2 + 24x
_____
-x + 8
-(-x + 8) _____
The remainder is 0.
Example
4
618 Saxon Algebra 1