Study Guide and Intervention (continued) - MathnMind

12-5
Divide Polynomials by Binomials To divide a polynomial by a binomial, factor the
dividend if possible and divide both dividend and divisor by the GCF. If the polynomial
cannot be factored, use long division.
Example
Find (x 2 7x 10) (x 3).
Step 1 Divide the first term of the dividend, x 2 by the first term of the divisor, x.
x
x 3
x2 7x 10
() x 2 3x Multiply x and x 3.
4x Subtract.
Step 2 Bring down the next term, 10. Divide the first term of 4x 10 by x.
x 4
x 3
x2 7x 10
x2 3x
4x 10
() 4x 12 Multiply 4 and x 3.
2 Subtract.
2
The quotient is x 4 with remainder 2. The quotient can be written as x 4 . x 3
Exercises
NAME ______________________________________________ DATE ____________ PERIOD _____
Study Guide and Intervention (continued)
Dividing Polynomials
Find each quotient.
1. (b 2 5b 6) (b 2) 2. (x 2 x 6) (x 3)
3. (x 2 3x 4) (x 1) 4. (m 2 2m 8) (m 4)
5. (x 2 5x 6) (x 2) 6. (m 2 4m 4) (m 2)
7. (2y 2 5y 2) (y 2) 8. (8y 2 15y 2) (y 2)
m
9. 10.
2 8x 5m 6
m 6
2 6x 9
4x 3
6m
11. 12.
3 11m2 x 4m 35
2m 5
3 1
x 2
13. 14. 8p3 6a 27
2p 3
2 7a 5
2a 5
© Glencoe/McGraw-Hill 730 Glencoe Algebra 1