2.5 Divide Polynomials.notebook
October 17, 2016
Homework Answers: EXTRA PRACTICE
1. x = 0, ­5, ­3 2. x = 0 , 2
3. x = 4, 1 4. x = 5. x = 0, 10, ­10 6. x = 0, 7. x = ­1, ± i 8. x = 0, ­7, ­2
9. x = 6, ­3 ± 3i√3 10. x = ­8, 2
11. x = 12. x = 0, ­ 3
13. x = 0, 14. x = ­3,
15. x = 2, ­2, ± 2i 16. x = 1, ­1,
17. x = 2, ­2, ± √14 18. skip
19. x = ± √6, ± i√6 20. x = 0, ­1, 1
21. x = ± 3√3
HW Answers
Oct 27­3:09 PM
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2.5 Divide Polynomials.notebook
October 17, 2016
page 114
Problem solving
Problem Solving
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2.5 Divide Polynomials.notebook
October 17, 2016
2.5 Apply the Remainder and Factor Theorems
Polynomial Division
remainder
polynomial
divisor
quotient
When you divide a polynomial by a divsior, you get a quotient and a remainder.
The degree of the remainder must be less than the degree of the divisor.
Long Division
I. Long Division of Polynomials
Let's review long division.
quotient
divisor
dividend
Long Division
3
2.5 Divide Polynomials.notebook
October 17, 2016
Let's apply long division to polynomials.
STEPS:
1. Write the dividend in descending order
with every power of the variable
represented.
2. Divide the term with the highest power (in the
dividend) by the leading term of the divisor.
Write the result as the next term of the quotient.
3. Multiply the term of the quotient with the divisor.
Write the product below the dividend.
4. Subtract the product of step 3 by adding the
opposite of each term.
5. Bring down the next term of the dividend.
6. Repeat steps 2-5 until remainder is a lower
degree than the divisor.
CHECK YOUR ANSWER: Multiply the divisor and
quotient, then add the remainder.
Polynomial Long Division
EXAMPLE 2
STEPS:
1. Write the dividend in descending order
with every power of the variable
represented.
2. Divide the term with the highest power (in the
dividend) by the leading term of the divisor.
Write the result as the next term of the quotient.
3. Multiply the term of the quotient with the divisor.
Write the product below the dividend.
4. Subtract the product of step 3 by adding the
opposite of each term.
5. Bring down the next term of the dividend.
6. Repeat steps 2-5 until remainder is a lower
degree than the divisor.
CHECK YOUR ANSWER: Multiply the divisor and
quotient, then add the remainder.
Example 2
4
2.5 Divide Polynomials.notebook
October 17, 2016
EXAMPLE 3
Ex 3 Missing Term
TRY THESE:
4
2
2
1. (x + 2x - x + 5)
3
2
(x - x + 1)
2. (x - x - 2x + 8)
3
2
3. (x - 6x + 1)
(x + 2)
(x - 2)
Practice
5