section 5.7 dividing polynomials. 5.7 lecture guide: dividing polynomials objective 1: divide a...
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Section 5.7
Dividing Polynomials
5.7 Lecture Guide: Dividing Polynomials
Objective 1: Divide a polynomial by a monomial.
Find each quotient and assume the variables are restricted to values that avoid division by zero.
5 4
2 2
183x yx y
1.5 3
2 6
1640x yx y
2.
Dividing a Polynomial by a Monomial:
Verbally
To divide a polynomial by a monomial, divide each ____________ of the polynomial by the monomial.
Algebraic Example2 26 4 6 42 2 2
3 2
x x x xx x x
x
Find each quotient and assume the variables are restricted to values that avoid division by zero.
4 3 2 2
2
21 6 9
3
x x y x y
x
3.
Find each quotient and assume the variables are restricted to values that avoid division by zero.
4.2 2 328 8 12
4
x y xy y
y
5.4 2 3 3 3 2
3 2
12 9 3
3
x y x y x y
x y
Find each quotient and assume the variables are restricted to values that avoid division by zero.
6.
Find each quotient and assume the variables are restricted to values that avoid division by zero.
3 2 2 3
2
28 8 12
4
x y x y xy
x y
Objective 2: Use long division of polynomials.
Step 1. Write the polynomials in long-division format, expressing each in _______________ form.
Step 2. Divide the first term of the divisor into the first term of the dividend. The result is the first term of the __________.
Step 3. Multiply the first term of the quotient times every term in the divisor, and write this product under the dividend, aligning like terms.
Step 4. _______________ this product from the dividend, and bring down the next term.
Step 5. Use the result of Step 4 as a new dividend, and repeat Steps 2-4 until either the remainder is zero or the degree of the remainder is less than the degree of the divisor.
Long Division of Polynomials
7. Find the quotient 24 5 8 2 15.x x x
8. Check the answer in problem 7 by multiplying the divisor by the quotient.
Find each quotient.
9. 25 4 10 17 20x x x
Find each quotient.
10. 26 5 18 9 20x x x
3 12 16
2
x x
x
Hint: Watch out for the missing term.
Find each quotient.
11.
Hint: This will have a non-zero remainder.
Find each quotient.
12.23 4 10
2
x x
x
13. The area of a triangle is 24 4 35x x mm2.
The base of the triangle is 2 7x mm.
Find the altitude of the triangle. (Hint: ). 12
A bh
14. Using x to represent the number of units produced, a factory determined that the cost in dollars to produce these units was 150 540.C x x
(a) Write an expression for A x , the average cost ofproducing x units.
(b) Evaluate and interpret 10C .
(b) Evaluate and interpret . 10A
15. (a) One factor of 3 26 11 17 30x x x is . Determine the other factor.
3 5x
15. (b) Another factor of 3 26 11 17 30x x x is . Complete this equation:
3 26 11 17 30 2 3 3 5 ___________x x x x x
Hint: Divide into the quotient from part (a).
2 3x
2 3x
16. When a polynomial is divided by , the quotient is 10
33 4
xx
. Determine this polynomial.
3 4x