Download Lesson 7-4 Synthetic Division

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Algebra 2: Lesson 7-4 Synthetic Division
Learning Goals
1) How do we perform long division on polynomials?
2) How do we perform synthetic division on polynomials?
3) When can we use synthetic division when asked to divide polynomials?
Do Now: Divide the following using long division.
Divide x3 + 4x2 – 3x – 5 by x + 3
What is the degree of the following polynomials?
1) 5x2 – 7x + 5
2) 4x + 6x5 + 8x2 – 4
3) 8x7 – 4x2 + 9x10
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Now we will take the “do now” problem and divide by a method called synthetic division.
Divide x3 + 4x2 – 3x – 5 by x + 3 using synthetic
division.
Step 1: Arrange the coefficients in descending
order. {Remember to include placeholders for
any missing variables}.
Step 2: Write the constant of the divisor x – r {in
this case -3}
Step 3: Bring down the first coefficient.
Step 4: Multiply the first coefficient by r {in this
case -3}. Place that product under the 2nd
coefficient.
Step 5: Add the column. Then multiply that sum
by r.
Step 6: Repeat step 5 for all coefficients.
Step 7: The final sum represents the remainder.
The other numbers are the coefficients of the
quotient polynomial which has degree one less
than the dividend.
Synthetic division can only be used when
The divisor is a factor of the dividend when
Practice: Divide each of the following using synthetic division.
1) Divide x3 – x2 + 2 by x + 1
2) Divide and find the factors of (2x3 – 3x2 + x) ÷ (x – 1).
Divide each of the following using synthetic division. Then state whether the binomial is a factor of the
polynomial.
3) (2x4 + 4x3 – x2 + 9) ÷ (x + 1)
4) (2x3 – 3x2 – 10x + 3) ÷ (x – 3)
5) Use synthetic division to find all of the factors of
x3 + 6x2 – 9x – 54 if one of the factors is x – 3.