1. Divide by using long division. (8x 3 + 6x 2 + 7) (x + 2)

Transcription

1 Bellwork Divide by using long division. (8x + 6x 2 + 7) (x + 2)

2 Synthetic division is a shorthand method of dividing a polynomial by a linear binomial by using only the coefficients. For synthetic division to work, the polynomial must be written in standard form, using 0 and a coefficient for any missing terms, and the divisor must be in the form (x a). 2

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4 Example 2A: Using Synthetic Division to Divide by a Linear Binomial Divide using synthetic division. (x 2 + 9x 2) (x ) Step Find a. Then write the coefficients and a in the synthetic division format. a = For (x ), a =. 9 2 Write the coefficients of x 2 + 9x 2. 4

5 Example 2A Continued Step 2 Bring down the first coefficient. Then multiply and add for each column. 9 2 Draw a box around the remainder. Step Write the quotient. 5

6 Check Multiply (x ) Example 2A Continued x x (x ) + 0 (x ) + x x (x ) = x 2 + 9x 2 6

7 Example 2B: Using Synthetic Division to Divide by a Linear Binomial Divide using synthetic division. (x 4 x + 5x ) (x + 2) Step Find a. a = 2 For (x + 2), a = 2. Step 2 Write the coefficients and a in the synthetic division format. Use 0 for the coefficient of x 2. 7

8 Example 2B Continued Step Bring down the first coefficient. Then multiply and add for each column Step 4 Write the quotient. 8

9 Check It Out! Example 2a Divide using synthetic division. (6x 2 5x 6) (x + ) Step Find a. For (x + ), a = Step 2 Write the coefficients and a in the synthetic division format Write the coefficients of 6x 2 5x 6. 9

10 Check It Out! Example 2a Continued Step Bring down the first coefficient. Then multiply and add for each column Step 4 Write the quotient. 0

11 Check It Out! Example 2b Divide using synthetic division. (x 2 x 8) (x 6) Step Find a. Step 2 Write the coefficients and a in the synthetic division format. Write the coefficients of x 2 x 8.

12 You can use synthetic division to evaluate polynomials. This process is called synthetic substitution. The process of synthetic substitution is exactly the same as the process of synthetic division, but the final answer is interpreted differently, as described by the Remainder Theorem. 2

13 Example A: Using Synthetic Substitution Use synthetic substitution to evaluate the polynomial for the given value. P(x) = 2x + 5x 2 x + 7 for x = Write the coefficients of the dividend. Use a = 2. Check Substitute 2 for x in P(x) = 2x + 5x 2 x + 7

14 Example B: Using Synthetic Substitution Use synthetic substitution to evaluate the polynomial for the given value. P(x) = 6x 4 25x x + 5 for x =. Write the coefficients of the dividend. Use 0 for the coefficient of x 2. Use a =. 4

15 Check It Out! Example a Use synthetic substitution to evaluate the polynomial for the given value. P(x) = x + x for x =. Write the coefficients of the dividend. Use 0 for the coefficient of x 2 Use a =. Check Substitute for x in P(x) = x + x P( ) = ( ) + ( )

16 Check It Out! Example b Use synthetic substitution to evaluate the polynomial for the given value. P(x) = 5x 2 + 9x + for x =. 5 Write the coefficients of the dividend. Use a =. 5 6

17 Lesson Quiz. Divide by using synthetic division. (x x + 5) (x + 2) 2. Use synthetic substitution to evaluate P(x) = x + x 2 6 for x = 5 and x =.. Find an expression for the height of a parallelogram whose area is represented by 2x x 2 20x + and whose base is represented by (x + ). 2x 2 7x + 7

18 Homework: Workbook Page, #'s - all 8