October 11th

copyright2009merrydavidson

Happy August Birthday to:Collin Stipe

If you divide 12 by 3 the remainder is zero, therefore 3 is a

“factor” of 12.

Divide (x4 – 1) by (x + 1)

What is the remainder?

Conclusion: (x + 1) is a FACTOR

of (x4 – 1).

zero

The Remainder TheoremThe value of a function at a specific “x”

is the same as the remainder when divided by that value.

FOR f(x) = 3x3 + 8x2 + 5x -7FIND f(-2) =

Now use Synthetic Division for x = -2

3(-2)3+8(-2)2+5(-2)-7=9

What was the remainder? 9

Practice

Find the remainder if:

f(x) = x3 – 4x2 + 2x –5

is divided by (x – 3). Do you need to

perform division?

Find f(3). -8

No you can use direct substitution.

The Factor Theorem

If the binomial (x – r) is a factor of f(x) then f(r ) = 0

What does this mean?

If (x – 7) is a factor,

Then f(7) = 0

Practice

Is (x – 5) a factor of

P(x) = x3 – 4x2 – 7x + 10?

yes

Practice

Is (x + 2) a factor of

f(x) = 5x3 + 8x2 – x + 6?

no

Show that (x+3)is a factor off(x) = x3 + 4x2 + x – 6

Then find the remaining factors.Step 1: divide f(x) by (x+3) to show it has a remainder of zero

Step 2: factor the remaining quadratic.

Step 3: Write the polynomial in factored form.

Show that (x-2) and (x+3)are factors off(x) = 2x4 + 7x3 – 4x2 – 27x -18

Then find the remaining factors.

Step 1: divide f(x) by (x-2)

Step 2: divide the depressed polynomial by (x+3).

Step 3: factor the remaining quadratic.

Step 4: Write the polynomial in factored form.

Homework

WS 3-6