Warm Up 1. Divide f(a) = 4a2 – 3a + 6 by a – 2 using any method. Now find f(2). List any similarities. Why do you think this occurs?

Remainder and Factor Theorem 6-7 Remainder and Factor Theorem SWBAT use the remainder to find the remainder of dividing polynomials. use the factor theorem to factor polynomials Holt McDougal Algebra 2 Holt Algebra 2

Recall that if a number is divided by any of its factors, the remainder is 0. Likewise, if a polynomial is divided by any of its factors, the remainder is 0. The Remainder Theorem states if a polynomial is divided by (x – a) the remainder is the value of the function at a.

Find the remainder of: f(x) = 3x3 – 2x2 + x – 11 and x – 3

Factor Theorem: If the remainder of your equation = 0 Then x – a is a factor of the quotient You have to use Synthetic or Long Division f(x) = x4 + x3 – 17x2 – 20x + 32 and x – 4 (x – 4) (x3 + 5x2 + 3x – 8)

Determine whether the given binomial is a factor of the polynomial P(x). A. (x + 1); (x2 – 3x + 1) Find P(–1) by synthetic substitution. P(–1) = 5 P(–1) ≠ 0, so (x + 1) is not a factor of P(x) B. (x + 2); (3x4 + 6x3 – 5x – 10) Find P(–2) by synthetic substitution. P(–2) = 0, so (x + 2) is a factor of P(x)

Factor Theorem Show that x + 3 is a factor of f(x) = x3 + 6x2 – x – 30. Then solve for x. (x+3)(x – 2)(x + 5), so x = -3, 2, -5

Try on your own. Pg 358 #2

Homework: Page 359 #10-22 Even Bring in book tomorrow

Warm Up – do not share books/ipads PG 360 # 43

Remainder and Factor Theorem 6-7 Remainder and Factor Theorem SWBAT use the remainder to find the remainder of dividing polynomials. use the factor theorem to factor polynomials Holt McDougal Algebra 2 Holt Algebra 2

Factor Theorem Use the graph of the polynomial. To factor the x3 – 3x2 – 6x + 8 completely.

PARCC Example Answer: W: x – 4 L: x + 8 H: x – 1 Try on your own: pg 359 # 3

Real World Example (use calc) Pg 359 #3-5

Use synthetic division. PARCC Question Write an expression that represents the area of the top face of a rectangular prism when the height is x + 2 and the volume of the prism is x3 – x2 – 6x. The volume V is related to the area A and the height h by the equation V = A  h. Rearranging for A gives A = . V h x3 – x2 – 6x x + 2 A(x) = Substitute. Use synthetic division. The area of the face of the rectangular prism can be represented by A(x)= x2 – 3x.

PARCC Example Write an expression for the length of a rectangle with width y – 9 and area y2 – 14y + 45. The area A is related to the width w and the length l by the equation A = l  w. y2 – 14y + 45 y – 9 l(x) = Substitute. Use synthetic division. The length of the rectangle can be represented by l(x)= y – 5.

Did We Reach Our Objective? Use the factor theorem. Use the remainder theorem.

HOMEWORK Pg 360 # 29 – 33 all