University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2014
Views:

456

Pages:

4
Author:

Selena Curtis

Math 1l Review Polynomials A.APR.1, A.APR.2, A.APR.3, A.REI.4b, F.IF.7b, F.IF.8, N.CN.7 Adding polynomials - Add like terms, the exponents don't changel: Ex/[3x* - 4 + 2x) + (5x-6x* +7) = -3x7 + 7x + 3 Subtracting polynomials - Keep the first polynomial the same, change the subtraction to addition, and change the signs of the second polynomial. Exponents don't change. Ex/(3x' -4 + 2x) - (5x - 6x? +7) = 9x7 - 3x - 11 Multiplying Polynomials. - Each term in a polynomial has to be multiplied to each term in the other polynomial. Exponents change when terms are multiplied. Ex/ (2x* - 6x + 1)(x + 3) 2x3 + 6x3 - 6x2 - 18x +x+3 2x3 - 17x +3 Ex/ (x + 5)(x - 2)(3x + 4) x* -- 2x + 5x - 10 (3x + 4) (22 + 3x - 10)(3x + 4) 3x3 + 4x7 + 9x2 + 12x - 30х - 40 3x3: +13x? - 18x - 40 Dividing Pofynomials -- Can divide using synthetic or long division Synthetic (2x3 - 13x2 + 26x - 24) + (x - 4) Long Division (2x3 - 137 + 26x - 24) + (x - 4) 2x2 - 5x +6 1-427 - 1327 + 262 - 24 4j 2 - 24 8 - 20 24 (-) 20 - 802% -502 ÷ 26x - 5 (-) -5x* + 20x 6x - 24 (-) бх - 24 Roots, Zeroes, X-Intercepts - Are all solutions to polynomials Finding the polynomial given the roots Ex/ Find a 3" degree polynomial given the raots 2 and 31 (x - 2)(x - 30)(× + 31) (x - 2)(×2 + 3x1 - 3x1 - 919) (× - 2)(x* + 9) x* - 2x2 + 9x - 18 Ex/ Find the roots of x3 - 4x7 + 4x - 16 -Graph the potynomial and find a zero. This polynomial crosses the x-axis at 4: -Divide (x - 4) from the polynomial. 4/1 - 4 -16 4 Q 16 So the polynomial is reduced to x? + 4. Can use either QF or solve the square root equation. x₴ + 4=0 -4 x* = -4 Vx7 = tv=4 x= +21 So the roots of the polynomial are 4, 21, -21 Review Examples Which expression is equivalent to (x + 3)ª - 9x(x + 3)? x? + 27 ×3 - 27 x3 - 9x3 - 27x + 27 D. x3 - 9x7 + 27x + 27 x 3+27 (x+3)(143) (*+ex+9)(x+3) +3+66x9484+33718427 +3+97+274+27-9177 * 0x127