Objective  SWBAT solve polynomial equations. Section 9.4 “Solve Polynomial Equations in Factored Form” If ab = 0, then a = 0 or b = 0. The zero-product.

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Presentation transcript:

Objective  SWBAT solve polynomial equations

Section 9.4 “Solve Polynomial Equations in Factored Form” If ab = 0, then a = 0 or b = 0. The zero-product property is used to solve an equation when one side of the equation is ZERO and the other side is the product of polynomial factors. (x – 4)(x + 2) = 0 Zero-Product Property The solutions of such an equation are called ROOTS. x – 4 = 0 x + 2 = 0 x = 4 x = -2

Solve the equations (x – 5)(x + 1) = 0 x – 5 = 0 x + 1 = 0 x = 5 x = -1 (2x – 3)(4x + 1) = 0 2x – 3 = 0 4x + 1 = 0 x = 3/2 x = -1/4

“Solving Equations By Factoring” Look for common terms 2x² + 8x = 0 When using the zero-product property, sometimes you may need to factor the polynomial, or write it as a product of other polynomials. Look for the greatest common factor (GCF) of the polynomial’s terms. GCF- the monomial that divides evenly into EACH term of the polynomial. GCF

Solve Equations By Factoring 2x = 0 x + 4 = 0 x = 0 x = -4 2x² + 8x = 0 2x(x + 4) = 0 Factor left side of equation Zero product property The solutions of the equation are 0 and -4.

Solve Equations By Factoring 3x = 0 2x - 5 = 0 x = 0 x = 5/2 6x² - 15x = 0 3x(2x - 5) = 0 Factor left side of equation Zero product property The solutions of the equation are 0 and 5/2.

Solve Equations By Factoring 14p = 0 3p + 1 = 0 p = 0 p = -1/3 42p² + 14p = 0 14p(3p + 1) = 0 Factor left side of equation Zero product property The solutions of the equation are 0 and -1/3. 42p² = -14p Bring all variables to one side

Factor Challenge