Solving Polynomial Equations in Factored Form PDF
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This document explains how to solve polynomial equations using factoring. It provides worked examples and exercises illustrating the concept of the zero-product property and factoring out the greatest common factor (GCF).
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# January 16 th ## Algebra 1, Unit 7 "Solving Polynomial Equations in Factored Form" ### Objectives: Students will be able to factor and solve a polynomial equation ### A factored form is when a polynomial is written as a product of its factors ### A zero product property if *ab* = 0, then either...
# January 16 th ## Algebra 1, Unit 7 "Solving Polynomial Equations in Factored Form" ### Objectives: Students will be able to factor and solve a polynomial equation ### A factored form is when a polynomial is written as a product of its factors ### A zero product property if *ab* = 0, then either *a* = 0 or *b* = 0 ### Examples: 1. *x*(*x* - 1) = 0 * *x* = 0 or *x* - 1 = 0 * *x* = 0 or *x* = 1 2. 3*t*(*t* + 2) = 0 * 3*t* = 0 or *t* + 2 = 0 * *t* = 0 or *t* = -2 3. (*y* - 4)(*y* - 6) = 0 * *y* - 4 = 0 or *y* - 6 = 0 * *y* = 4 or *y* = 6 4. (*b* + 7)^2 = 0 * (*b* + 7)(*b* + 7) = 0 * *b* + 7 = 0 * *b* = -7 * A repeated root is when the roots of the equation are the same numbers 5. (*d* - 2)(*d* + 6)(*d* + 8) = 0 * *d* - 2 = 0 or *d* + 6 = 0 or *d* + 8 = 0 * *d* = 2 or *d* = -6 or *d* = -8 ### The root are the solutions of the polynomial equation ## Factoring a polynomial using the GCF - Find the GCF of the terms in the given polynomial (Hint: look for the lowest power in the common variable) - Divide each term by the GCF - Rewrite the polynomial as a product of the GCF and the reduced terms. - Solve the equation ### Examples: 1. **Factor:** 6*d*<sup>2</sup>- 21*d* = 3*d*(2*d* - 7) 2. **Factor:** 20*x*<sup>3</sup> + 30*x*<sup>2</sup> = 10*x*<sup>2</sup>(2*x* + 3) 3. **Factor:** 12*a*<sup>4</sup> + 8*a = 4*a*(3*a*<sup>3</sup> + 2) ### Factor and Solve 4. 8*y*<sup>2</sup> - 24*y* = 0 * 8*y* (*y* - 3) = 0 * 8*y* = 0 or *y* - 3 = 0 * *y* = 0 or *y* = 3 5. *a*<sup>2</sup> + 5*a* = 0 * *a*(*a* + 5) = 0 * *a* = 0 or *a* + 5 = 0 * *a* = 0 or *a* = -5 6. 3*x*<sup>2</sup> - 9*x* = 0 * 3*x*(*x* - 3) = 0 * 3*x* = 0 or *x* - 3 = 0 * *x* = 0 or *x* = 3 7. 4*x*<sup>2</sup> = 2*x* * 4*x*<sup>2</sup> - 2*x* = 0 * 2*x*(2*x* - 1) = 0 * 2*x* = 0 or 2*x* - 1 = 0 * *x* = 0 or *x* = 1/2 8. -28*r* = 4*r*<sup>2</sup> + 28*r* * +28*r* * 4*r*<sup>2</sup> + 28*r* = 0 * 4*r*(*r* + 7) = 0 * 4*r* = 0 or *r* + 7 = 0 * *r* = 0 or *r* = -7
