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actor completely: 2x We will factor out the GCF, 2x, first. Then we will factor the resulting trinomial using the grouping method. The first step in factoring any polynomial is to factor out the GCF. We begin by factoring out the GCF, 2x, from 2x3 - 20x2 + 18x. 2x3 - 20x² + 18x = 2x(x² – 10x + 9) Key number = 9 b = -10 Factors Sum -9(-1) = 9 -9 + (-1) = -10 To factor x2 - 10x + 9 by grouping, we must find two integers whose product is the key number 9 and whose sum is b = -10. Such a pair is -9 and -1. x² - 10x + 9 = x² – 9x – 1x + Express -10x as -9x -1x. (-1x – 9x could also be used.) - x(x -0)- 1(x - 9) Factor x out of x2 - 9x and -1 out of -1x + 9. - (* - 9)(x - O) = (x Factor out x - 9. The complete factorization of the original trinomial is 2x3 - 20x2 + 18x = x(x - 9)(x - 1) Don't forget to write the GCF, 2x. Check the factorization by multiplying. Factor completely: 3m3 - 9m2 + 6m.

actor completely: 2x We will factor out the GCF, 2x, first. Then we will factor the resulting trinomial using the grouping method. The first step in factoring any polynomial is to factor out the GCF. We begin by factoring out the GCF, 2x, from 2x3 - 20x2 + 18x. 2x3 - 20x² + 18x = 2x(x² – 10x + 9) Key number = 9 b = -10 Factors Sum -9(-1) = 9 -9 + (-1) = -10 To factor x2 - 10x + 9 by grouping, we must find two integers whose product is the key number 9 and whose sum is b = -10. Such a pair is -9 and -1. x² - 10x + 9 = x² – 9x – 1x + Express -10x as -9x -1x. (-1x – 9x could also be used.) - x(x -0)- 1(x - 9) Factor x out of x2 - 9x and -1 out of -1x + 9. - (* - 9)(x - O) = (x Factor out x - 9. The complete factorization of the original trinomial is 2x3 - 20x2 + 18x = x(x - 9)(x - 1) Don't forget to write the GCF, 2x. Check the factorization by multiplying. Factor completely: 3m3 - 9m2 + 6m.

Elementary Algebra
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter7: Factoring
Section7.3: Factor Quadratic Trinomials With Leading Coefficient Other Than 1
Problem 209E: Height of a toy rocket The height of a toy rocket launched with an initial speed of 80 feet per...
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Factor completely: 2x³ – 20x² + 18x. We will factor out the GCF, 2x, first. Then we will factor the resulting trinomial using the grouping method. The first step in factoring any polynomial is to factor out the GCF. We begin by factoring out the GCF, 2x, from 2x3 – 20x² + 18x. 2x3 – 20x2 + 18x = 2x(x² – 10x + 9) Key number = 9 b = -10 %3D Factors Sum -9(-1) = 9 -9 + (-1) = -10 To factor x2 – 10x + 9 by grouping, we must find two integers whose product is the key number 9 and whose sum is b = -10. Such a pair is -9 and -1. x2 - 10x + 9 = x2 – 9x – 1x + Express -10x as —9х —1x. (-1х — 9х сould also be used.) (x-0)- - (x - 9)(x -O) = X 1(х — 9) Factor x out of x2 9x and -1 out of –1x + 9. Factor out x – 9. The complete factorization of the original trinomial is 2x3 – 20x2 + 18x = X(x – 9)(x – 1) Don't forget to write the GCF, 2x. Check the factorization by multiplying. Factor completely: 3m3 – 9m2 + 6m.
Transcribed Image Text:Factor completely: 2x³ – 20x² + 18x. We will factor out the GCF, 2x, first. Then we will factor the resulting trinomial using the grouping method. The first step in factoring any polynomial is to factor out the GCF. We begin by factoring out the GCF, 2x, from 2x3 – 20x² + 18x. 2x3 – 20x2 + 18x = 2x(x² – 10x + 9) Key number = 9 b = -10 %3D Factors Sum -9(-1) = 9 -9 + (-1) = -10 To factor x2 – 10x + 9 by grouping, we must find two integers whose product is the key number 9 and whose sum is b = -10. Such a pair is -9 and -1. x2 - 10x + 9 = x2 – 9x – 1x + Express -10x as —9х —1x. (-1х — 9х сould also be used.) (x-0)- - (x - 9)(x -O) = X 1(х — 9) Factor x out of x2 9x and -1 out of –1x + 9. Factor out x – 9. The complete factorization of the original trinomial is 2x3 – 20x2 + 18x = X(x – 9)(x – 1) Don't forget to write the GCF, 2x. Check the factorization by multiplying. Factor completely: 3m3 – 9m2 + 6m.
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