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Factor: 12x5 – 17x4 + 6x³.

Factor: 12x5 – 17x4 + 6x³.

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: 12x5 – 17x4 + 6x³. We will factor out the GCF, x³, 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. The GCF of the three terms of the trinomial is x3. 12:5 – 17x* + 6x? = x*(12x² -Ox + 6) To factor 12x? 17x + 6, we need to find two integers whose product is 12(6) = 72 and whose sum is –17. Two such numbers are -8 and -9. 12x2 – 17x + 6 = 12x2 – 8x 9х + 6 Express -17х as —8x —— 9х. x(3х — 2) — 3(3х — 2) Factor out 4x and factor out -3. | 2»(4x - O) (3х — Factor out 3x – 2. The complete factorization is the following. 12x5 – 17x4 + 6x³ = x³( 3x - O)(4x – 3) Don't forget to write the GOCF, x³. Check the result. Factor: 18a4 – 13a3 + 2a?.
Transcribed Image Text:Factor: 12x5 – 17x4 + 6x³. We will factor out the GCF, x³, 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. The GCF of the three terms of the trinomial is x3. 12:5 – 17x* + 6x? = x*(12x² -Ox + 6) To factor 12x? 17x + 6, we need to find two integers whose product is 12(6) = 72 and whose sum is –17. Two such numbers are -8 and -9. 12x2 – 17x + 6 = 12x2 – 8x 9х + 6 Express -17х as —8x —— 9х. x(3х — 2) — 3(3х — 2) Factor out 4x and factor out -3. | 2»(4x - O) (3х — Factor out 3x – 2. The complete factorization is the following. 12x5 – 17x4 + 6x³ = x³( 3x - O)(4x – 3) Don't forget to write the GOCF, x³. Check the result. Factor: 18a4 – 13a3 + 2a?.
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