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Answer» ong>Answer: Course menu Socratic Q&A logo Search icon How do you factor x 3 − 2 x 2 − x + 2 by grouping? Algebra FACTORING by Grouping 1 Answer Mahek ☮ Mar 11, 2018 = ( x − 1 ) ( x + 1 ) ( x − 2 )
Explanation: x 3 − 2 x 2 − x + 2
= x 3 − x − 2 x 2 + 2
Grouping the 1 s t
2 terms together and the 2 n d
2 together: = x ( x 2 − 1 ) − 2 ( x 2 − 1 )
= ( x 2 − 1 ) ( x − 2 )
Using the identity: a 2 − b 2 = ( a + b ) ( a − b )
= ( x 2 − 1 2 ) ( x − 2 )
= ( x − 1 ) ( x + 1 ) ( x − 2 )
Alternate Method:-
The above method is an easy on to solve this question. For factorizing other cubic POLYNOMIALS, the following method can be used: First, by trial and error method, you can find one factor as follows: x 3 − 2 x 2 − x + 2
When replacing 1, ⇒ 1 3 − 2 × 1 2 − 1 + 2
⇒ 1 − 2 − 1 + 2
⇒ 0
So, we GET ( x − 1 ) as factor. Then by long division, divide ( x − 1 ) by ( x 3 − 2 x 2 − x + 2 )
You get ⇒ ( x − 1 ) ( x 2 − x − 2 )
Then you have to factorize it by splitting the middle term method. ⇒ ( x − 1 ) [ x 2 + x − 2 x − 2 ]
⇒ ( x − 1 ) [ x ( x + 1 ) − 2 ( x + 1 ) ]
⇒ ( x − 1 ) ( x + 1 ) ( x − 2 )
~Hope this helps! :) Answer link Related topic Factoring by Grouping Questions Related questions What is Factoring by Grouping? How do you factor by grouping four-term polynomials and trinomials? Why does factoring polynomials by grouping work? How do you factor 2 x + 2 y + a x + a y ? How do you factor 3 x 2 + 8 x + 4 by using the grouping method? How do you factor 6 x 2 − 9 x + 10 x − 15 ? How do you group and factor 4 j k − 8 j 2 + 5 k − 10 j ? What are the factors of 2 m 3 + 3 m 2 + 4 m + 6 ? How do you factor quadratics by using the grouping method? How do you factor x 4 − 2 x 3 + 5 x − 10 ? iOS Android Privacy Terms Help |
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