Write polynomial P as a product of linear factors : P(x) = 5x^3 -2x^2 + 5x - 2
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
We have to write the polynomial P(x) = 5x^3 -2x^2 + 5x - 2 as a product of linear factors.
P(x) = 5x^3 -2x^2 + 5x - 2
=> P(x) = x^2( 5x - 2) + 1( 5x - 2)
=> P(x) = (x^2 + 1)(5x - 2)
The term x^2 + 1 cannot be factorized into linear terms.
If instead we had P(x) = 5x^3 -2x^2 - 5x + 2 we could have had P(x) = (5x - 2)(x - 1)(x + 1), which are linear terms.
The factors of P(x) = 5x^3 -2x^2 + 5x - 2 are
(x^2 + 1)(5x - 2).
Related Questions
- Write polynomial P as a product of linear factors : P(x) = -x^3 - 2x^2 + 5x + 6
- 1 Educator Answer
- What is k(x)= 2x^3-5x^2-x+6 written in standard form and as a product of linear factors?
- 1 Educator Answer
- The polynomial p(x) = x^3 + x - 10. Show x-2 is a factor of p(x) and express p(x) in the form...
- 1 Educator Answer
- Factorise 2x^2 - 5x + 3
- 1 Educator Answer
- Solve by factoring: 3x^2 + 5x - 2 = 0.Solve by factoring. 1. x^2 + 5x + 6 = 0 2. 2x^2 - x - 3 =...
- 2 Educator Answers
calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Given the polynomial P(x) = 5x^3 - 2x^2 + 5x -2
We need to factor P(x).
First we will rearrange the terms of P(x).
==> P(x) = 5x^3 + 5x - 2x^2 - 2
Now we will factor 5x from the first two terms.
==> P(x) = 5x (x^2 +1) - 2x^2 -2
Now we will factor -2 from the last two terms.
==> P(x) = 5x(x^2 +1) -2 ( x^2 + 1)
Now we will factor (x^2+1).
==> P(x) = (x^2 + 1) (5x-2)
Now we will factor (x^2 +1)
==> P(x) = (x-i)(x+i) ( 5x-2)