How do you factor y=x^3−2x^2+x−2?

Carol Valentine

Carol Valentine

Answered question

2021-12-17

How do you factor y=x32x2+x2?

Answer & Explanation

alexandrebaud43

alexandrebaud43

Beginner2021-12-18Added 36 answers

(x2)(x+i)(xi)
Explanation:
factor the terms by grouping
=x2(x2)+1(x2)
take out the common factor (x2)
=(x2)(x2+1)
x2+1 can be factored using difference of squares
a2b2=(ab)(a+b)
with a=x and b=i(i=1)
=(x2)(x+i)(xi)in factored form
alexandrebaud43

alexandrebaud43

Beginner2021-12-19Added 36 answers

y=(x2)×(x2+1)
Explanation:
x32x2 can be written as x2×(x2)
y=x2×(x2)+(x2)
or
y=x2×(x2)+1×(x2)
and bringing the common factor (x2) to the front, gives the factors:
y=(x2)×(x2+1)
solving the equation for y=0 gives the solution x=2 meaning that the graph of the equation crosses the x-axis at the point (2,0)
solving the equation for x=0 gives y=2 , meaning that the graph of the equation crosses the y-axis at (0,-2)
graph {x32x2+x2[10,10,5,5]}
RizerMix

RizerMix

Expert2021-12-29Added 656 answers

y=(x2+1)(x2)
Explanation:
y=x32x2+x2
We will use a factoring method called grouping. If we group the first and the third and the second and the fourth together, each grout has its own greatest common factor:
y=x(x2+1)2(x2+1)
Now we see another CF between the two terms : x2+1 . We can factor it out.
y=(x2+1)(x2)

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