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# Algebra

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if (x^2 -x-2) is a factor of f(x)=2x^3 -2ax^2 +3bx-4, what will a+b equal to?

Mar 25, 2021

#1
+291
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if x^2-x-2 is a factor, then both (x-2) and (x+1) will be factors as well.

According to the remainder theorem, f(2) and f(-1) must be equal to zero. That means that:

\(2(2)^3-2(2)^2a+3(2)b-4=0\\16-8a+6b-4=0\\-4a+3b+6=0\)

and

\(2(-1)^3-2(-1)^2a+3(-1)b-4=0\\-2a-3b-6=0\)

both must be true. Add up the 2 system of equations to get:

\(-6a=0\\ a=0\)

Substitute back in a:

\(-4(0)+3b+6=0\\ b=-2\)

Therefore, \(a+b=\boxed{-2}\)

Mar 25, 2021

#1
+291
+2

if x^2-x-2 is a factor, then both (x-2) and (x+1) will be factors as well.

According to the remainder theorem, f(2) and f(-1) must be equal to zero. That means that:

\(2(2)^3-2(2)^2a+3(2)b-4=0\\16-8a+6b-4=0\\-4a+3b+6=0\)

and

\(2(-1)^3-2(-1)^2a+3(-1)b-4=0\\-2a-3b-6=0\)

both must be true. Add up the 2 system of equations to get:

\(-6a=0\\ a=0\)

Substitute back in a:

\(-4(0)+3b+6=0\\ b=-2\)

Therefore, \(a+b=\boxed{-2}\)

textot Mar 25, 2021