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[tex]\((x-2)\)[/tex] is a factor of [tex]\(x^4+2x^3-7x^2-8x+12\)[/tex]. The other factors are:
[tex]\(x+2\)[/tex],
[tex]\(x+3\)[/tex],
and [tex]\(x-1\)[/tex].

Sagot :

GinnyAnsweridn
To factor the polynomial [tex]\( x^4 + 2x^3 - 7x^2 - 8x + 12 \)[/tex] with the given factor [tex]\((x - 2)\)[/tex]:

1. Polynomial Division:

We start by dividing the polynomial [tex]\( x^4 + 2x^3 - 7x^2 - 8x + 12 \)[/tex] by [tex]\( x - 2 \)[/tex].

The quotient from this division is [tex]\( x^3 + 4x^2 + x - 6 \)[/tex].

2. Factoring the Quotient Polynomial:

Now we need to factor [tex]\( x^3 + 4x^2 + x - 6 \)[/tex].

3. Finding the Factors:

After factoring [tex]\( x^3 + 4x^2 + x - 6 \)[/tex], we get the factors [tex]\( (x - 1) \)[/tex], [tex]\( (x + 2) \)[/tex], and [tex]\( (x + 3) \)[/tex].

So, the other factors of the polynomial [tex]\( x^4 + 2x^3 - 7x^2 - 8x + 12 \)[/tex] besides [tex]\( (x - 2) \)[/tex] are:

[Choose [tex]\( x + 2 \)[/tex]],
[Choose [tex]\( x + 3 \)[/tex]], and
[Choose [tex]\( x - 1 \)[/tex]].
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