Find the other two factors of p(x)=x2-4x2+x+6 if the first factor is x+1.
To find the other two factors of the polynomial \(p(x) = x^3 - 4x^2 + x + 6\), we can perform polynomial long division or use synthetic division to divide \(p(x)\) by \(x + 1\).
Performing the division, we get:
x - 5
____________________________
x + 1 | x^3 - 4x^2 + x + 6
- (x^3 + x^2)
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-5x^2 + x
-(-5x^2 - 5x)
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6x + 6
- (6x + 6)
__________
0
Therefore, the other two factors of the polynomial \(p(x) = x^3 - 4x^2 + x + 6\) are \(x - 5\) and \(x + 1\).