x⁴ − 2x³ − 7x² + 8x + 12

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Solution

Let be the given polynomial.

Now, putting we get

Therefore, is a factor of polynomial f(x).

Now,
$f (x) = x^{4} - 3 x^{3} + x^{3} - 3 x^{2} - 4 x^{2} + 12 x - 4 x + 12$

Where

Putting we get

Therefore, is the factor of g(x).

Now,
$g (x) = x^{3} - 2 x^{2} - x^{2} - 6 x + 2 x + 12$

From equation (i) and (ii), we get

Hence are the factors of polynomial f(x).

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Similar questions

x^{4} + 2 x^{3} - 7 x^{2} - 8 x + 12

x^{4} + 2 x^{3} - 7 x^{2} - 8 x + 12 = 0

x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 12

Using factor theorem,factorize the polynomial:

1) x⁴-2x³-7x²+8x+12

x^{4} + 2 x^{3} - 7 x^{2} - 8 x + 12; - 3, - 2, 1, 2

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