x⁴ + 10x³ + 35x² + 50x + 24

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Solution

Let $f (x) = x^{4} + 10 x^{3} + 35 x^{2} + 50 x + 24$ be the given polynomial.

Now, putting we get

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

Now,

Where

Putting we get

Therefore, is the factor of g(x).

Now,

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

Hence are the factors of polynomial f(x).

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Similar questions

\sqrt{x^{4} + 10 x^{3} + 35 x^{2} + 50 x + 25}

If the quotient on dividing x^{4} + 10 x^{3} + 35 x^{2} + 50 x + 29 by (x + 4) is x^{3} - a x^{2} + b x + 6, then find the value of a, b and also remainder.

f (x) = x^{4} - 10 x^{3} + 35 x^{2} - 50 x + c

(x^{4} + 10 x^{3} + 35 x^{2} + 50 x + 29)

(x + 4)

(x^{3} - a x^{2} + b x + 6)

a, b

x^{4} + 9 x^{3} + 35 x^{2} - x + 4

x^{2} + 10 x + 29

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