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Polynomials

2 x4-7 x3-13 ...

Question

2x⁴ − 7x³ − 13x² + 63x − 45

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Solution

Let be the given polynomial.

Now, putting we get

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

Now,

Where

Putting we get

Therefore, is a 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

Q. Using factor theorem, factorize:

p (x) = 2 x^{4} - 7 x^{3} - 13 x^{2} + 63 x - 45

Using factor theorem, factorize each of the following polynomials

$2 x^{4} - 7 x^{3} - 13 x^{2}$ + 63x - 45

Q. Find the quotient and remainder using synthetic division.

(2 x^{4} - 7 x^{3} - 13 x^{2} + 63 x - 48) \div (2 x - 1)

1

3

are the zeros of the polynomial

p (x) = 2 x^{4} - 7 x^{3} - 13 x^{2} + 63 x - 45

,then find the remaining zeros of

p (x)

Q. Use the factor theorem to determine whether g(x) is a factor of p(x) in the following case.

p (x) = 2 x^{4} - 7 x^{3} - 13 x^{2} + 63 x - 45; g (x) = x - 1

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