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Factor Theorem

If the degree...

Question

If the degree of p(x) is 4 and the degree of q(x) is 2, the n what is the degree of p(x) + q(x)?

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Solution

Degree of p(x) = 4

Degree of q(x) = 2

Between p(x) and q(x), p(x) has a higher degree. Therefore, the degree of {p(x) + q(x)} is equal to the degree of p(x).

∴ Degree of {p(x) + q(x)} = 4

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Similar questions

p (x) = x^{2} - 2 x + 1

q (x) = x^{3} - 3 x^{2} + 2 x - 1

p (x) \times q (x)

and check the degree of

p (x) \times q (x)

lim x \to \infty \frac{2 x^{3} + 3 x^{2} - 4 x + 7}{3 x^{3} + 4 x^{2} - x - 9} = \frac{2}{3}

Reason: If p(x) & q(x) are polynomials then

lim x \to \infty \frac{p (x)}{q (x)}

is a finite non zero number if degree of p(x)=degree of q(x).

p (x)

q (x)

are two polynomials whose degrees are

8

m

and the degree of polynomial

p (x) \times q (x)

104

, then the value of

m

p (x)

q (x)

are two polynomials whose degrees are 8 and m respectively and the degree of polynomial

p (x) \times q (x)

is 104, then the value of m is

p (x) = x^{3} + 8 x^{2} - 7 x + 12

g (x) = x - 1

p (x)

g (x)

q (x)

r (x)

as quotient and remainder respectively. If

a

is the degree of

q (x)

b

is the degree of

r (x)

(a - b) = ?

.

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