The factor theorem states that if there is a polynomial of degree greater than or equal to one and ‘a’ be a real number such that P(a) = 0, then (x – a) is the factor of the polynomial P(x). Is this true or false?

True

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False

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Solution

The correct option is A
True

If a polynomial of degree greater than or equal to one exists and ‘a’ be a real number such that P(a) = 0, then factor theorem states that (x – a) is a factor of the polynomial P(x), i.e, if (x – a) is a factor of the polynomial P(x) then P(a) = 0.

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Similar questions

The remainder theorem states that if a polynomial say p(x) is divided by (x-a) (where a is any real number) then the remainder will be p(a). Is this true or false?

The polynomial $(x^{2} + a)$ cannot be factorized if $a > 0$ . Is this statement true or false?

If a polynomial p(x) has a factor (x-a), then p(a)=0.

Say true or false:

For polynomials

p (x)

and any non-zero polynomial

g (x)

, there are polynomials

q (x)

and

r (x)

such that

p (x) = g (x) q (x) + r (x)

, where

r (x) = 0

or degree

r (x) <

degree

g (x) .

This statement is correctly explains the remainder theorem.

Q. Assertion :If p(x) is a polynomial of degree

\geq

1 and ax+b is a factor of p(x) then we have

p (- \frac{b}{a}) = 0

. Reason: If p(x) is a polynomial of degree

\geq

1, then polynomial (x-a)(x-b) is a factor of p(x) if p(a)=0 and p(b)=0.

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The factor theorem states that if there is a polynomial of degree greater than or equal to one and ‘a’ be a real number such that P(a) = 0, then (x – a) is the factor of the polynomial P(x). Is this true or false?

The correct option is A True If a polynomial of degree greater than or equal to one exists and ‘a’ be a real number such that P(a) = 0, then factor theorem states that (x – a) is a factor of the polynomial P(x), i.e, if (x – a) is a factor of the polynomial P(x) then P(a) = 0.

The correct option is A
True

If a polynomial of degree greater than or equal to one exists and ‘a’ be a real number such that P(a) = 0, then factor theorem states that (x – a) is a factor of the polynomial P(x), i.e, if (x – a) is a factor of the polynomial P(x) then P(a) = 0.