What is the remainder of p x when divided by x 1?

The remainder when P(x) is divided by (x-1) is P(1). The answer is 2.

What is the remainder when the given polynomial P x is divided by X?

Answer: If a polynomial p(x) is divided by x-a, then it’s remainder is p(a). Step-by-step explanation: Remainder theorem: According to the remainder theorem, if a polynomial P(x) is divided by the polynomial (x-c), then the remainder is defined as P(c).

How do we know if the divisor XC is a factor of the polynomial P x?

The proof of The Factor Theorem is a consequence of what we already know. If (x – c) is a factor of p(x), this means p(x)=(x – c)q(x) for some polynomial q. Hence, p(c)=(c – c)q(c) = 0, so c is a zero of p. Conversely, if c is a zero of p, then p(c) = 0.

When P x is divided by x 2 then the remainder is?

If a polynomial p(x) is divided by x−2, the quotient is 2x and remainder is 4.

When X 3 is divided by x 1 What is the remainder?

zero
So, when f(x) = x3 + 1 is divided by x + 1, the remainder obtained is zero. Therefore, the remainder is 0.

When a polynomial P x is divided by a binomial X a then the remainder obtained is?

A polynomial P(x) is divided by a binomial x−a . The remainder is zero.

Is X 1 a factor?

1 Expert Answer By the factor theorem, if P(1)=0, then x-1 is a factor. therefore, x-1 is a factor of P(x).

Is X 1 a factor of F x?

x – 1 is not a factor of f (x).

When can we say that the binomial XR is a factor of the polynomial P x?

x-r is a factor of Px if the remainder is negative. x-r is a factor of Px if the remainder is zero.

What theorem states that if the polynomial P x is divided by XR then the remainder is equal to p r?

The remainder theorem
The remainder theorem simply states that if a polynomial f(x) is divided by a linear expression x-r, the value of f(r) is equal to the remainder.

Which expression is equivalent to Mn )( x?

Therefore, the expression which is equivalent to (mn) (x) is 5×3 + 9×2 + 15x + 27.

When is X-a the factor of P(x)?

It states that when the polynomial p (x) is equally divided by another polynomial g (x) with the divisor x-a and if the remainder is zero i.e. R (x) = 0. So x-a is said to be the factor of that polynomial p (x).

How do you find the remainder of a polynomial?

1 When a polynomial a (x) is divided by a linear polynomial b (x) whose zero is x = k, the remainder is given by r = a (k) 2 The remainder theorem formula is: p (x) = (x-c)·q (x) + r (x). 3 The basic formula to check the division is: Dividend = (Divisor × Quotient) + Remainder.

What is the remainder when divided by T – 1?

By the Remainder Theorem, 2 is the remainder when is divided by t – 1.

What happens when you divide a polynomial by a factor?

According to this theorem, if we divide a polynomial P (x) by a factor ( x – a); that isn’t essentially an element of the polynomial; you will find a smaller polynomial along with a remainder. This remainder that has been obtained is actually a value of P (x) at x = a, specifically P (a).