How will you find the remainder when a polynomial in x?

If a polynomial f(x) is divided by x−a , the remainder is the constant f(a) , and f(x)=q(x)⋅(x−a)+f(a) , where q(x) is a polynomial with degree one less than the degree of f(x) . Synthetic division is a simpler process for dividing a polynomial by a binomial.

How do you find the remainder using the remainder theorem?

Important Notes

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 x 3 2x 2 x 1 is divided by x 1?

Hence by the remainder theorem, 0 is the remainder when x3 + 3×2 + 3x + 1 is divided by x + 1.

What is the remainder when x 3 1 is divided by x 2?

zero
The remainder when (x3 + 1) is divided by (x2 – x + 1) is zero.

What is the remainder formula?

In the abstract, the classic remainder formula is: Dividend/Divisor = Quotient + Remainder/Divisor. If we multiply through by the Divisor, we get another helpful variant of the remainder formula: Dividend = Quotient*Divisor + Remainder.

How do you find the remainder?

Work the division in your calculator as normal. Once you have the answer in decimal form, subtract the whole number, then multiply the decimal value that’s left by the divisor of your original problem. The result is your remainder.

What is the remainder when x 4 x 3 2 x square x 1 is divided by X minus one?

the divisor by which the number is divided. Hence, the remainder when \[{x^4} + {x^3} – 2{x^2} + x + 1 = 0\]it is divided by\[x – 1\]is $R = 2$.

What is the remainder when 3x 3 2x 2 5x 6 is divided by x 1 )?

-7
The remainder when 3×3 + kx2 + 5x – 6 is divided by (x + 1) is -7.

What is the remainder when x 3 1 is divided by x 1?

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

What is the remainder of (X-1) = f(x)?

8 clever moves when you have $1,000 in the bank. We’ve put together a list of 8 money apps to get you on the path towards a bright financial future. and (x-1) = f (x). The easiest process is to put the the value of x in f (x) = 0, in F (x). The value of F (x) will be the remainder. = 6. So the remainder will be 6. It can be written as.

What is an example of remainders in math?

Example 8: Let R 1 and R 2 are the remainders when the polynomials x 3 + 2x 2 –5ax–7 and x 3 + ax 2 – 12x + 6 are divided by x + 1 and x – 2 respectively. If 2R 1 + R 2 = 6, find the value of a.

When p(x) is divided by (x + 2)?

When p (x) is divided by (x + 2), then by remainder theorem, the required remainder will be p (–2). Example 4: Determine the remainder when the polynomial p (x) = x 4 – 3x 2 + 2x + 1 is divided by x – 1. Solution: By remainder theorem, the required remainder is equal to p (1).

How do you prove the remainder theorem?

Remainder Theorem. Theorem: Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a). Proof: Let p(x) be any polynomial with degree greater than or equal to 1.