How do you solve factor and remainder theorem?

How do you solve factor and remainder theorem?

The Factor and Remainder Theorems If p(x) is a polynomial of degree 1 or greater and c is a real number, then when p(x) is divided by x−c, the remainder is p(c). If x−c is a factor of the polynomial p, then p(x)=(x−c)q(x) for some polynomial q. Then p(c)=(c−c)q(c)=0, showing c is a zero of the polynomial.

What is remainder theorem answer?

Remainder Theorem is an approach of Euclidean division of polynomials. 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.

What is factor theorem explain with example?

Answer: An example of factor theorem can be the factorization of 6×2 + 17x + 5 by splitting the middle term. In this example, one can find two numbers, ‘p’ and ‘q’ in a way such that, p + q = 17 and pq = 6 x 5 = 30. After that one can get the factors.

What is the remainder theorem formula?

The remainder theorem formula is: p(x) = (x-c)·q(x) + r(x). The basic formula to check the division is: Dividend = (Divisor × Quotient) + Remainder.

What is the factor of x³ 125?

=(x+5)(x2−5x+25)

What is factor theorem Class 9?

Factor Theorem. Factor Theorem. x – a is a factor of the polynomial p(x), if p(a) = 0. Also, if x – a is a factor of p(x), then p(a) = 0, where a is any real number. This is an extension to remainder theorem where remainder is 0, i.e. p(a) = 0.

What is factor theorem Class 10?

In mathematics, factor theorem is used when factoring the polynomials completely. It is a theorem that links factors and zeros of the polynomial. According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then, (x-a) is a factor of f(x), if f(a)=0.

How do you solve a factor theorem question?

Example 1: Examine whether x + 2 is a factor of x3 + 3×2 + 5x + 6 and of 2x + 4. Solution: The zero of x + 2 is –2. So, by the Factor Theorem, x + 2 is a factor of x3 + 3×2 + 5x + 6. So, x + 2 is a factor of 2x + 4.

Is remainder theorem and factor theorem same?

Basically, the remainder theorem links remainder of division by a binomial with the value of a function at a point, while the factor theorem links the factors of a polynomial to its zeros.

What is the factor of x2 6x 9?

Look: (x + 3)2 = x2 + 6x + 9, and (x – 3)2 = x2 – 6x + 9! Here 9 can be written as (−3)2, so the middle term is 2(−3)x = −6x. So when the sign of the middle term is negative, the trinomial may be factored as (a – b)2….