Question

Are hit and trial method and factor theorem are same??
If not then tell me the difference​

Answer 1

Answer:

Step-by-step explanation:

A polynomial is an algebraic expression with one or more terms in which a constant and a variable are separated by an addition or a subtraction sign.

The general form of a polynomial is axn + bxn-1 + cxn-2 + …. + kx + l, where each variable has a constant accompanying it as its coefficient.

Now that you have an understanding on how to use the Remainder Theorem to find the remainder of polynomials without actual division, the next theorem to look at in this article is called the Factor Theorem.

We will study how the Factor Theorem is related to the Remainder Theorem and how to use the theorem to factor and find the roots of a polynomial equation. But, before jumping into this topic, let’s revisit what factors are.

In mathematics, a factor is a number or expression that divides another number or expression to get a whole number with no remainder. In other words, a factor divides another number or expression by leaving zero as a remainder.

For example, 5 is a factor of 30 because, when 30 is divided by 5, the quotient is 6 which a whole number, and the remainder is zero. Consider another case where 30 is divided by 4 to get 7.5. In this case, 4 is not a factor of 30 because, when 30 is divided by 4, we get a number which is not a whole number. 7.5 is the same as saying 7 and a remainder of 0.5.

What is a Factor Theorem?

Consider a polynomial f (x) of degree n ≥ 1. If the term ‘a’ is any real number, then we can state that;

(x – a) is a factor of f (x), if f (a) = 0.

Proof of the Factor Theorem

Given that f (x) is a polynomial being divided by (x – c), if f (c) = 0 then,

⟹ f(x) = (x – c) q(x) + f(c)

⟹ f(x) = (x – c) q(x) + 0

⟹ f(x) = (x – c) q(x)

Hence, (x – c) is a factor of the polynomial f (x).

Hence, the Factor Theorem is a special case of Remainder Theorem, which states that a polynomial f (x) has a factor x – a, if and only if, a is a root i.e. f (a) = 0.

Answer 2

Answer:

sorry about this i am not sure