Factor Theorem Factorization Class 10 ICSE Maths Revision Notes Chapter 7 PDF

Hi students, Welcome to Amans Maths Blogs (AMB). In this article, you will get Factor Theorem Factorization ICSE Class 10 Maths Revision Notes & Solutions Chapter 7 PDF.

Factor Theorem Factorization ICSE Class 10 Math Revision Notes

Rational Integral Function

A polynomial in x, in which no term contains power of x, or a negative power of x, is called Rational Integral Function of x. It is denoted by f(x), F(x) or p(x) etc.

Example: p(x) = 3x⁴ – 5x³ + 2x + 1

Value of Function

The value of function f(x) at x = a is denoted by f(a) and its value can be obtained by putting x = a in the function f(x). 

Example: The value of p(x) = 3x⁴ – 5x³ + 2x + 1 at x = 2 is p(2) = 3(2)⁴ – 5(2)³ + 2(2) + 1 = 48 – 40 + 4 + 1 = 13 

Remainder Theorem

Let f(x) be any rational integral function of x or polynomial of degree greater than or equal to 1 and ‘a’ be any real number. If f(x) is divided by (x – a), then the remainder is always equal to f(a).

Note 1: If f(x) is divided by (x + a), then the remainder is f(-a).

Note 2: If f(x) is divided by (ax – b), then the remainder is f(b/a).

Note 3: If f(x) is divided by (ax + b), then the remainder is f(-b/a).

Factor Theorem

If f(x) be a polynomial of degree greater than or equal to 1 and ‘a’ be any real number such that f(a) = 0, then (x – a) is factor of f(x).

Hence, we can say that if (x – a) is factor of f(x), then f(a) = 0.

Note 1: If f(-a) = 0, then (x + a) is factor of f(x).

Note 2: If f(-a/b) = 0, then (bx + a) is factor of f(x).

Note 3: If f(a) = 0 and f(b) = 0, then (x – a)(x – b) is factor of f(x).

This is all about Factor Theorem Factorization Class 10 ICSE Maths Revision Notes.

Now get the solutions of this chapter by clicking the links below.

Join Telegram to get PDF