Factorization
If a polynomial can be written as the product of two or more expressions, then each expression is called the factor of the given polynomial.If a polynomial can be written as the product of two or more expressions, then each expression is called the factor of the given polynomi..
Type (ii) By expressing the polynomial as the difference of two squares
121x 2 - 25y 2 = (11x) 2 - (5y) 2 = (11x + 5y) (11x - 5y) [Using the identity a 2 -b 2 =(a-b)(a+b)] Factorise: (5a + 6b) 2 - 49b 2 Let x = 5a + 6b Then the given expression = (x) 2 - (7b) 2 = (x + 7b) (x - 7b) Re-substituting the value of x, we get = [(5a + 6b + 7b)] [(5a + 6b) - 7b]..
121x 2 - 25y 2 = (11x) 2 - (5y) 2 = (11x + 5y) (11x - 5y) [Using the identity a 2 -b 2 =(a-b)(a+b)] Factorise: (5a + 6b) 2 - 49b 2 Let x = 5a + 6b Then the given expression = (x) 2 - (7b) 2 = (x + 7b) (x - 7b) Re-substituting the value of x, we get = [(5a + 6b + 7b)] [(5a + 6b) - 7b]..Factorising Trinomials
When the coefficient of the highest power is 1. i.e., ax 2 bx c, when a = 1 and b and c are integers. When two binomials are multiplied the product is a trinomial. Thus (x + 4) (x + 5) = x 2 + 9x + 20 (1) (x - 4) (x - 5) = x 2 - 9x + 20 (2) In this chapter we try to express a trinomia..
When the coefficient of the highest power is 1. i.e., ax 2 bx c, when a = 1 and b and c are integers. When two binomials are multiplied the product is a trinomial. Thus (x + 4) (x + 5) = x 2 + 9x + 20 (1) (x - 4) (x - 5) = x 2 - 9x + 20 (2) In this chapter we try to express a trinomia..Second Method:
x 2 - 7x - 8x + 56 Write -15x as -7x and -8x = x (x - 7) - 8 (x - 7) = (x - 7) (x - 8) Now, we consider a case where the third term of the trinomial is negative. Resolve into factors: x 2 + 3x - 28 Since the third term of the trinomial is -28, find two factors of 28 which differ by 3. The gr..
x 2 - 7x - 8x + 56 Write -15x as -7x and -8x = x (x - 7) - 8 (x - 7) = (x - 7) (x - 8) Now, we consider a case where the third term of the trinomial is negative. Resolve into factors: x 2 + 3x - 28 Since the third term of the trinomial is -28, find two factors of 28 which differ by 3. The gr..Factorising a3
b3
The product of a + b and a 2 - ab + b 2 is a 3 + b 3 . Hence when a 3 + b 3 is factorised, we get: a 3 + b 3 = (a + b) (a 2 - ab + b 2 ) Similarly, a 3 - b 3 = (a - b) (a 2 + ab + b 2 ) Factorise: x 3 + 8 x 3 + 8 = (x) 3 + (2) 3 = (x + 2) (x 2 - 2x + 4) Factorise 64x 3 - 125. ..
b3 The product of a + b and a 2 - ab + b 2 is a 3 + b 3 . Hence when a 3 + b 3 is factorised, we get: a 3 + b 3 = (a + b) (a 2 - ab + b 2 ) Similarly, a 3 - b 3 = (a - b) (a 2 + ab + b 2 ) Factorise: x 3 + 8 x 3 + 8 = (x) 3 + (2) 3 = (x + 2) (x 2 - 2x + 4) Factorise 64x 3 - 125. ..Summary
In a given sentence, the variables are replaced by letters and the different operations are replaced by their mathematical symbols. We now arrive at a formula. In a given sentence, the variables are replaced by letters and the different operations are replaced by their mathematical symbols. We n..
Formula
A formula is formed by using: (a) mathematical symbols and variables (b) given conditions, and (c) simplificatio..
Summary
In a given sentence, the variables are replaced by letters and the different operations are replaced by their mathematical symbols. We now arrive at a formula. ..
Representation of a Function
A function can be represented by the following methods:A function can be represented by the following metho..
See what our Users say :
i really understood it and this teachers left me amazed and opened my eyes to the real world of math! Thanks a lot ,i mean it - Alina
This is my favorite tutoring ever. i might say that to others to, but this tutoring has thought me the most from any tutorings!! -Ashlyn
It is a really good tutoring. The tutors are thoughtful, helpful, active to help students. A lot of ideas they have. Encouraging students too. -Riley
She should be the head of Tutor Vista. She knows how to treat her students. Her teaching style is spectacular.
Looking for More Help!
