Middle Term Break

By Ritesh|Updated : November 15th, 2022

Dividing the middle word into two factors is used in quadratic factorization in this method. In a quadratic factorization employing splitting of the middle term, where x is the product of two factors and the last term is the sum of the two factors:

To Factor the form: ax2 + bx + c

Factor: 6x2 + 19x + 10

Step 1) Identify the first- and last-product. term's ( a x c). 6 x 10 = 60

Step 2) Calculate the factors of 60 in which15 x 4 = 60

subtraction or addition of that factors gives 15 + 4 = 19

the middle term (19x)

Step 3) With the help of the sum of the6x2 + 15x + 4x + 10

two new factors, write the center term

with the proper signs.

Step 4) to form pairs group the terms - the first two3x (2x + 5) + 2 (2x + 5)

terms and the last two terms. Factor each pair

by finding common factors.

Step 5) Factor out the shared (common) binomial (3x + 2) (2x + 5)

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Factorisation in Maths

Factoring an algebraic expression means writing a given expression as the product of its factors. These factors can be numbers, variables, or algebraic expressions. For coefficients, number means dividing into numbers that can be multiplied together to get the original number.

Factorisation in Algebra:

1, 2, 6, and 12 are all divisors of 12 because they divide 12 evenly. This is an important algebraic process, used to simplify expressions, simplify fractions, and solve equations. Also called algebraic factorization.

Methods of factorisation:

There are four methods to factorise algebraic expressions.

Common factors method
Regrouping terms method
Factorisation using identities
Factors of the form (x+a) (x+b)

Summary: