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Factorization of a Quadratic Trinomial

Middle term b...

Question

Middle term break

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Solution

Quadratic factorization using splitting of middle term : In this method splitting of middle term in to two factors.

In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term.

To Factor the form :ax² + bx + c Factor : 6x² + 19x + 10

1) Find the product of 1st and last term( a x c). 6 x 10 = 60

2) Find the factors of 60 in such way that
addition or subtraction of that factors is
the middle term (19x)(Splitting of middle term) 15 x 4 = 60
and 15 + 4 = 19

3) Write the center term using the sum of the
two new factors, including the proper signs. 6x² + 15x + 4x + 10

4) Group the terms to form pairs - the first two
terms and the last two terms. Factor each pair by finding common factors. 3x ( 2x + 5)+ 2(2x + 5)

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

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Factorize by splitting the middle term:

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To Factor the form :ax² + bx + c	Factor : 6x² + 19x + 10
1) Find the product of 1st and last term( a x c).	6 x 10 = 60
2) Find the factors of 60 in such way that addition or subtraction of that factors is the middle term (19x)(Splitting of middle term)	15 x 4 = 60 and 15 + 4 = 19
3) Write the center term using the sum of the two new factors, including the proper signs.	6x² + 15x + 4x + 10
4) Group the terms to form pairs - the first two terms and the last two terms. Factor each pair by finding common factors.	3x ( 2x + 5)+ 2(2x + 5)
5) Factor out the shared (common) binomial parenthesis.	(3x + 2) ( 2x + 5)