3x2 -16-12 factorization
Answers
3x² - 16x - 12
3x²-18x+2x - 12
3x(x-6) + 2(x-6)
(3x+2)(x-6)
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Factorization - Splitting the middle term
What is factorization?
Factorization is a method used to express any number as a product of it's factors.
To factorize any given expression we can use different methods.
- Identities
- Grouping
- Splitting the middle term
In this sum we have used the 3rd method- Splitting the middle term.
As the name suggests we split the middle term into 2 parts, so that when added gives the middle term and when multiplied gives the product as the last term.
Example : x² + 7x + 12
Factors of 12 = 1,2,3,4,6,12.
Here, 4 + 3 gives me 17 and 4 × 3 = 12
x² + 4x + 3x + 12
x(x+4) + 3(x+4)
[(x+4) is common]
(x+4)(x+3) is the answer. This is when the first term has a numerical coefficient as 1.
In this sum, the first term has 3 as it's numerical coefficient.
In cases such as these, we have to multiply the constant (last term) with the numerical coefficient of the first term.
3 × (-12) = (-36)
As we have seen we have to split the middle term here into 2 parts so that the sum equals to the middle term but the product equals to what we got when we multiplied the constant with the coefficient.
3x² - 16x - 12
16x = (-18x) + 2x
(-18) × 2 = (-36x)
3x² -18x + 2x - 12
3x(x-6) + 2(x-6)
[(x-6) is common]
(x-6)(3x+2)
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Some important points to note :
(-) × (-) = (+)
(+) × (-) = (-)
(+) × (+) = (+)
(-) × (+) = (-)
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