Find the factors of 6 x 2-13 x -6-0A- 3 x-12 x-3B- 3 x-22 x-3C- x-22 x-3D- 3 x-2x-3

The correct option is B (3x – 2 ) ( 2x – 3) 6x^2 13x + 6 —– gt;(1) Using the method of splitting the middle term. x term is the sum of two factors and pro ...

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Byju's Answer

Standard VIII

Mathematics

Factorisation by Regrouping Terms

Find the fact...

Question

Find the factors of $6 x^{2} - 13 x + 6 = 0$

$(x - 2) (2 x - 3)$

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$(3 x - 1) (2 x - 3)$

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$(3 x - 2) (x - 3)$

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$(3 x - 2) (2 x - 3)$

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Solution

The correct option is D
$(3 x - 2) (2 x - 3)$

$6 x^{2} - 13 x + 6$ ----->(1)
Using the method of splitting the middle term.
x term is the sum of two factors and product equal to the last term.
Here a = 6,b = -13,and C = 6
a.c = Product of 6 and 6 = 36
Factors of 36 = 2,18
= 3,12
= 4,9
Only the factors 4 and 9 gives 13 ⟶ (4 + 9)
For -13 , both the factors have negative sign. (- 4 - 9 = - 13)
Equation (1) ⇒ $6 x^{2} - 4 x - 9 x + 6$

$\Rightarrow 2 x (3 x - 2) - 3 (3 x - 2)$

$\Rightarrow (3 x - 2) (2 x - 3) a r e t h e f a c t o r s .$

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Find the factors of 6x2−13x+6=0

Find the factors of $6 x^{2} - 13 x + 6 = 0$