Question

Which of the following is the correct factored form of the given equation? 4x 2 - 11x + 6 = 0
2x + 3)(2x + 2) = 0
(2x - 3)(2x - 2) = 0
(4x - 3)(x - 2) = 0

Answer 1

(4x-3)(x-2)=0 is the correct answer

Answer 2

The correct factored form of the given equation 4x^2 - 11x + 6 = 0 is (4x - 3)(x - 2) = 0

Solution:

Given equation is:

$4x^2 - 11x + 6 = 0$

We have to find the factored form of the equation

From given,

$4x^2 - 11x + 6 = 0 \\\\Split\ the\ middle\ term\\\\4x^2 - 3x - 8x + 6 = 0 \\\\\mathrm{Break\:the\:expression\:into\:groups} \\\\\left(4x^2-3x\right)+\left(-8x+6\right) = 0\\\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}4x^2-3x\mathrm{:\quad } \\\\x(4x - 3) + (-8x + 6) = 0 \\\\\mathrm{Factor\:out\:}-2\mathrm{\:from\:}-8x+6\mathrm{:\quad }\\\\x\left(4x-3\right)-2\left(4x-3\right) = 0 \\\\\mathrm{Factor\:out\:common\:term\:}4x-3\\\\\left(4x-3\right)\left(x-2\right) = 0$

Thus the factored form is found

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