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Question

Resolve each of the following quadratic trinomial into factor:
7x − 6 − 2x2

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Solution

The given expression is 7x-6-2x2. (Coefficient of x2=-2, coefficient of x=7 and constant term=-6)We will split the coefficient of x into two parts such that their sum is 7 and their product equals the product of the coefficient of x2 and the constant term, i.e., (-2)×(-6)=12.Now, 4+3=7 and 4×3=12Replacing the middle term 7x by 4x+3x, we have:7x-6-2x2=-2x2+4x+3x-6 =(-2x2+4x)+(3x-6) =2x(2-x)-3(2-x) =(2x-3)(2-x)

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