Factor (2x^2-13x+7)-(1-12x)

Problem

(2*x2−13*x+7)−(1−12*x)

Solution

1. Distribute the negative sign into the second set of parentheses to remove them.

2*x2−13*x+7−1+12*x

2. Combine like terms by grouping the x terms and the constant terms.

2*x2+(−13*x+12*x)+(7−1)

3. Simplify the expression to obtain a standard quadratic trinomial.

2*x2−x+6

4. Check for factorability by calculating the discriminant b2−4*a*c or looking for two numbers that multiply to 12 (2×6 and add to −1

(−1)2−4*(2)*(6)=1−48=−47

5. Conclude that since the discriminant is negative and there are no two integers that satisfy the conditions, the quadratic cannot be factored over the set of real numbers using rational coefficients.

Final Answer

(2*x2−13*x+7)−(1−12*x)=2*x2−x+6

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