Well, well, well, look who's trying to factor a quadratic equation! To factor 2x^2 + 11x + 14, you need to find two numbers that multiply to 28 (2*14) and add up to 11. Those numbers are 2 and 14. So, the factored form is (2x + 7)(x + 2). Voila!
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To factor the quadratic expression 2x^2 - 11x + 14, we need to find two numbers that multiply to the product of the coefficient of the x^2 term (2) and the constant term (14), which is 28, and add up to the coefficient of the x term (-11). The two numbers are -7 and -4. Therefore, we can rewrite the expression as 2x^2 - 7x - 4x + 14. Factoring by grouping, we get 2x(x - 7) - 2(x - 7), which simplifies to (2x - 2)(x - 7) or 2(x - 1)(x - 7).
(2x + 7)(x - 2)
It doesn't factor evenly if it were x**2-11x+10: x**2-11x+10 = (x-1)(x-10)
The "difference of squares" has a formula. (11x + 1)(11x - 1)
(2x2 - 1)(2x2 - 1) or (2x2 - 1)2
x2 -11x-12= (x-12)(x+1)