What is the expression in factored in factored form?
2x^2 = 10x + 12
To express the expression 2x^2 = 10x + 12 in factored form, we need to rewrite it as an equation set equal to zero.
2x^2 - 10x - 12 = 0
To factor this quadratic equation, we need to find two numbers that multiply to give -24 (the product of the leading coefficient and the constant term) and add up to -10 (the coefficient of the x term).
The numbers that satisfy these conditions are -12 and +2:
2x^2 - 12x + 2x - 12 = 0
Now, we can factor the equation by grouping:
2x(x - 6) + 2(x - 6) = 0
Notice that we have a common factor of (x - 6) in both terms, so we can factor that out:
(2x + 2)(x - 6) = 0
Therefore, the expression 2x^2 = 10x + 12 in factored form is (2x + 2)(x - 6) = 0.