How do you factor -2x^2+x+15=0? I know it should be (2x ) (x ) but I cannot find two other factors which will yield 15 AND x. 5 and 3 doesn't work and neither does 15 and 1. Could you explain what could?
To factor the quadratic equation -2x^2 + x + 15 = 0, we need to find two binomials that when multiplied together, give us the original quadratic expression.
First, let's work on finding the factors. The factors of the coefficient of x^2 (-2) are -2 and 1, while the factors of the constant term (15) are 1 and 15, -1, and -15.
To find the combination of factors that will yield the coefficient of x (1), we need to identify the pair that sums up to 1. In this case, the pair is -2 and -1.
So, we can write the equation using the -2 and -1 factors as follows:
-2x^2 - 2x - x + 15 = 0.
Now, we can group the terms in pairs:
(-2x^2 - 2x) + (-x + 15) = 0.
Next, we use distributive property to factor out common terms from each pair:
-2x(x + 1) - 1(x + 15) = 0.
Now, we can factor out the common binomial (x + 1) from both terms:
(x + 1)(-2x - 1) = 0.
So, the factored form of the quadratic equation -2x^2 + x + 15 = 0 is:
(x + 1)(-2x - 1) = 0.