i have trouble factoring this equation any time x^2 has a number before it i get confused and don't know how to factor
how would you solve this
-3x^2+5x-2
Find two factors for each end term (3,-1 or -3,1) and (2,-1 or -2,1).
Figure how they could be summed to get the middle term.
However, I could not do this. Do you have a typo?
3x^2 + 5x - 2 = (3x-1)(x+2)
To factor a quadratic equation like -3x^2+5x-2, you can follow these steps:
Step 1: Write down the equation in the form of ax^2 + bx + c = 0. In this case, the given equation is already in that form.
Step 2: Find the factors of the coefficient 'a' (the number in front of x^2), which is -3 in this case. The factors of -3 are -1 and 3.
Step 3: Break down the middle term (bx) into two terms whose coefficients multiply to give 'ac' (product of 'a' and 'c') and add up to 'b'. In this case, 'a' is -3, 'b' is 5, and 'c' is -2.
-1 * 3 = -3 (product of 'a' and 'c')
-1 + 3 = 2 (middle term 'b')
Step 4: Now, rewrite the given equation by splitting the middle term using the factors from Step 3:
-3x^2 - x + 3x - 2
Step 5: Group the terms and factor them separately:
(-3x^2 - x) + (3x - 2)
Step 6: Factor out the greatest common factor (GCF) from each group:
-x(3x + 1) + 1(3x - 2)
Step 7: Simplify the equation:
-(3x + 1)(x - 2)
Therefore, the factored form of the given equation -3x^2+5x-2 is -(3x + 1)(x - 2).