Factorize the following trinomial by middle term spilt.
7x-6-2X^2
pls help to solve
I find it helps to have the highest powers first:
-2x^2+7x-6
-(2x^2-7x+6)
-(2x-3)(x-2)
To factorize the trinomial 7x - 6 - 2x^2 using the middle term split method, we need to rewrite the expression as two separate binomials.
Step 1: Rearrange the trinomial in descending order of the powers of x:
-2x^2 + 7x - 6
Step 2: Multiply the coefficient of the quadratic term (-2) with the constant term (-6):
-2 * -6 = 12
Step 3: Find two numbers whose product is equal to the result from Step 2 (12) and whose sum is equal to the coefficient of the linear term (7). In this case, the two numbers are 4 and 3:
4 * 3 = 12
4 + 3 = 7
Step 4: Rewrite the linear term (7x) as the sum of the two numbers found in Step 3:
-2x^2 + 4x + 3x - 6
Step 5: Group the terms and factor by grouping:
(-2x^2 + 4x) + (3x - 6)
2x(-x + 2) + 3(x - 2)
Step 6: Factor out the common terms from each group:
2x * (-1)(x - 2) + 3(x - 2)
Step 7: Combine the two groups and the common factor:
(2x - 1)(x - 2)
The factorization of the trinomial 7x - 6 - 2x^2 using the middle term split method is (2x - 1)(x - 2).