6x^2+21x-45
ac method.
-45*6=270.
Factors are 30 and 9.
6x^2+30x-9x-45
6x(x+5)-9(x+5)
(6x-9)(x+5)
To simplify the expression 6x^2 + 21x - 45, we can look for common factors and then apply techniques of factoring.
First, we'll check if there is a common factor among the coefficients 6, 21, and -45. In this case, the greatest common factor (GCF) is 3.
Dividing each term by 3 yields:
(6x^2 + 21x - 45)/3 = 2x^2 + 7x - 15
Now we can attempt to factor the quadratic expression 2x^2 + 7x - 15 by splitting the middle term.
We need to find two numbers that multiply to give -30 (product of the coefficient of x^2, which is 2, and the constant term, which is -15), and add up to give 7 (the coefficient of the middle term).
Let's try different pairs of numbers that satisfy these conditions.
Factors of -30: (-1, 30), (1, -30), (-2, 15), (2, -15), (-3, 10), (3, -10), (-5, 6), (5, -6)
Out of these pairs, (-5, 6) satisfies both requirements.
Splitting the middle term, we rewrite the expression as follows:
2x^2 - 5x + 6x - 15
Next, we group the terms:
(2x^2 - 5x) + (6x - 15)
Now, we factor out the greatest common factor from the two groups:
x(2x - 5) + 3(2x - 5)
Notice that we have a common binomial factor, (2x - 5), which can be factored out:
(2x - 5)(x + 3)
Therefore, the expression 6x^2 + 21x - 45 can be factored as (2x - 5)(x + 3).