Factor the trinomial: 6x^2 + 7x - 20
Have you no ideas at all on how to do these? Don't just dump your homework here.
To factor the trinomial 6x^2 + 7x - 20, we need to find two binomials that, when multiplied together, equal the trinomial.
To factor the trinomial, we will use a method called "factoring by grouping." Here's how it works:
Step 1: Multiply the coefficient of the leading term (6) by the constant term (-20). In this case, 6 * -20 = -120.
Step 2: Find two numbers whose product is -120 and whose sum is the coefficient of the middle term (7).
The numbers that satisfy these conditions are 15 and -8 (since 15 * -8 = -120 and 15 + (-8) = 7).
Step 3: Rewrite the trinomial using the two numbers found in step 2:
6x^2 + 15x - 8x - 20
Step 4: Group the terms:
(6x^2 + 15x) + (-8x - 20)
Step 5: Factor out the greatest common factor from each group:
3x(2x + 5) - 4(2x + 5)
Step 6: Notice that both groups have a common binomial factor (2x + 5). Factor it out:
(3x - 4)(2x + 5)
Therefore, the factored form of the trinomial 6x^2 + 7x - 20 is (3x - 4)(2x + 5).