Need help on factoring. HOw exactly would I solve these(big test coming up):
-3x to the second+18x+12
-5x to the second-13x=6
-5x to the second-6x_1
-and xto the second + 6x=10
Thanks.
Note: on the third problem there is a typo. I meant 5x to the second-6x+1, and the dashes on all of the problems at begin, are not negatives.
Use the quadratic equation on each of them.
To solve these factoring problems, you'll need to follow a step-by-step process. Let's go through each problem individually:
Problem 1: -3x^2 + 18x + 12
Step 1: Look for the greatest common factor (GCF) among the three terms. In this case, the GCF is 3, so we can factor it out:
-3(x^2 - 6x - 4)
Step 2: We are left with a quadratic trinomial inside the parentheses. Now we need to find two binomial factors whose product equals the trinomial. The factors also need to have a sum equal to the coefficient of the middle term (-6x). In this case, the binomial factors are:
(x - 2) and (x - 2)
Step 3: Combine the GCF and the binomial factors to get the final factored form:
-3(x - 2)(x - 2)
Problem 2: -5x^2 - 13x + 6
Step 1: Look for the GCF among the three terms, which is 1 in this case. Since it's negative, we can include it in the factoring:
-5x^2 - 13x + 6 = -(5x^2 + 13x - 6)
Step 2: Similar to Problem 1, we need to find two binomial factors whose product equals the quadratic trinomial. The factors also need to have a sum equal to the coefficient of the middle term (13x). In this case, the binomial factors are:
(5x - 1) and (x + 6)
Step 3: Combine the GCF and the binomial factors (with the negative sign):
-(5x - 1)(x + 6)
Problem 3: -5x^2 - 6x - 1
Step 1: No common factor can be factored out here.
Step 2: Again, we need to find two binomial factors whose product equals the quadratic trinomial. The factors also need to have a sum equal to the coefficient of the middle term (-6x). Unfortunately, -1 cannot be factored, so we can't factor this quadratic trinomial.
Problem 4: x^2 + 6x - 10
Step 1: No common factor to factor out.
Step 2: Find two binomial factors whose product equals the quadratic trinomial. The factors also need to have a sum equal to the coefficient of the middle term (6x). Though this trinomial can't be factored nicely, it can be factored using the quadratic formula or completing the square method.
Final note: Sometimes, quadratic trinomials cannot be factored algebraically, and in those cases, you would use methods like the quadratic formula or completing the square.