I really need the answers to these few questions I just can't figure these out pls help!!
Find the solutions to each quadratic trinomial by factoring.
5) x2 + 4x - 12 =0
6) x2 - 8x + 15 =0
7) x2 + x - 72 =0
8) x2 - 4x + 4 = 0
9) 2x2 + 6x - 8= 0 (HINT: factor the GCF first!)
Do you mean
2x or 2^2?
2 times x or 2 to the 2nd power?
Online "^" is used to indicate an exponent, e.g., x^2 = x squared.
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
However, I will do one for you. Factor the -12. It can give you 2*6 or 3*4. However, to get the 4 and the -12, you would need 6 and -2.
Therefore, x2 + 4x - 12 =0 leads to (x-2)(x+6).
I hope this helps.
5. x^2 + 4x - 12 = 0.
-12 = -1*12 = -2*6.
Select the pair of factors whose sum equals B:
-2 + 6 = 4 = B.
(x-2)(x+6) = 0.
x-2 = 0, X = 2.
x + 6 = 0, X = -6.
Solution: X = 2, and -6.
6. x^2 - 8x + 15 = 0.
15 = (-1)*(-15) = (-3)*(-5). Choose (-3) and (-5) because their sum = B.
(x-3)(x-5) = 0.
x-3 = 0, X = 3.
x-5 = 0, X = 5.
Solutions: = X = 3, and 5.
Sure, I can help you with these quadratic trinomial problems. To find the solutions to each equation by factoring, we need to factorize the quadratic trinomials and set each factor equal to zero.
Let's go step by step.
5) x^2 + 4x - 12 = 0:
To factorize this quadratic trinomial, we need to find two numbers that multiply to give -12 and add up to 4. The numbers are 6 and -2. Hence, the factored form is:
(x + 6)(x - 2) = 0
Setting each factor equal to zero:
x + 6 = 0 or x - 2 = 0
Solving these equations gives the solutions:
x = -6 or x = 2
6) x^2 - 8x + 15 = 0:
To factorize this quadratic trinomial, we need to find two numbers that multiply to give 15 and add up to -8. The numbers are -3 and -5. Hence, the factored form is:
(x - 3)(x - 5) = 0
Setting each factor equal to zero:
x - 3 = 0 or x - 5 = 0
Solving these equations gives the solutions:
x = 3 or x = 5
7) x^2 + x - 72 = 0:
To factorize this quadratic trinomial, we need to find two numbers that multiply to give -72 and add up to 1. The numbers are -8 and 9. Hence, the factored form is:
(x - 8)(x + 9) = 0
Setting each factor equal to zero:
x - 8 = 0 or x + 9 = 0
Solving these equations gives the solutions:
x = 8 or x = -9
8) x^2 - 4x + 4 = 0:
This quadratic trinomial is a perfect square trinomial. It can be factored as a square of a binomial:
(x - 2)^2 = 0
Setting the perfect square trinomial equal to zero:
x - 2 = 0
Solving this equation gives the solution:
x = 2
9) 2x^2 + 6x - 8 = 0:
To factorize this quadratic trinomial, we need to find the greatest common factor (GCF). In this case, the GCF is 2. Factoring out the GCF, we get:
2(x^2 + 3x - 4) = 0
Now, we can proceed to factorize the quadratic trinomial inside the parentheses. We need to find two numbers that multiply to give -4 and add up to 3. The numbers are 4 and -1. Hence, the factored form is:
2(x + 4)(x - 1) = 0
Setting each factor equal to zero:
2(x + 4) = 0 or 2(x - 1) = 0
Solving these equations gives the solutions:
x = -4/2 or x = 1/2
Simplifying them, the solutions are:
x = -2 or x = 1/2
I hope this helps you understand how to factorize and solve these quadratic trinomials. If you have any further questions, feel free to ask!