Factoring Trinomials
9x^2 + 6x +8
this does not factor. The discriminant is negative.
b^2-4ac = 36-4*9*8 = -252
The quadratic has two complex roots.
To factor the trinomial 9x^2 + 6x + 8, we need to find two binomials that, when multiplied together, give us the original trinomial.
One approach is to use the factoring-by-grouping method. Here's how to do it:
Step 1: Multiply the coefficient of the x^2 term (9) by the constant term (8). In this case, 9 * 8 = 72.
Step 2: Find two numbers that multiply to give 72 and add up to the coefficient of the x term (6). In this case, the numbers are 2 and 36. (2 * 36 = 72) and (2 + 36 = 38).
Step 3: Rewrite the middle term (6x) using the two numbers found in the previous step. Split the middle term as 2x + 36x.
Now, we can factor by grouping:
9x^2 + 2x + 36x + 8
Step 4: Group the terms:
(9x^2 + 2x) + (36x + 8)
Step 5: Factor out the greatest common factor from each group:
x(9x + 2) + 4(9x + 2)
Step 6: Notice that (9x + 2) is a common factor in both groups. Factor it out:
(9x + 2)(x + 4)
Therefore, the factored form of the trinomial 9x^2 + 6x + 8 is (9x + 2)(x + 4).