Answer:
See the explanation of the method and the solution below.
Step-by-step explanation:
(In bold is what you'd write in an answer to a question. The extra writing is the explanation.)
3x^2 - 11x + 10 =
This trinomial is in the form
ax^2 + bx + c.
a = 3; b = -11; c = 10
Step 1. Multiply coefficients ac.
ac = 3(10) = 30
Step 2. Find 2 factors of ac multiply to ac and add to b.
In this case, find two factors of 30 that multiply to 30 and add to -11.
-6 and -5 work since (-6)(-5) = 30 and (-6) + (-5) = -11
-6 and -5
Step 3. Break up the middle term in to a sum using the numbers from step 2.
We will break up -11x into -6x - 5x
Now we have
= 3x^2 - 6x - 5x + 10
Step 4. To factor by grouping, factor out a common factor out of the first two terms and factor out a common factor out of the last two terms.
= 3x(x - 2) - 5(x - 2)
Step 5. Factor out the common binomial.
= (x - 2)(3x - 5)
