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Can someone help me with some factor by grouping and please show step by step

problem: 3x^2-11x+10

1 Answer

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Answer:

See the explanation of the method and the solution below.

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)

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