Explain how to use grouping to factor each polynomial. 3x^2-5x-12

Question

Explain how to use grouping to factor each polynomial. 3x²-5x-12

Answer 1

3x^2-5x-12

=3x^2 +4x -9x -12

at this point two ways to group

= (3x^2-9x) + (4x-12)

= 3x(x-3) +4(x-3)

=(3x+4)(x-3)

or

= (3x^2+ 4x) + (-9x-12)

= x(3x+4) -3(3x+4)

=(x-3)(3x+4)

Answer 2

Hi, Fazle!

First, we can note that the polynomial here is of the form ax² + bx + c (in our case, a = 3, b = -5, and c = -12). When we use grouping to factor a polynomial of this form, we can use the following process:

Step 1: Multiply a•c

Step 2: Write out the pairs of factors of the product ac

Step 3: Choose a factor pair whose sum is equal to b

Step 4: Split the center term up into two terms with coefficients corresponding to that factor pair

Step 5: Group the first two terms and last two terms together and factor out the GCF of each one

Step 6: Factor out like parenthesis

Ok, so now that we have the steps of our process, we can apply it to this problem:

Step 1: a•c = (3) • (-12) = -36

Step 2: Now we write out the factor pairs of -36:

-36

-1 36

-2 18

-3 12

-4 9

-6 6

-9 4

-12 3

-18 2

-36 1

Step 3: Now we choose one of the factor pairs that we wrote above whose sum is equal to our b, which is -5. Based on this b, we can choose the pair of -9 and 4, since -9 + 4 = -5 = b

Step 4: We rewrite our original polynomial using these factors:

3x² - 5x -12 = 3x² - 9x + 4x -12

Step 5: We group our first two terms and last two terms, then factor out the GCF of each one:

(3x² - 9x) + (4x -12) = 3x(x - 3) + 4(x - 3)

Step 6: Finally, we can factor out our like parenthesis since the terms inside the parenthesis of our two terms match:

3x(x - 3) + 4(x - 3) = (x - 3)(3x + 4)

Thus, we are left with our final answer: 3x² - 5x -12 = (x - 3)(3x + 4)

I hope this explanation was helpful, and please don't hesitate to reach out if you have any further questions!

Answer 3

(3)(-12) = -36

Find two numbers with product -36 and sum -5: The numbers are 4 and -9

Rewrite -5x as 4x - 9x:

3x² - 5x - 12 = 3x² + 4x - 9x - 12 = x(3x + 4) - 3(3x + 4) = (3x + 4)(x - 3)