Factoring polynomials

Question

Factor this polynomial using the T method

Polynomial is 3x² + 3x - 6

Answer 1

There are several methods you can use to solve this problem. Below are two potential ways you can use the t-method to solve this problem.

You can factor out the 3 and simplify while incorporating the t-method.

3x²+3x-6

3(x²+1x-2)

Looking only at the trinomial in the parentheses, you can factor using the t-method.

Standard Form: ax²+ (p+q)x + (pq)

[You may have also been taught ax²+bx+c where the 2 multiples of c must add up to b]

x²+1x-2

[Visualize this as a t-chart] Factors of -2: (-1 x 2) (-2 x 1)

We can then check to see which factors equal b or (p+q). In this case, we are looking for the two numbers that add up to equal +1.

-1 + 2 = 1

-2 + 1 = -1

Therefore, we simplify x²+1x-2 into (x-1)(x+2)

Don't forget to put the factored out 3 in front of the final answer.

Final answer: 3(x-1)(x+2)

If the a value is not a multiple of 3, you can use the expanded steps below. But always check to see if you can factor out the a value before factoring.

Standard Form: ax²+ bx + c [Again, c= (pq), b= (p+q)

3x²+3x-6

1) Find the factors of a x c in your t-chart

ac = -18 or pq = -18

Factors of -18: (-1 x 18) (-2 x 9) (-3 x 6) (-6 x 3) (-9 x 2) (-18 x 1)

2) Determine which factors add up to our b value or +3 [p + q = +3]

(-1 + 18 = 17) (-2 + 9 = 7) (-3 + 6 = 3) (-6 + 3 = -3) (-9 + 2 = -7) (-18 + 1 = -17)

3) Place those factors in the equation. Remember, our new expanded form is ax² +px + qx + c

3x²-3x+6x-6

4) Break the equation into two parts, the first 2 terms and the last 2 terms

(3x²-3x)+(6x-6)

4) Find the GCF of each set of parentheses and factor out.

3x(x-1)+6(x-1)

4) This gives us a more simplified form of the polynomial, but we are not fully factored down.Factor out the 3 from the first equation and you are finished.

(3x+6)(x-1)

3(x+2)(x-1)

Answer 2

3(x^2+x-2) = 3( x + 2 )( x - 1 )