Question

Choose the binomial or trinomial that is a factor of the given polynomial.
1. 3x^2+4x+1
2. 4x^2+11x+6
3. 2x^2+3x-20
4. 6x^2-5x-6
5. 8x^3-27
Can someone show/help me do these.

Answer 1

1. 3x^2+4x+1 = (3x + ?)(x + ?) = (3x + 1)(x + 1)
we can check this by FOIL = 3x*x + 3x*1 + x*1 + 1*1
= 3x^2 + 3x + x + 1
= 3x^2 + 4x + 1
(doing 2 now :) )

Answer 2

2. 4x^2 + 11x + 6 = (2x + ?)(2x + ?) OR (4x + ?)(x + ?)
the factors of six are 1, 2, 3, 6
Because the coefficient of 2 is on both the x's in the first one and our middle term is odd, we must use the second set of factor options.
(4x + 1)(x + 6) comes out to 4x^2 + 25x + 6
(4x + 6)(x + 1) comes out to 4x^2 + 10x + 6
(4x + 2)(x + 3) comes out to 4x^2 + 14x + 6
(4x + 3)(x + 2) comes out to 4x^2 + 11x + 6, which is what we are looking for, so these factors are our answer.

Answer 3

So for number one my answer choices are (x-1) (2x+1) (3x-1) (3x+1) so would i just choose (3x+1) ?

Answer 4

3. 2x^2 + 3x - 20 = (2x +/- ?)(x +/- ?)
the factors are 1, 20 2,10 4,5 , and one of each set must be negative, because a positive term * a negative term = a negative term
I am going to go straight to the answer this time.
(2x - 5)(x + 4), because 2x*x + -5x + 8x + -20
= 2x^2 + 3x -20

Answer 5

Just choose (3x + 1), if the question is asking for only one factor they won't provide both. :)

Answer 6

4. 6x^2 - 5x - 6 = (6x +/- ?)(x +/- ?) OR (2x +/- ?)(3x +/- ?)
The factors of 6 are still 1,6 and 2,3.
The factors of this polynomial are (2x - 3)(3x + 2)
2x*3x + -9x + 4x + -6
= 6x^2 -5x -6

Answer 7

Thank you, i kinda get it. This kind of stuff is so confusing to me.

Answer 8

5. 8x^3 - 27 = (2x +/- ?)(2x +/- ?)(2x +/- ?)
Honestly, cubic roots are the most difficult roots that you'll regularly see.
The binomial root is 2x-3, because if we cube it, we get 8x-27
(2x*2x*2x + -3*-3*-3 = 8x^3 - 27)
The remaining trinomial root is 4x^2 + 6x + 9 (which can be found by dividing out our binomial root.) If one of these roots is not in your answers, we would have to try factoring out the trinomial root (and if it doesn't factor nicely, using the quadratic equation.)

Answer 9

I really hope I was able to help. :) Factoring is my favorite. Let me know how that last answer turns out!

Answer 10

Thank you so much. That was the correct answer, Can you help me with a few more?

Answer 11

Sure! Send them my way.

Answer 12

6. x^3 + 1/8