Question

Factor completely: 3x^2 + 5x + 1

Answer 1

Can it be factored?

Answer 2

I don't think so because there aren't any like terms?

Answer 3

This one doesn't factor, as far as I can tell. Using the ac method, there are no factorizations of three that add to five.

Answer 4

\[\huge{x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}\]
\[\huge{x = \frac{-5\pm\sqrt{25-12}}{2(3)}}\]
\[\huge{x=\frac{-5\pm\sqrt{13}}{6}}\]
the solutions are :

\[\Huge{x_1=\frac{-5+\sqrt{13}}{6}}\]
\[\Huge{x_2=\frac{-5-\sqrt{13}}{6}}\]

Answer 5

wait

Answer 6

Not exactly a factorization yet...

Answer 7

wait

Answer 8

Wait, so it would be prime right?

Answer 9

this means that :

\[\Huge{x-(\frac{-5+\sqrt{13}}{6})}\]
\[\Huge{x-(\frac{-5-\sqrt{13}}{6})}\]

Answer 10

these are the factors

Answer 11

Do y'all need the answer choices?

Answer 12

That would help.

Answer 13

It could be shown as\[(x-x_1)(x-x_2)=3x^2+5x+1\]With x_1 and x_2 as above.

Answer 14

It might be considered prime with respect to the integers or rationals, since the roots are irrational.

Answer 15

A. (3x + 1)(x + 1)
B. (3x + 5)(x + 1)
C. (3x − 5)(x + 1)
D. Prime

Answer 16

Prime

Answer 17

D is the only answer of those that makes sense.

Answer 18

Yup D :).

Answer 19

Thank you!

Answer 20

You're welcome!