Question

4x2 + 25x + 6

D.) (2x + 6)(2x + 1)
C.) (2x + 3)(2x + 2)
B.) (4x + 6)(x + 1)
A.) (4x + 1)(x + 6)

Answer 1

find 2 numbers which adds to 25 and multiplied to 4*6=24

Answer 2

I don't understand how to work it at all

Answer 3

You need to find two numbers that when multiplied give you 4. Every option has that.
So the next step is you need to find two numbers that when multiplied and added to another give 25.

Answer 4

but how do I even know what numbers to use???

Answer 5

4*1=4
4*6=24
+1=25
A lot of it is educated guesses, and practice.

Answer 6

So, in conclusion.... (A) is the correct choice.

Answer 7

thanks!

Answer 8

your numbers will be the factors of "6" in this case
that is the factors of the constant
factors of "6" are 3, 2, 1, 6

and the factors of 4
that is the leading term coefficient
factors of 4 are 2, 2, 1, 4

Answer 9

Also, for problems similar to this, you could also FOIL out the possibilities and get your answer.

Answer 10

how do you use FOIL I never understood how

Answer 11

FOIL= First Outer Inner Last

Answer 12

Lets use option D as an example.
(2x + 6)(2x + 1)
You would multiply 2x & 2x to get 4x^2
Then you would multiply the outer terms, 2x & 1 to get 2x
Then the inner terms, 6 & 2x to get 12x
And Last, 6 & 1 to get 6
\[4x^2+2x+12x+6\]
Condense to get
\[4x^2+14x+6\]

Answer 13

o ok that helps thanks!

Answer 14

so, why does A work?
well, let's see
$$
(4x + 1)(x + 6)\\
4x \times x = \color{red}{4x^2}\\
(4x \times 6) + (1 \times x) \implies 24x + x = \color{red}{25x}\\
+1 \times +6 = \color{red}{+6}\\
\color{red}{4x^2+25x+6}
$$

Answer 15

that makes a lot more sense thanks!