Question

Factor completely: 4x^2 + 25x + 6

A. (4x + 1)(x + 6)

B.(4x + 6)(x + 1)

C.(2x + 3)(2x + 2)

D.(2x + 6)(2x + 1)

Answer 1

I see.. This is easy once you understand

Answer 2

How would I do the ( x + a) and (x+b)

Answer 3

1) Find the product of numerical coefficients of a and c first.

Answer 4

I mean product of a and c.

Answer 5

How do I do that?

Answer 6

ok..

Answer 7

Um.. I don't know.

Answer 8

a is 4 and c is 6...

Answer 9

How did you get that?

Answer 10

\(\Large \color{Black}{\Rightarrow ax^2 + bx + c }\)
Trinomials are in this form. Remember? compare this with the question

Answer 11

okay so a would be ..4 and c would be 6.

Answer 12

I see. okay now what?

Answer 13

Yes, find their product.

Answer 14

Product..

Answer 15

of 4 ..

Answer 16

2

Answer 17

6 would be 3.

Answer 18

no no.... 4 * 6

Answer 19

24

Answer 20

Ok, now that you have done it, then find two numbers that have the sum as b and the product as the product of a and c.

Answer 21

b = 25 right?

Answer 22

Correct. Find two number such that the sum equals b and the product equals a and c.

Answer 23

So, finding a product of 24.

Answer 24

12 * 2?

Answer 25

Two numbers that have a sum of 25 and their multiplication equals 6 * 4.

Answer 26

I see that the numbers are 24 and 1.

Answer 27

Ah because 24 * 1 = 24 and 24+1 = 25.

Answer 28

Now, just split the middle term like this.

\(\Large \color{Black}{\Rightarrow 4x^2 + 24x + 1x + 6 }\)

Factor first two terms and last two terms.

\(\Large \color{Black}{\Rightarrow 4x(x + 6) + 1(x + 6) }\)

Now just group them.

\(\Large \color{Black}{\Rightarrow (4x + 1)(x + 6)}\)

Answer 29

okay can we try another one?