Question

I don't know how to do this equation..
(5x^2 + x – 4)(x + 2)

Answer 1

Make the factors of first parenthesis..
See tell me the two numbers with sum = 1 and product = -20??

Answer 2

I don't know how to do that.

Answer 3

See, try with 4 and 5..
we need -20..

in what way I multiply 4 and 5 to get -20?

Answer 4

Negative + positive?

Answer 5

Which one should be negative and which one should be positive?

Answer 6

It doesn't matter. Either one works.. (-4)(5)=-20 and (-5)(4)=-20

Answer 7

But if I say that their sum should be 1 then which sign you will apply to which?

Answer 8

I don't know.

Answer 9

See,
you told we can take -4 and 5 or -5 and 4

just add them to get 1.

which will it adds up to 1?

-5 + 4

Or,

-4 + 5

??

Answer 10

-4+5

Answer 11

Yes now you got it..

or if I multiply x to both -4 and 5 what you get??

x(-4 + 5)

distribute x inside..

Answer 12

-4x+5x

Answer 13

Yes so you agree?

1x = (-4 + 5)x ??

Answer 14

Yes.

Answer 15

Now tell me the expression in first parenthesis?

Answer 16

Um.. what expression?

Answer 17

See in the question what is the expression in first bracket?

it is quadratic for which we are solving for..

Answer 18

5x^2 ?

Answer 19

tell me the whole..

Answer 20

5x^2 + x - 4

Answer 21

Yes..
now I make you agree that 1x = (5 - 4)x

Yes or not?

Answer 22

Is x = (5-4)x

right??

Answer 23

Yes?

Answer 24

Then replace the middle term of the expression:
5x^2 + x - 20


Here you can replace middle term x with (5-4)x

can you do it?

Answer 25

5x^2 + (5-4) - 20

But how did you replace the - 4 with the 20?

Answer 26

no no..

See we are to replace middle term only using the two numbers we got..

See:

\[5x^2 + x -20 = 5x^2 + 5x - 4x -20\]

This step are you getting??
I just repace x by (5-4)x and then distribute x to get 5x - 4x

Getting or not?

Answer 27

Yes, I understand.

Answer 28

Now take common that can you take out..

Answer 29

See:
from:
\[5x^2 + 5x\]

What can be taken out of it as common?

Answer 30

The 5x?

Answer 31

Yes..

so you have:

\[5x(x + 1) -4x - 20\]

Now from the next part what can be taken out?

Answer 32

How did you get 5x(x+1)-4-20 ?

Answer 33

After taking 5x as common tell me what you are left with?