x^2 + 5x +4 =?

Question

I'm more interested in how we get the answer that the answer itself.

Answer 1

(x+1)(x+4)

the way i learned it was that u find factors of the first and last numbers (so factor of 1 for x^2 and factors of 4).

factors of 1 are always one so u only need to worry about the factors of 4, which can be 1x4, 2x2, or 4x1.

once u find these factors make a set up like this
1 1
1 4
or
1 2
1 2
or
1 4
1 1

once u have these, cross multiply (1x1, 1x4: 1x2, 1x2: 1x1, 1x4) and then add the results. the sum of these results that equals the middle term, 5, will be the constants that u will use in both sections of the factored result
from the set up above:

1x4=4, 1x1=1
1+4=5

1x2=2, 1x2=2
2+2=4

1x1=1, 1x4=4
1+4=5

in this case u have two sets of numbers that equal 5 so either one will suffice.

Answer 2

Right, I'm assuming you want to factorise this equation?

First you need to know that this is a quadratic, so before it was simplified it was in the form:
(x + _) (x +_)

So to work out the numbers, all you need to do is say to yourself what two numbers multiply to make 4 and add to make 5. The answer is 4 and 1 (4 x 1 = 4 and 4 + 1 = 5)

So it's: (x+4) (x+1)

You can check this by multiplying it out using the FOIL method to see if you get the right answer:

X x X = x^2
X x 1 = x
X x 4 = 4x
1 x 4 = 4

x^2 + 4x + x + 4
= x^2 + 5x + 4

If you need to work out the answer to the quadratic then you need to know that a quadratic always has 4 answers. You've already got two of the answers (4 and 1) but you also need the other two. So using the quadratic we just factorised: (x+4) (x+1) you must equal it to 0

So
(x + 4) = 0
So, x = -4

(x+1) = 0
So, x = -1

Voila!

Answer 3

This is of the form ax^2 + bx + c. For example, x^2 + 2x + 1 can be expressed as (X + 1) (x + 1). Just check that it is correct by reverse multiplication. In the present case, 5 can be taken as 4 + 1 and so we can write,

x^2 + 5x + 4 = (x + 4) (x + 1)

We can check that our answer is correct by multiplying those two factors:

(x + 4) X (x + 1) = x^2 + x + 4x + 4 = x^2 + 5x + 4

Answer 4

(x + 2/3) (x2 + 5x + a million) = 0 the 1st effect is x = -2/3 you will get that by placing the (x2 + 5x + a million) to 0 and transposing the two/3... for the others, set the x + 2/3 to 0 element the (x2 + 5x + a million) making use of the x = [-b +/- sqrt(b2 - 4ac)] / 2a i cant sparkling up it by psychological math via sqrt(21) the effect would be the two xs x = [-5 + sqrt(21)] /2 and x = [-5 - sqrt(21)] /2 Gotchapon?

Answer 5

well you know that 4 can be factored into two forms 2x2 and 4x1. when you use reverse foil you find that the factors 2 and 2 will not give you your desired middle term the 5x. the other factor 4 and 1 will give you five when foiled out.

so (x+1) (x+4) is your answer


hope that helped

Answer 6

you take the x and since it is only 1 you take that and times it by just the last number and get 4
you then have 4, what are all the multiples of 4?
1,4
2,2
-1,-4
-2,-2
the 1,4 you can do 1x and 4 x to get 5x and split it down even farther.

x^2+1x+4x+4, then from there you can bring it down tp
x(x+1)+4(x+1)

or (x+4)(x+1)=0
(x+4)=0
x=-4

x+1=0
x=-1

so your final answer is x=-1,-4

Answer 7

(x + 4) * (x + 1) =

Answer 8

You can either factor (basically, look for the factors of 4, and see which of them will add up to 5), or you can use the quadratic equation (which is harder and more of a mess).

Any time you have to factor

x^2 + bx + c

Look at all of the paired factors of c, and then figure which will add up to b. If c is negative, you have to look for the pair of factors such that one factor minus the other equals b. If you have

ax^2 + bx + c

it's a little more complicated, because you have to look at both the factors of c and the factors of a, and manipulate them such that you end up getting the middle term correct.

Answer 9

look, if you put x=-1 you have the expression =0 so one root is -1, the other is -4

if an equation has a root a , it is divisible by (x-a)

so (x+4) (x+1) is your solution

Answer 10

(X x X) + 5x = - 4