help factorise.x squared - x - 110. i am unable to split the middle term?

Answer 1

Roots are x = 11 and x = -10

Thus factorization is (x - 11)(x +10)

Answer 2

This is a guess and check method. Look at all the factors of the first and last terms. For 1 you have 1and 1.For 110, there is 110 and 1, 55 and 2, 22 and 5, 11 and 10. . Use a T table and place the 1x and 1x at the top of each column where you would normally place x and y. Then below each of those you place your guess of the factors of 110, like so:
1x 1x
110 1
55 2
22 5
11 10

Now cross multiply, 1x times 1 = 1x, and 1x times 110 = 110x. 1x and 110x can not get you the -1x you need in the middle by adding or subtracting. So draw line through the 110 and 1 and try the next pair. Hopefully you see quickly the only pair that can work is the 10 and 11, since 10x - 11x will get you the -1x in the middle.
so (x+10)(x-11)...Good Luck!
P.S. This one actually was too easy to even go through all this. You should plug numbers into the binomails and FOIL check if the x^2 coefficient is a 1.....

Answer 3

This is what you have to do to factorize x^2 - x -110.
Look at the three coefficients.
They are
1 is the coefficient for x^2
-1 is the coefficient for x
ans -110 is the coefficient for the unity term.
Now multiply the first and third coefficients.
You get -110.
Find two factors of -110 whose sum is the middle coefficient, that is -1.
The factors are -11 and 10. Because -11 +10 = -1
and -11*10 = -110
Now you can split the middle term into two terms given by these factors, that is -x= -11x +10x
Rewrite the whole thing as
x^2 -11x +10x -110
= (x^2 -11x) +(10x-110)
=x(x-11) +10(x-11)
=(x-11)(x+10)
and you have got the factors.

Answer 4

x² - x - 110 = 0

find the sum of the middle term

Multiply the first term 1 times the last term 110 equals 110 and factor

Factors of 110 = 1, 2, 5, 10, 11, 22, 55 110

- 11 and 10 satisfy the sum of the middle term

insert - 11x and 10 x into the equation

x² - x - 110 = 0

x² - 11x + 10x - 110 = 0

x(x - 11) + 10(x - 11)= 0

(x + 10)(x - 11) = 0

- - - - - - - - - - - - - s-

Answer 5

The middle term is -1 and the factors of -110 are either -11x10 or 11x-10. [I obviously have ignored irrelevant factors]
It's factors of the last term (when a=1) which can add to the middle term that you need to look for.
Obviously, -11x10 makes the last term and -11 + 10 makes the middle term so, it's (x-11)(x+10)

Answer 6

x² - x - 110 = (x - 11).(x + 10)
Check
x.(x + 10) - 11.(x + 10)
= x² + 10.x - 11.x - 110
= x² - x - 110 as required

Answer 7

you need two numbers their product = 110
difference between them = 1 ( because last sign is -ve )
bigger takes middle sign
(x - 11 )(x + 10 )
check -11x +10x = -1x ok
hotp that helpppsss

Answer 8

(x+10)(x-11)
Please give me best answer thanks!