Factor x^2 − 11x + 18.?

Question

Please show the steps, I dont know how to factor yet

Answer 1

Factor x^2 - 11x + 18

First: multiply the 1st & 3rd term to get 18. find two numbers that give you 18 when multiplied & (-11) when added/subtracted. the numbers are (-9 & -2). Rewrite the expression with the new middle terms.

x^2 - 9x - 2x + 18

Sec: with 4 terms - group "like" terms & factor both sets of parenthesis.

(x^2 - 2x) - (9x + 18)

x(x - 2) - 9(x - 2)

Third: make sure the inner terms are the same;combine the inner term (once) with the outer term.

(x - 2)(x - 9)

Answer 2

First find the prime numbers which are factors of 18
3, 3, and 2 are the prime factors, because 3*3*2=18.
By trial and error, find the combination of these numbers that add up to -11.
2*3 = 6
6+3=9 no
-2 * 3 = -6
-6 + 3 = -3 no
-2 * 3 = -6
-6 -3 = -9 no
-2 * (-3) = 6 we have already seen that this leads nowhwer

3*3 = 9
9 + 2 = 11 close but no cegar! but that suggests the strategy of making both numbers negative and then adding them!
-9 + (-2) = -11 bingo!
so, (x-2)*(x-9) = x^2 -11x +18

Answer 3

You need factors of 18 that add up to 11. That's 9 times 2.
So your factors are (x - 9)(x - 2)

Answer 4

Step 1: Make two sets of parentheses with x in each one...(x....)(x....) because u know it's gonna have x in both since when u multiply it out it's x^2..

Step 2: Try to find two numbers that multiply to equal eighteen but add up to -11. Figure out your options such as...6(3)=18 but 6+3=9...so 6 and 3 don't work. so try something else like 9(2)=18 and 9+2=11.

Step 3: Find the right signs...u know the 18 is positive but the 11 is negative so if both 9 and 2 are negative...multiplied out they give the positive 18 and added they give the negative 11.

Answer: (x-9)(x-2)

FOIL it out to check...
F-First terms (x)(x)= x^2
O-Outer terms (x)(2)=2x
I-Inner terms (x)(9)=9x (add the 2x to get 11x)
L-Last terms (9)(2)=18

Hope this helped! :)

Answer 5

(x-2)(x-9)

the numbers in the ( )'s are multiples of the second number in the equation (18) and the two numbers also have to equal the middle number in equation when combined (11). as for the signs in the answers, if the second sign in the equation is a +, then both signs in the answer are the same. and since the first sign is a negative (-), both signs in the answer are negative. if it was a +11x then the answer would have been (x+2)(x+9). got it?

Answer 6

(x-2)(x-9);

Let a=coefficient of the 1st term (1)
Let b=coefficient of the 2nd term (-11)
Let c=coefficient of th 3rd term (18)

So, using the quadradic formula,

-b ± the square root of b^2 - 4 (a*c) / 2*a =

(11± sqrt(121 - 4(18)) / 2 =

(11± sqrt(49)) /2 =

(11± 7) /2

So x is either 9 ---- (11+7) / 2

or 2 ---- (11-7) / 2

Answer 7

Try my new factoring calculator at http://www.poodwaddle.com/mathfactor.html
It will teach you all the steps and will give you the answer.

Answer 8

(x-9)(x-2)

-11 = -9 + -2
18 = -9 x -2