x²-x+110. Factorise it please it is urgent
Answers
Answer:
Factoring x2-x-110
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -110
Step-1 : Multiply the coefficient of the first term by the constant 1 • -110 = -110
Step-2 : Find two factors of -110 whose sum equals the coefficient of the middle term, which is -1 .
-110 + 1 = -109
-55 + 2 = -53
-22 + 5 = -17
-11 + 10 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -11 and 10
x2 - 11x + 10x - 110
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-11)
Add up the last 2 terms, pulling out common factors :
10 • (x-11)
Step-5 : Add up the four terms of step 4 :
(x+10) • (x-11)
Which is the desired factorization
Simplifying
x2 + x + -110 = 0
Reorder the terms:
-110 + x + x2 = 0
Solving
-110 + x + x2 = 0
Solving for variable 'x'.
Factor a trinomial.
(-11 + -1x)(10 + -1x) = 0
Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:
Simplifying
-11 + -1x = 0
Solving
-11 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11
Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11
Combine like terms: 0 + 11 = 11
-1x = 11
Divide each side by '-1'.
x = -11
Simplifying
x = -11
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:
Simplifying
10 + -1x = 0
Solving
10 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10
Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10
Combine like terms: 0 + -10 = -10
-1x = -10
Divide each side by '-1'.
x = 10
Simplifying
x = 10
Solution
x = {-11, 10}
Answer:
So, x² -21x+110=(x−10)(x−11)
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