X2 - 22x + 117 ÷ x- 13
Answers
Answer:
HI...
Step-by-step explanation:
(x - 9) • (x - 13)
x2-22x+117/x-13
Final result :
x3 - 22x2 - 13x + 117
—————————————————————
x
Step by step solution :
Step 1 :
117
Simplify ———
x
Equation at the end of step 1 :
117
(((x2) - 22x) + ———) - 13
x
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a fraction to a whole
Rewrite the whole as a fraction using x as the denominator :
x2 - 22x (x2 - 22x) • x
x2 - 22x = ———————— = ——————————————
1 x
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
x2 - 22x = x • (x - 22)
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x • (x-22) • x + 117 x3 - 22x2 + 117
———————————————————— = ———————————————
x x
Equation at the end of step 3 :
(x3 - 22x2 + 117)
————————————————— - 13
x
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x as the denominator :
13 13 • x
13 = —— = ——————
1 x
Polynomial Roots Calculator :
4.2 Find roots (zeroes) of : F(x) = x3 - 22x2 + 117
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 117.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3 ,9 ,13 ,39 ,117
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 94.00
-3 1 -3.00 -108.00
-9 1 -9.00 -2394.00
-13 1 -13.00 -5798.00
-39 1 -39.00 -92664.00
-117 1 -117.00 -1902654.00
1 1 1.00 96.00
3 1 3.00 -54.00
9 1 9.00 -936.00
13 1 13.00 -1404.00
39 1 39.00 25974.00
117 1 117.00 1300572.00
Polynomial Roots Calculator found no rational roots
Adding fractions that have a common denominator :
4.3 Adding up the two equivalent fractions
(x3-22x2+117) - (13 • x) x3 - 22x2 - 13x + 117
———————————————————————— = —————————————————————
x x
Checking for a perfect cube :
4.4 x3 - 22x2 - 13x + 117 is not a perfect cube
Trying to factor by pulling out :
4.5 Factoring: x3 - 22x2 - 13x + 117
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -13x + 117
Group 2: x3 - 22x2
Pull out from each group separately :
Group 1: (x - 9) • (-13)
Group 2: (x - 22) • (x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
4.6 Find roots (zeroes) of : F(x) = x3 - 22x2 - 13x + 117
See theory in step 4.2
In this case, the Leading Coefficient is 1 and the Trailing Constant is 117.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3 ,9 ,13 ,39 ,117
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 107.00
-3 1 -3.00 -69.00
-9 1 -9.00 -2277.00
-13 1 -13.00 -5629.00
-39 1 -39.00 -92157.00
-117 1 -117.00 -1901133.00
1 1 1.00 83.00
3 1 3.00 -93.00
9 1 9.00 -1053.00
13 1 13.00 -1573.00
39 1 39.00 25467.00
117 1 117.00 1299051.00
Polynomial Roots Calculator found no rational roots
Final result :
x3 - 22x2 - 13x + 117
—————————————————————
x
HOPE THIS HELPS YOU!