-x • (x2 - 208x + 814)
——————————————————————
26
Step-by-step explanation:
Step 1 :
x2 + 8
Simplify ——————
26
Polynomial Roots Calculator :
Find roots (zeroes) of : F(x) = x2 + 8
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 8.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,8
Let us test
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 9.00
-2 1 -2.00 12.00
-4 1 -4.00 24.00
-8 1 -8.00 72.00
1 1 1.00 9.00
2 1 2.00 12.00
4 1 4.00 24.00
8 1 8.00 72.00
Polynomial Roots Calculator found no rational roots
Equation at the end of step 1 :
8 (x2+8)
((8•(x2))-((— ÷ 8•——————)•x2))-31x
x 26
:
8
Simplify —
x
Equation at the end of step 2 :
8 (x2+8)
((8•(x2))-((— ÷ 8•——————)•x2))-31x
x 26
8
Divide — by 8
x
1 (x2+8)
((8•(x2))-((—•——————)•x2))-31x
x 26
Equation at the end of step 4 :
(x2 + 8)
((8 • (x2)) - (———————— • x2)) - 31x
26x
Dividing exponential expressions :
x2 divided by x1 = x(2 - 1) = x1 = x
Equation at the end of step 5 :
x • (x2 + 8)
((8 • (x2)) - ————————————) - 31x
26
Equation at the end of step 6 :
x • (x2 + 8)
(23x2 - ————————————) - 31x
26
Rewriting the whole as an Equivalent Fraction :
Subtracting a fraction from a whole
Rewrite the whole as a fraction using 26 as the denominator :
23x2 23x2 • 26
23x2 = ———— = —————————
1 26
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
Adding fractions that have a common denominator :
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:
23x2 • 26 - (x • (x2+8)) -x3 + 208x2 - 8x
———————————————————————— = ————————————————
26 26
Equation at the end of step 7 :
(-x3 + 208x2 - 8x)
—————————————————— - 31x
26
Rewriting the whole as an Equivalent Fraction :
Subtracting a whole from a fraction
Rewrite the whole as a fraction using 26 as the denominator :
31x 31x • 26
31x = ——— = ————————
1 26
Pulling out like terms :
Pull out like factors :
-x3 + 208x2 - 8x = -x • (x2 - 208x + 8)
Trying to factor by splitting the middle term
Factoring x2 - 208x + 8
The first term is, x2 its coefficient is 1 .
The middle term is, -208x its coefficient is -208 .
The last term, "the constant", is +8
Multiply the coefficient of the first term by the constant 1 • 8 = 8
Find two factors of 8 whose sum equals the coefficient of the middle term, which is -208 .
-8 + -1 = -9
-4 + -2 = -6
-2 + -4 = -6
-1 + -8 = -9
1 + 8 = 9
2 + 4 = 6
4 + 2 = 6
8 + 1 = 9
Adding fractions that have a common denominator : Adding up the two equivalent fractions
-x • (x2-208x+8) - (31x • 26) -x3 + 208x2 - 814x
————————————————————————————— = ——————————————————
26 26
Pulling out like terms :
10.1 Pull out like factors :
-x3 + 208x2 - 814x = -x • (x2 - 208x + 814)
Trying to factor by splitting the middle term
10.2 Factoring x2 - 208x + 814
The first term is, x2 its coefficient is 1 .
The middle term is, -208x its coefficient is -208 .
The last term, "the constant", is +814
Multiply the coefficient of the first term by the constant 1 • 814 = 814
Find two factors of 814 whose sum equals the coefficient of the middle term, which is -208 .
-814 + -1 = -815
-407 + -2 = -409
-74 + -11 = -85
-37 + -22 = -59
-22 + -37 = -59
-11 + -74 = -85
-2 + -407 = -409
-1 + -814 = -815
1 + 814 = 815
2 + 407 = 409
11 + 74 = 85
22 + 37 = 59
37 + 22 = 59
74 + 11 = 85
407 + 2 = 409
814 + 1 = 815
