ANSWER: 5x2 - 5x + 26
———————
5
Step-by-step explanation: /> Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
(2): "2.2" was replaced by "(22/10)".
Step by step solution :
Step 1 :
3
Simplify —
1
Equation at the end of step 1 :
22
(—— - x) + ((x2) + 3)
10
Step 2 :
11
Simplify ——
5
Equation at the end of step 2 :
11
(—— - x) + (x2 + 3)
5
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 5 as the denominator :
x x • 5
x = — = —————
1 5
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 :
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:
11 - (x • 5) 11 - 5x
———————————— = ———————
5 5
Equation at the end of step 3 :
(11 - 5x)
————————— + (x2 + 3)
5
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 5 as the denominator :
x2 + 3 (x2 + 3) • 5
x2 + 3 = —————— = ————————————
1 5
Polynomial Roots Calculator :
4.2 Find roots (zeroes) of : F(x) = x2 + 3
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 3.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3
Let us test
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 4.00
-3 1 -3.00 12.00
1 1 1.00 4.00
3 1 3.00 12.00
Polynomial Roots Calculator found no rational roots
Adding fractions that have a common denominator :
4.3 Adding up the two equivalent fractions
(11-5x) + (x2+3) • 5 5x2 - 5x + 26
———————————————————— = —————————————
5 5
Trying to factor by splitting the middle term
4.4 Factoring 5x2 - 5x + 26
The first term is, 5x2 its coefficient is 5 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is +26
Step-1 : Multiply the coefficient of the first term by the constant 5 • 26 = 130
Step-2 : Find two factors of 130 whose sum equals the coefficient of the middle term, which is -5 .
-130 + -1 = -131
-65 + -2 = -67
-26 + -5 = -31
-13 + -10 = -23
-10 + -13 = -23
-5 + -26 = -31
-2 + -65 = -67
-1 + -130 = -131
1 + 130 = 131
2 + 65 = 67
5 + 26 = 31
10 + 13 = 23
13 + 10 = 23
26 + 5 = 31
65 + 2 = 67
130 + 1 = 131
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
5x2 - 5x + 26
—————————————
5
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