add 2+x-x^2+6x^3, -6-2x+4x^2, 3-3x^3 +x^3
Answers
:
9
Simplify —
x
Equation at the end of step
1
:
9
((((2•(x3))-(4•(x2)))-3x)-—)-3
x
STEP
2
:
Equation at the end of step
2
:
9
((((2•(x3))-22x2)-3x)-—)-3
x
STEP
3
:
Equation at the end of step
3
:
9
(((2x3 - 22x2) - 3x) - —) - 3
x
STEP
4
:
Rewriting the whole as an Equivalent Fraction
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using x as the denominator :
2x3 - 4x2 - 3x (2x3 - 4x2 - 3x) • x
2x3 - 4x2 - 3x = —————————————— = ————————————————————
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
5
:
Pulling out like terms
5.1 Pull out like factors :
2x3 - 4x2 - 3x = x • (2x2 - 4x - 3)
Trying to factor by splitting the middle term
5.2 Factoring 2x2 - 4x - 3
The first term is, 2x2 its coefficient is 2 .
The middle term is, -4x its coefficient is -4 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -4 .
-6 + 1 = -5
-3 + 2 = -1
-2 + 3 = 1
-1 + 6 = 5
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Adding fractions that have a common denominator :
5.3 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 • (2x2-4x-3) • x - (9) 2x4 - 4x3 - 3x2 - 9
———————————————————————— = ———————————————————
x x
Equation at the end of step
5
:
(2x4 - 4x3 - 3x2 - 9)
————————————————————— - 3
x
STEP
6
:
Rewriting the whole as an Equivalent Fraction :
6.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x as the denominator :
3 3 • x
3 = — = —————
1 x
Checking for a perfect cube :
6.2 2x4 - 4x3 - 3x2 - 9 is not a perfect cube
Trying to factor by pulling out :
6.3 Factoring: 2x4 - 4x3 - 3x2 - 9
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -3x2 - 9
Group 2: 2x4 - 4x3
Pull out from each group separately :
Group 1: (x2 + 3) • (-3)
Group 2: (x - 2) • (2x3)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Answer:
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x4 - 3x3 + 4x2 - 6x + 3
———————————————————————
x • (x + 2)
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