Math, asked by khokarangel, 7 months ago

add 2+x-x^2+6x^3, -6-2x+4x^2, 3-3x^3 +x^3​

Answers

Answered by Anonymous
1

:

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.

Answered by Reeyan777
1

Answer:

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x4 - 3x3 + 4x2 - 6x + 3

———————————————————————

x • (x + 2)

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