Question

(y+2) ^3-6(y+2) ^2+3(y+2) -2=0 simplify the equation step by step plz​

Answer 1

Answer:

1. euyou is a very different kind and sanitation
2. I will not

Answer 2

Step-by-step explanation:

Simplify ——

y2

Equation at the end of step

1

:

y 6

(((— + 3) - 2y) - ——) - 9

y y2

STEP

2

:

y

Simplify —

y

Equation at the end of step

2

:

6

(((1 + 3) - 2y) - ——) - 9

y2

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using y2 as the denominator :

4 - 2y (4 - 2y) • y2

4 - 2y = —————— = —————————————

1 y2

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

4

:

Pulling out like terms

4.1 Pull out like factors :

4 - 2y = -2 • (y - 2)

Adding fractions that have a common denominator :

4.2 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:

-2 • (y-2) • y2 - (6) -2y3 + 4y2 - 6

————————————————————— = ——————————————

y2 y2

Equation at the end of step

4

:

(-2y3 + 4y2 - 6)

———————————————— - 9

y2

STEP

5

:

Rewriting the whole as an Equivalent Fraction :

5.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using y2 as the denominator :

9 9 • y2

9 = — = ——————

1 y2

STEP

6

:

Pulling out like terms :

6.1 Pull out like factors :

-2y3 + 4y2 - 6 = -2 • (y3 - 2y2 + 3)

Polynomial Roots Calculator :

6.2 Find roots (zeroes) of : F(y) = y3 - 2y2 + 3

Polynomial Roots Calculator is a set of methods aimed at finding values of y for which F(y)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers y 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 0.00 y + 1

-3 1 -3.00 -42.00

1 1 1.00 2.00

3 1 3.00 12.00

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

y3 - 2y2 + 3

can be divided with y + 1

Polynomial Long Division :

6.3 Polynomial Long Division

Dividing : y3 - 2y2 + 3

("Dividend")

By : y + 1 ("Divisor")

dividend y3 - 2y2 + 3

- divisor * y2 y3 + y2

remainder - 3y2 + 3

- divisor * -3y1 - 3y2 - 3y

remainder 3y + 3

- divisor * 3y0 3y + 3

remainder 0

Quotient : y2-3y+3 Remainder: 0

Trying to factor by splitting the middle term

6.4 Factoring y2-3y+3

The first term is, y2 its coefficient is 1 .

The middle term is, -3y its coefficient is -3 .

The last term, "the constant", is +3

Step-1 : Multiply the coefficient of the first term by the constant 1 • 3 = 3

Step-2 : Find two factors of 3 whose sum equals the coefficient of the middle term, which is -3 .

-3 + -1 = -4

-1 + -3 = -4

1 + 3 = 4

3 + 1 = 4

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

6.5 Adding up the two equivalent fractions

-2 • (y2-3y+3) • (y+1) - (9 • y2) -2y3 - 5y2 - 6

————————————————————————————————— = ——————————————

y2 y2

STEP

7

:

Pulling out like terms :

7.1 Pull out like factors :

-2y3 - 5y2 - 6 = -1 • (2y3 + 5y2 + 6)

Polynomial Roots Calculator :

7.2 Find roots (zeroes) of : F(y) = 2y3 + 5y2 + 6

See theory in step 6.2

In this case, the Leading Coefficient is 2 and the Trailing Constant is 6.

The factor(s) are:

of the Leading Coefficient : 1,2

of the Trailing Constant : 1 ,2 ,3 ,6

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 9.00

-1 2 -0.50 7.00

-2 1 -2.00 10.00

-3 1 -3.00 -3.00

-3 2 -1.50 10.50

-6 1 -6.00 -246.00

1 1 1.00 13.00

1 2 0.50 7.50

2 1 2.00 42.00

3 1 3.00 105.00

3 2 1.50 24.00

6 1 6.00 618.00

Polynomial Roots Calculator found no rational roots

Final result :

-2y3 - 5y2 - 6

——————————————

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