Question

(x^3 + 6x^2 + 6x + 1) divided by x + 1​

Answer 1

Answer:

Step by step solution :

STEP

1

:

Equation at the end of step 1

(((x3) - (2•3x2)) + 6x) - 1 = 0

STEP

2

:

Checking for a perfectparately :

Group 1: (x3-1) • (1)

Group 2: (x-1) • (-6x)

Bad news !! Factoring byegers

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 -1.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1

Let us test ....

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

-1 1 -1.00 -14.00

1 1 1.00 0.00 x-1

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

x3-6x2+6x-1

can be divided with x-1

Polynomial Long Division :

2.4 Polynomial Long Division

Dividing : x3-6x2+6x-1

("Dividend")

By : x-1 ("Divisor")

dividend x3 - 6x2 + 6x - 1

- divisor * x2 x3 - x2

remainder - 5x2 + 6x - 1

- divisor * -5x1 - 5x2 + 5x

remainder x - 1

- divisor * x0 x - 1

remainder 0

Quotient : x2-5x+1 Remainder: 0

Trying to factor by splitting the middle term

2.5 Factoring x2-5x+1

The first term is, x2 its coefficient is 1 .

The middle term is, -5x its coefficient is -5 .

The last term, "the constant", is +1

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

Step-2 : Find two factors of 1 whose sum equals the coefficient of the middle term, which is -5 .

-1 + -1 = -2

1 + 1 = 2