Question

How can we divide x 4 + x 3 - 7x 2 - x + 6 by x- 1?

Answer 1

Step-by-step explanation:

By long division they are divide

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Answer 2

Answer:

x=-3

Step-by-step explanation:

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (x4)-(x3)-7x2)+x)+6  = 0

Step  2  :

Polynomial Roots Calculator :

2.1    Find roots (zeroes) of :       F(x) = x4-x3-7x2+x+6

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  6.

The factor(s) are:

of the Leading Coefficient :  1

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

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

  x4-x3-7x2+x+6

can be divided by 4 different polynomials,including by  x-3