x^3-4x^2-31x+70 Help
Answers
Answer:
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 70.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,5 ,7 ,10 ,14 ,35 ,70
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 96.00
-2 1 -2.00 108.00
-5 1 -5.00 0.00 x+5
-7 1 -7.00 -252.00
-10 1 -10.00 -1020.00
-14 1 -14.00 -3024.00
-35 1 -35.00 -46620.00
-70 1 -70.00 -360360.00
1 1 1.00 36.00
2 1 2.00 0.00 x-2
5 1 5.00 -60.00
7 1 7.00 0.00 x-7
10 1 10.00 360.00
14 1 14.00 1596.00
35 1 35.00 36960.00
70 1 70.00 321300.00
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
x3-4x2-31x+70
can be divided by 3 different polynomials,including by x-7