Answer:
4p3 + 6p2 - 8p - 7
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "p2" was replaced by "p^2". 1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
(((4 • (p3)) + (2•3p2)) - 7) - 8p
STEP
2
:
Equation at the end of step
2
:
((22p3 + (2•3p2)) - 7) - 8p
STEP
3
:
Checking for a perfect cube
3.1 4p3+6p2-8p-7 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 4p3+6p2-8p-7
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -8p-7
Group 2: 4p3+6p2
Pull out from each group separately :
Group 1: (8p+7) • (-1)
Group 2: (2p+3) • (2p2)
3.3 Find roots (zeroes) of : F(p) = 4p3+6p2-8p-7
Polynomial Roots Calculator is a set of methods aimed at finding values of p for which F(p)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers p 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 4 and the Trailing Constant is -7.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4
of the Trailing Constant : 1 ,7
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 3.00
-1 2 -0.50 -2.00
-1 4 -0.25 -4.69
-7 1 -7.00 -1029.00
-7 2 -3.50 -77.00
-7 4 -1.75 3.94
1 1 1.00 -5.00
1 2 0.50 -9.00
1 4 0.25 -8.56
7 1 7.00 1603.00
7 2 3.50 210.00
7 4 1.75 18.81
Final result :
4p3 + 6p2 - 8p - 7
where (h,k) is the center and r is the radius.