3xcube +5xsquear-16x-2
Answers
Step-by-step explanation:
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Answer:
STEP
1
:
Equation at the end of step 1
(((3 • (x3)) + 5x2) - 16x) - 12
STEP
2
:
Equation at the end of step
2
:
((3x3 + 5x2) - 16x) - 12
STEP
3
:
Checking for a perfect cube
3.1 3x3+5x2-16x-12 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 3x3+5x2-16x-12
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -16x-12
Group 2: 3x3+5x2
Pull out from each group separately :
Group 1: (4x+3) • (-4)
Group 2: (3x+5) • (x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = 3x3+5x2-16x-12
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 3 and the Trailing Constant is -12.
The factor(s) are:
of the Leading Coefficient : 1,3
of the Trailing Constant : 1 ,2 ,3 ,4 ,6 ,12
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 6.00
-1 3 -0.33 -6.22
-2 1 -2.00 16.00
-2 3 -0.67 0.00 3x+2
-3 1 -3.00 0.00 x+3
-4 1 -4.00 -60.00
-4 3 -1.33 11.11
-6 1 -6.00 -384.00
-12 1 -12.00 -4284.00
1 1 1.00 -20.00
1 3 0.33 -16.67
2 1 2.00 0.00 x-2
2 3 0.67 -19.56
3 1 3.00 66.00
4 1 4.00 196.00
4 3 1.33 -17.33
6 1 6.00 720.00
12 1 12.00 5700.00
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
3x3+5x2-16x-12
can be divided by 3 different polynomials,including by x-2
Step-by-step explanation:
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