Can you factorize x^3 + 5x^2 +7x + 3
Answers
Answer:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
(((x3) - 5x2) + 7x) - 3
STEP
2
:
Checking for a perfect cube
2.1 x3-5x2+7x-3 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3-5x2+7x-3
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 7x-3
Group 2: x3-5x2
Pull out from each group separately :
Group 1: (7x-3) • (1)
Group 2: (x-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 :
2.3 Find roots (zeroes) of : F(x) = x3-5x2+7x-3
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 -3.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
(((x3) - 5x2) + 7x) - 3
STEP
2
:
Checking for a perfect cube
2.1 x3-5x2+7x-3 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3-5x2+7x-3
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 7x-3
Group 2: x3-5x2
Pull out from each group separately :
Group 1: (7x-3) • (1)
Group 2: (x-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 :
2.3 Find roots (zeroes) of : F(x) = x3-5x2+7x-3
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 -3.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -16.00
-3 1 -3.00 -96.00
1 1 1.00 0.00 x-1
3 1 3.00 0.00 x-3
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
x3-5x2+7x-3
can be divided by 2 different polynomials,including by x-3
Polynomial Long Division :
2.4 Polynomial Long Division
Dividing : x3-5x2+7x-3
("Dividend")
By : x-3 ("Divisor")
dividend x3 - 5x2 + 7x - 3
- divisor * x2 x3 - 3x2
remainder - 2x2 + 7x - 3
- divisor * -2x1 - 2x2 + 6x
remainder x - 3
- divisor * x0 x - 3
remainder 0
Quotient : x2-2x+1 Remainder: 0