factorize x^3+2x^2+5x+4
Answers
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 5x-4
Group 2: x3-2x2
Pull out from each group separately :
Group 1: (5x-4) • (1)
Group 2: (x-2) • (x2)
Find roots (zeroes) of : F(x) = x3-2x2+5x-4
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 -4.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -12.00
-2 1 -2.00 -30.00
-4 1 -4.00 -120.00
1 1 1.00 0.00 x-1
2 1 2.00 6.00
4 1 4.00 48.00
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
x3-2x2+5x-4
can be divided with x-1Polynomial Long Division
Dividing : x3-2x2+5x-4
("Dividend")
By : x-1 ("Divisor")
dividend x3 - 2x2 + 5x - 4
- divisor * x2 x3 - x2
remainder - x2 + 5x - 4
- divisor * -x1 - x2 + x
remainder 4x - 4
- divisor * 4x0 4x - 4
remainder 0
Quotient : x2-x+4 Remainder: 0
final answer is (x2 - x + 4) • (x - 1)
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