Divide f(x)=3x^3+5x^2-3x-7 by g(x)=x^3-5x^2+2 using long division method
Answers
Answer:
STEP
2
:
x3 - 5x2 - 3x - 7
Simplify —————————————————
x + 2
Checking for a perfect cube :
2.1 x3 - 5x2 - 3x - 7 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3 - 5x2 - 3x - 7
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -3x - 7
Group 2: x3 - 5x2
Pull out from each group separately :
Group 1: (3x + 7) • (-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 - 3x - 7
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 -7.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,7
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -10.00
-7 1 -7.00 -574.00
1 1 1.00 -14.00
7 1 7.00 70.00
Polynomial Roots Calculator found no rational roots
Polynomial Long Division :
2.4 Polynomial Long Division
Dividing : x3 - 5x2 - 3x - 7
("Dividend")
By : x + 2 ("Divisor")
dividend x3 - 5x2 - 3x - 7
- divisor * x2 x3 + 2x2
remainder - 7x2 - 3x - 7
- divisor * -7x1 - 7x2 - 14x
remainder 11x - 7
- divisor * 11x0 11x + 22
remainder - 29
Quotient : x2 - 7x + 11
Remainder : -29
Final result :
x3 - 5x2 - 3x - 7
—————————————————
x + 2
See results of polynomial long division:
1. In step #02.04
Terms and topics
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