Divide f(x) = 3x4 - 8x3 - 2 - 5x -5 by x - 3
Answers
Step-by-step explanation:
Final result :
3x3 - 2x2 + x - 1
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 2 more similar replacement(s).
Step by step solution :
Step 1 :
Equation at the end of step 1 :
Step 2 :
Equation at the end of step 2 :
Step 3 :
Equation at the end of step 3 :
Step 4 :
3x4 - 8x3 + 5x2 - 3x + 2 Simplify ———————————————————————— x - 2
Polynomial Roots Calculator :
4.1 Find roots (zeroes) of : F(x) = 3x4 - 8x3 + 5x2 - 3x + 2
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 2.
The factor(s) are:
of the Leading Coefficient : 1,3
of the Trailing Constant : 1 ,2
Let us test ....
P Q P/Q F(P/Q) Divisor -1 1 -1.00 21.00 -1 3 -0.33 3.89 -2 1 -2.00 140.00 -2 3 -0.67 9.19 1 1 1.00 -1.00 1 3 0.33 1.30 2 1 2.00 0.00 x - 2 2 3 0.67 0.44
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
3x4 - 8x3 + 5x2 - 3x + 2
can be divided with x - 2
Polynomial Long Division :
4.2 Polynomial Long Division
Dividing : 3x4 - 8x3 + 5x2 - 3x + 2
("Dividend")
By : x - 2 ("Divisor")
dividend 3x4 - 8x3 + 5x2 - 3x + 2 - divisor * 3x3 3x4 - 6x3 remainder - 2x3 + 5x2 - 3x + 2 - divisor * -2x2 - 2x3 + 4x2 remainder x2 - 3x + 2 - divisor * x1 x2 - 2x remainder - x + 2 - divisor * -x0 - x + 2 remainder 0
Quotient : 3x3-2x2+x-1 Remainder: 0
Polynomial Roots Calculator :
4.3 Find roots (zeroes) of : F(x) = 3x3-2x2+x-1
See theory in step 4.1
In this case, the Leading Coefficient is 3 and the Trailing Constant is -1.
The factor(s) are:
of the Leading Coefficient : 1,3
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor -1 1 -1.00 -7.00 -1 3 -0.33 -1.67 1 1 1.00 1.00 1 3 0.33 -0.78
Polynomial Roots Calculator found no rational roots
Canceling Out :
4.4 Cancel out (x-2) which appears on both sides of the fraction line.
Final result :
3x3 - 2x2 + x - 1
Hope it helps you
PLZ MARK ME AS BRAINLIEST
#BE brainly
