What is the constant term of the quotient when 2x^3-3x^2 + 4x-2 is divided by x^2-x+2?
1 answer:
Answer:
-1
Step-by-step explanation:
See the attachment for the polynomial long division. The constant in the quotient is -1.
_____
Here, there is a remainder of -x. If there were no remainder the constant in the quotient is the ratio of the constant in the dividend to the constant in the divisor: -2/2 = -1.
That could be a first guess in a "guess and check" solution approach.
<em>Guess</em>: first term of binomial quotient is (2x^3)/x^2 = 2x; last term of binomial quotient is -2/2 = -1. So, the quotient is guessed to be (2x -1).
<em>Check</em>: (2x -1)(x^2 -x +2) = 2x^3 -3x^2 +5x -2
Subtracting this from the actual dividend gives a remainder of -x. This has a lower degree than the divisor, so no further adjustment of the quotient is required.
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Answer:
Step-by-step explanation:
The given polynomials can be added together by adding like terms together as shown below:
=> Add together, the coefficient of all terms that have the power of 3.
=>
=>
=>
The answer =
Answer:
If:
(1)
And we have to rewrite the following expresion in terms of :
(2)
Firstly we have to rearrange the right side of equation (2) in terms of , factorizing by the common factor:
Then, we can substitute by
:
And set it equal to zero:
>>>>This is the resulting equation
Now, each term of an algebraic expresion (like the equation above) is composed of sign, coefficient, variable and exponent. The terms are separated from each other by the plus sign (+) or the minus sign (-).
In this case, the variable is and the number that multiplies the variable (the coefficient) is
, whereas the constant (which is the term with no variable) is