If on dividing a polynomial, a zero remain
-der is obtained, then the divisor is a dash of the dividend
Answers
Answer:
ANSWER
We know that the division algorithm states that:
Dividend=(Divisor×quotient)+Remainder
Here it is given that the dividend is p(x)=4x
3
+2x
2
−10x+2, the divisor is g(x), the quotient is 2x
2
+4x+1 and the remainder is 5, therefore,
4x
3
+2x
2
−10x+2=[g(x)(2x
2
+4x+1)]+5
⇒g(x)=
2x
2
+4x+1
4x
3
+2x
2
−10x+2
The division is shown above.
Hence, from the above division, we get that the divisor is g(x)=2x−3
Answer:
Factor
Step-by-step explanation:
An analogous reasoning applies in the case of division of polynomials. Intuitively speaking, we want the quotient to be of as high a degree as possible, so the remainder will always have a degree less than the divisor.
In the case of linear polynomials as divisors, we can therefore conclude that the remainders will always be polynomials of degree 0, that is, constants.
If you are still not convinced that the degree of the remainder should be less than that of the divisor, try to think of a scenario where the remainder has a degree greater than that of the divisor, and then observe that the remainder itself can be further divided by the divisor, which defeats the whole purpose of it being a remainder.