The degree of the remainder r(x) when p (x) = bx3 + cx + d is divided by a polynomial of degree 4 is a.less than 4b.less than 3c.equal to 3d.less than or equal to 3
Question
The degree of the remainder r(x) when p (x) = bx3 + cx + d is divided by a polynomial of degree 4 is a.less than 4b.less than 3c.equal to 3d.less than or equal to 3
Solution
To determine the degree of the remainder when p(x) is divided by a polynomial of degree 4, we need to consider the degree of p(x) and the degree of the divisor polynomial.
Given that p(x) = bx^3 + cx + d, we can see that the highest power of x in p(x) is 3.
If the divisor polynomial has a degree of 4, it means that the highest power of x in the divisor is 4.
When we divide p(x) by a polynomial of degree 4, the degree of the remainder will be less than the degree of the divisor polynomial.
Therefore, the degree of the remainder r(x) is less than 4.
Hence, the correct answer is option a) less than 4.
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