Let $P(x)$ be a polynomial of degree 5 - HSC - SSCE Mathematics Extension 1 - Question 3 - 2022 - Paper 1
Question 3
Let $P(x)$ be a polynomial of degree 5. When $P(x)$ is divided by the polynomial $Q(x)$, the remainder is $2x + 5$.
Which of the following is true about the degre... show full transcript
Worked Solution & Example Answer:Let $P(x)$ be a polynomial of degree 5 - HSC - SSCE Mathematics Extension 1 - Question 3 - 2022 - Paper 1
Step 1
The degree must be 1.
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Answer
This statement is incorrect. The degree of Q(x) cannot be 1 when dividing P(x) which has a degree of 5, as the remainder is of degree 1.
Step 2
The degree could be 1.
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Answer
This statement is incorrect. Since the remainder is 2x+5, it cannot happen when Q is of degree 1.
Step 3
The degree must be 2.
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Answer
This statement is also incorrect. The degree of Q does not specifically have to be 2. It could be higher than 2.
Step 4
The degree could be 2.
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Answer
This statement is correct. The polynomial Q(x) could have a degree of 2, since the highest degree of the remainder does not exceed that of Q. Therefore, the degrees could match or Q could even be of a higher degree.
