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 degree ... 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 option can be rejected because the degree of the remainder (2x+5) is 1, and thus the degree of Q(x) must be less than or equal to the degree of P(x) which is 5.
Step 2
The degree could be 1.
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Answer
This option is possible because if Q(x) has degree 1, it can indeed divide P(x), resulting in a remainder that fits the equation.
Step 3
The degree must be 2.
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Answer
This option can be rejected because no specific condition mandates that Q(x) must have degree 2.
Step 4
The degree could be 2.
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Answer
This option is plausible since Q(x) could be of degree 2 or less, given that the remainder is of degree 1.
