4 (a) Use the factor theorem to prove that $x + 3$ is a factor of $p(x)$
Given the polynomial:
$$ p(x) = 2x^3 + 7x^2 + 2x - 3 $$
To use the factor theorem, we need to evaluate $p(-3)$ and check if it equals 0. - AQA - A-Level Maths Pure - Question 4 - 2017 - Paper 1
Question 4
4 (a) Use the factor theorem to prove that $x + 3$ is a factor of $p(x)$
Given the polynomial:
$$ p(x) = 2x^3 + 7x^2 + 2x - 3 $$
To use the factor theorem, we nee... show full transcript
Worked Solution & Example Answer:4 (a) Use the factor theorem to prove that $x + 3$ is a factor of $p(x)$
Given the polynomial:
$$ p(x) = 2x^3 + 7x^2 + 2x - 3 $$
To use the factor theorem, we need to evaluate $p(-3)$ and check if it equals 0. - AQA - A-Level Maths Pure - Question 4 - 2017 - Paper 1
Step 1
Evaluate $p(-3)$
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Answer
Substituting x=−3 into the polynomial:
p(−3)=2(−3)3+7(−3)2+2(−3)−3
Calculating each term:
2(−3)3=2(−27)=−54
7(−3)2=7(9)=63
2(−3)=−6
−3=−3
Combining these results:
p(−3)=−54+63−6−3
Therefore:
p(−3)=0
Since p(−3)=0, by the factor theorem, x+3 is a factor of p(x).
