← Complex numbers: past papers
AS 91577 · 2023 paper · a remainder, an unknown from a quotient, a surd equation, comparing parts, and a pair of conditions
Question 3(a) Achieved
Practises Polynomial equations with complex roots
Five separate parts: a remainder, an unknown found from a quotient, an equation with two square roots, two unknowns found from a reciprocal, and a constant pinned down by two conditions at once.
When the polynomial 2x3 + px2 + 7x − 3 is divided by x + 3, the remainder is 30. Find the value of p.
Work it out
Try it on paper first. Stuck? Take one hint at a time.
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1 Dividing by x + 3 leaves 30. Which value of x do you put in?
x = −3, the value that makes x + 3 zero. The remainder theorem says f(−3) = 30. -
2 Substitute and solve for p.
2(−3)3 + p(−3)2 + 7(−3) − 3 = 30
−54 + 9p − 21 − 3 = 30
9p = 108, so p = 12.
What the marker wanted
- Achieved The value of p.
In our words, from NZQA’s 2023 marking schedule.
How did it go?
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