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Original question & working

Use the remainder theorem · source reference

2021/RI/Prelim/I/1 · Question pp. 2 · Working pp. 7

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Printed question

Given the polynomial x4+ax2+bx+cx^4+ax^2+bx+c has a factor (x−2)(x-2) and gives remainders 12 and 26 when divided by (x−3)(x-3) and (x−4)(x-4) respectively, find the values of a,b,ca,b,c. [4]

[2021/RI/Prelim/I/1]

Printed working

f(x)=x4+ax2+bx+cf(x)=x^4+ax^2+bx+c.

f(2)=0⇒16+4a+2b+c=0⇒4a+2b+c=−16f(2)=0\Rightarrow16+4a+2b+c=0\Rightarrow4a+2b+c=-16 — (1).

f(3)=12⇒81+9a+3b+c=12⇒9a+3b+c=−69f(3)=12\Rightarrow81+9a+3b+c=12\Rightarrow9a+3b+c=-69 — (2).

f(4)=26⇒256+16a+4b+c=26⇒16a+4b+c=−230f(4)=26\Rightarrow256+16a+4b+c=26\Rightarrow16a+4b+c=-230 — (3).

Solving (1), (2) and (3), a=−54,b=217,c=−234a=-54,b=217,c=-234.

Printed answer key

a=−54,b=217,c=−234a=-54,b=217,c=-234.

Source provenance

2025 TJC H2 Math (9758) JC2 MSM: EQUATIONS. Question sheet printed pages 15–19; solution sheet printed pages 1–12. Original exam attribution is retained above. Currency dollar signs are spelled out outside maths to avoid confusing currency with TeX delimiters.