Problem 167 of 7
Complete the Remainder Theorem explanation using what happens when x equals the root of the divisor.
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use division identity p(x)=(x-a)q(x)+r.
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Use division identity and substitution x=a.
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Solution
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1. Write the division identity.
2. Substitute x=a.
3. Simplify (a-a)q(a) to zero and conclude p(a)=r.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Proof that assumes the theorem without using division identity.