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Find a positive value of p if the expression 2x² – px + p leaves a…

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Find a positive value of p if the expression 2x² – px + p leaves a remainder 6 when divided by x – p

A. 4

B. 3

C. 2

D. 1

QUICK ANSWER…

C

DETAILS…

Pay close attention and follow these steps to resolve questions like this.

  • Equate the divisor to zero, and make x the subject of the formula like this: x – p = 0, x = p
  • Substitute x for p in the main expression like this: 2x² – px + p = 2(p)² – p(p) + p = 2p² – p² + p = p² + p
  • Finally, equate the answer to the remainder like this: p² + p = 6

Solving this, we have:

p² + p = 6

p² + p – 6 = 0

factorizing, we have:

p² – 2p + 3p – 6 = 0

(p² – 2p) + (3p – 6) = 0

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p(p – 2) + 3(p – 2) = 0

(p – 2)(p + 3) = 0

Therefore,

P – 2 = 0, p = 2

Or p + 3 = 0, p = -3

So, p = 2 or -3

Taking the positive value as required by the question, we have p = 2

Now for the right answer to the above question:

  1. Option A is incorrect.
  2. Option B is incorrect.
  3. C is correct.
  4. D is not the correct answer.

KEY-POINTS…

You may please note these/this:

  • The steps are clear…
  • Firstly, make x the subject of the divisor.
  • Secondly, substitute x for p into the original expression.
  • Thirdly, we will be left with an equation containing only p, then solve to find p.
  • Take the positive value of p as the required answer.
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/ culled from 2020 JAMB-UTME mathematics past question 33 /

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