CLASS 9 MATHS · POLYNOMIALS

Value of a polynomial at a point

To find p(a), replace every x in p(x) by a and simplify.

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Worked examples

Example 1 · level 1

If p(x) = x² − x − 2, find p(3).

Show solution

p(3) = 3² − 3 − 2
= 9 + (−3) + (−2)
= 4.

Answer: 4

Example 2 · level 2

If p(x) = x³ + 6x² − 6x − 6, find p(−4).

Show solution

p(−4) = (−4)³ + 6 × (−4)² − 6 × (−4) − 6
= (−64) + 96 + 24 + (−6)
= 50.

Answer: 50

Example 3 · level 3

If p(x) = 4x³ − 7x² + 7x − 6, find p(−1).

Show solution

p(−1) = 4 × (−1)³ − 7 × (−1)² + 7 × (−1) − 6
= (−4) + (−7) + (−7) + (−6)
= −24.

Answer: -24