Find the quotient at remainder ol 4x 3 15) The polynomials ax + 3x2 + 5x - 4 and x - 4x - a when divided by x - 2 equal remainder are found. Find the value of a. 3.
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Let p(x) = ax3 + 4x2 + 3x – 4 and q(x) = x3 – 4x + a be the given polynomials.
When p(x) and q(x) are divided by (x – 3) the remainder are p(3) and q(3) respectively.
p(3) = q(3) given
a(3)3 + 4(3)2 + 3 × 3 – 4 = 33 – 4 × 3 + a
⇒ 27a + 36 + 9 – 4 = 27 – 12 + a
⇒ 26a = 15 – 41
⇒ 26a = - 26
∴ a = - 26/26 = - 1
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