Question

1) On dividing a polynomial p(x) by x2 – 4, quotient and remainder are
found to be x and 3 respectively. The polynomial p(x) is
(a) 3x2 + x - 12
(b) x3 – 4x + 3
+
(C) x2 + 3x - 4
© ) x3 – 4x - 3​

Answer 1

Answer:

Given: when p(x) / (x² - 4) we get remainder as 3 and quotient as x .

To find: polynomial p(x)

Solution:

To find the polynomial, we have the formula which states that p(x) can be found out by multiplication of quotient and dividend and then adding it to the remainder.

Formula for p(x) is:

p(x) = ( q(x) x g(x) ) + r(x)

Here, q(x) = x, g(x) = x² - 4 and r(x) = 3

So to find p(x) lets substitute all the values, we get

p(x) =( x × (x² - 4) )+ 3

p(x) =( x³ - 4x )+ 3

Answer:

So the polynomial obtained is p(x) = x³ - 4x + 3

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