The remainder of the polynomial P(x) = 3 $x^{2}$ + 5x + 8, when divided by x + 2 is___.

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Solution

The value of the remainder of a polynomial of degree greater than or equal to zero, when divide by a linear polynomial x – a is P(a). So, the value of the polynomial at x = -2 is the remainder of 3 $x^{2}$ + 5x + 8.

The value of polynomial 3 $x^{2}$ +5x+8 at x=-2 is 3 ${(- 2)}^{2}$ +5(-2)+8=10

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The remainder of the polynomial P(x) = 3 $x^{2}$ + 5x + 8, when divided by x + 2 is

Statement1: The polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ when divided by $x - 1$ gives zero as the remainder.

Statement2: $(x - 1)$ is a factor of the polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ .

p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + 3 a - 7

x + 1

19

a

p (x)

x + 2

p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + 3 a - 7

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