The polynomial P(x) = 4 $x^{3}$ + 7 $x^{2}$ – 5x + t, when divided by x + 1 gives 3 as the remainder. Find the value of ‘t’.

-3

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-4

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-5

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-6

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Solution

The correct option is C
-5

The remainder when P(x) is divided by x + 1 is 3, which simply means that P(-1) = 3, so upon solving we get 4 ${(- 1)}^{3}$ + 7 ${(- 1)}^{2}$ + 5(1) + t = 3, and hence t = -5.

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Similar questions

The polynomial $P (x) = 4 x^{3} + 7 x^{2} - 5 x + t$ , when divided by $x + 1$ gives 3 as the remainder.
Find the value of ‘t’.

p (x) = 4 x^{3} + 7 x^{2} - 5 x + t

x + 1

3

t

p (x) = 4 x^{3} + 7 x^{2} - 5 x + t

x + 1

3

t

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^{3} + 3 x^{2} + 2 x + t

(x - 1)

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