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’.

-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 $4 {(- 1)}^{3} + 7 {(- 1)}^{2} + 5 (- 1) + t = 3$ ,
$- 4 + 7 - 5 + t = 3$
Hence, $t = - 5$

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A polynomial
$P (x) = x^{2} + 2 x + 3$
leaves a remainder of ___ when divided by $x - 1$ .

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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