Question

If p(x)=(x³+4x-5) is divided by ( x-1) then find the remainder and hance determine whether (x-1) is a factor of p(x) or not?​

Answer 1

Answer:

Note:

To know whether (x - 1) is a factor of the polynomial. Add all the coefficients of x and if their sum is zero, then (x - 1) is the factor of the polynomial.

Here,

p (x) = x³ + 4x - 5

=> Coefficient of x³ = 1

=> Coefficient of x = 4

=> Coefficient of x⁰ = - 5

Here, 1 + 4 - 5 = 0

Therefore, (x - 1) is the factor of the p (x) = x³ + 4x - 5.

Answer 2

Step-by-step explanation:

Given: If $p(x) = {x}^{3} + 4x - 5$ is divided by $(x - 1)$.

To find: Find the remainder and hence determine whether (x-1) is a factor of p(x) or not?

Solution:

Divide p(x) by $(x - 1)$

$x - 1 \: ) \: {x}^{3} + 4x - 5 \: ( {x}^{2} + x + 5 \\ {x}^{3} \: \: \: \: \: \: \: \: \: \: - {x}^{2} \\ - - - - - - - \\ {x}^{2} + 4x - 5 \\ {x}^{2} - x \: \: \: \: \: \: \: \: \: \\ - - - - - \\ 5x - 5 \\ 5x - 5 \\ - - - - - \\ 0 \\ - - - - -$

Remainder is zero.

Thus,

$(x - 1) \:$ is a factor of p(x).

Final answer:

If $p(x)=( {x}^{3} +4x-5)$ is divided by $( x-1)$, then remainder is 0 and hence (x-1) is a factor of p(x) .

Hope it helps you.

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