The polynomial 3x² + mx? - nx - 10 has a factor of (x - 1). When divided by x + 2, the remainder is 36. What are the values of m and n?

Step-by-step explanation:

Given

Required

The values of m and n

For x - 1;

we have:

So:

Collect like terms

Because x - 1 divides the polynomial, then P(1) = 0;

So, we have:

Add 9 to both sides

--- (1)

For x + 2;

we have:

So:

Collect like terms

x + 2 leaves a remainder of 36, means that P(-2) = 36;

So, we have:

Collect like terms

Divide through by 2

--- (2)

Add (1) and (2)

Divide by 3

Substitute in (1)

Make n the subject

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step-by-step explanation: