Question

When dividing x^3 + nx^2 + 4nx - 6 by x + 3, the remainder is -48. What is the value of n?

Answer 1

5

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Use the Remainder Theorem.

The Remainder Theorem states that if a polynomial f(x) is divided by x - k, the remainder is f(k).

Since our divisor is x + 3, we use k = -3.

Substituting x with -3 into the polynomial gives us:

• (-3)³ + n(-3)² + 4n(-3) - 6 =
• -27 + 9n - 12n - 6 =
• -3n - 33

Setting that equal to the given remainder of -48 gives us the equation:

• -3n - 33 = -48
• -3n = - 15
• n = 5

So, the value of n is 5.

Answer 2

The value of n is determined by applying the Remainder Theorem to the given polynomial. Substituting x = -3 into the polynomial, simplifying the equation, and solving for n reveals that the value of n is 5.

Step-by-step explanation:

To find the value of n when dividing x^3 + nx^2 + 4nx - 6 by x + 3 with the remainder -48, we can apply the Remainder Theorem, which states that if a polynomial f(x) is divided by x - k, the remainder is f(k). In this case, we are dividing by x + 3, so k = -3. Substituting -3 into the polynomial gives us:

f(-3) = (-3)^3 + n(-3)^2 + 4n(-3) - 6 = -27 + 9n - 12n - 6 = -48.

Simplifying the equation:
-27 + 9n - 12n - 6 = -48
-3n - 33 = -48
-3n = -15
n = 5.

Therefore, the value of n is 5.