Verified answer

Given: P(x) = x³+x²-5x-k

Substitute the value of x to 2 and equate it to -4

• x³+x²-5x-k = -4
• (2)³+(2)²-5(2)-k = -4
• 8+4-10-k = -4
• 12-10-k = -4
• 2-k = -4
• -k = -4-2
• -k = -6
• k = -6/-1
• k = 6

Checking:

• x³+x²-5x-6 = -4
• (2)³+(2)²-5(2)-6 = -4
• 8+4-10-6 = -4
• 12-10-6 = -4
• 2-6 = -4
• -4 = -4

• The value of k is 6