Question

1. when (4x⁵ + 11x⁴ - 6x² + 24) is subtracted from (5x⁵ + 11x⁴ + 9x² - 25), what will be the result?

Explanation:

Step1: Set up the subtraction

We need to subtract \((5x^5 + 11x^4 + 9x^2 - 25)\) from \((4x^5 + 11x^4 - 6x^2 + 24)\), which means we calculate \((4x^5 + 11x^4 - 6x^2 + 24)-(5x^5 + 11x^4 + 9x^2 - 25)\).

Step2: Distribute the negative sign

Using the distributive property \(a-(b + c)=a - b - c\), we get \(4x^5+11x^4 - 6x^2+24 - 5x^5-11x^4 - 9x^2 + 25\).

Step3: Combine like terms

• For \(x^5\) terms: \(4x^5-5x^5=-x^5\)
• For \(x^4\) terms: \(11x^4-11x^4 = 0\)
• For \(x^2\) terms: \(-6x^2-9x^2=-15x^2\)
• For constant terms: \(24 + 25=49\)

Combining all these results, we have \(-x^5-15x^2 + 49\).

Answer:

\(-x^5-15x^2 + 49\)