Question

⑦. (2x - 1)(x³ + x² - 30)

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \(2x - 1\) with each term in \(x^3 + x^2 - 30\).
First, multiply \(2x\) with \(x^3\), \(x^2\), and \(-30\):
\(2x \cdot x^3 = 2x^4\), \(2x \cdot x^2 = 2x^3\), \(2x \cdot (-30) = -60x\)
Then, multiply \(-1\) with \(x^3\), \(x^2\), and \(-30\):
\(-1 \cdot x^3 = -x^3\), \(-1 \cdot x^2 = -x^2\), \(-1 \cdot (-30) = 30\)

Step2: Combine like terms

Combine the terms with the same power of \(x\):
For \(x^3\) terms: \(2x^3 - x^3 = x^3\)
The other terms remain as they are: \(2x^4\), \(-x^2\), \(-60x\), \(30\)
So the expanded form is \(2x^4 + x^3 - x^2 - 60x + 30\)

Answer:

\(2x^4 + x^3 - x^2 - 60x + 30\)