expand the expression to a polynomial in standard form

Question

(x-9)(x^2+x+2)

dont get anoter wrong please

Answer 1

To expand the expression \((x-9)(x^2+x+2)\), we can use the distributive property (also known as the FOIL method for binomials). Here’s how to do it step by step:

1. Distribute \(x\) across each term in the polynomial \((x^2 + x + 2)\): \[ x \cdot (x^2 + x + 2) = x^3 + x^2 + 2x \]

2. Next, distribute \(-9\) across each term in the polynomial \((x^2 + x + 2)\): \[ -9 \cdot (x^2 + x + 2) = -9x^2 - 9x - 18 \]

3. Now, combine all the results together: \[ x^3 + x^2 + 2x - 9x^2 - 9x - 18 \]

4. Combine like terms:

   • The \(x^2\) terms: \(x^2 - 9x^2 = -8x^2\)
   • The \(x\) terms: \(2x - 9x = -7x\)

So, combining everything together gives: \[ x^3 - 8x^2 - 7x - 18 \]

Thus, the polynomial in standard form is: \[ \boxed{x^3 - 8x^2 - 7x - 18} \]