To expand the expression [tex]\((-4x - 5)(-x^2 - x + 4)\)[/tex] and write it in standard form, we need to distribute each term in the first binomial to every term in the second trinomial.
1. Distribute [tex]\(-4x\)[/tex] to each term in [tex]\((-x^2 - x + 4)\)[/tex]:
[tex]\[
(-4x)(-x^2) + (-4x)(-x) + (-4x)(4)
\][/tex]
[tex]\[
4x^3 + 4x^2 - 16x
\][/tex]
2. Distribute [tex]\(-5\)[/tex] to each term in [tex]\((-x^2 - x + 4)\)[/tex]:
[tex]\[
(-5)(-x^2) + (-5)(-x) + (-5)(4)
\][/tex]
[tex]\[
5x^2 + 5x - 20
\][/tex]
3. Combine all the distributed terms:
[tex]\[
4x^3 + 4x^2 - 16x + 5x^2 + 5x - 20
\][/tex]
4. Combine like terms:
[tex]\[
4x^3 + (4x^2 + 5x^2) + (-16x + 5x) - 20
\][/tex]
[tex]\[
4x^3 + 9x^2 - 11x - 20
\][/tex]
So, the polynomial in standard form is:
[tex]\[
\boxed{4x^3 + 9x^2 - 11x - 20}
\][/tex]
