To find the polynomial in standard form for the given expression [tex]\(3x(x^2 - 5x + 6)\)[/tex], follow these steps:
1. Distribute [tex]\(3x\)[/tex] through each term in the polynomial [tex]\(x^2 - 5x + 6\)[/tex]:
[tex]\[
3x \cdot (x^2) + 3x \cdot (-5x) + 3x \cdot 6
\][/tex]
2. Perform the multiplication for each term:
[tex]\[
3x \cdot x^2 = 3x^3
\][/tex]
[tex]\[
3x \cdot (-5x) = -15x^2
\][/tex]
[tex]\[
3x \cdot 6 = 18x
\][/tex]
3. Combine these terms to write the polynomial in standard form:
[tex]\[
3x^3 - 15x^2 + 18x
\][/tex]
Thus, the polynomial in standard form for the expression [tex]\(3x(x^2 - 5x + 6)\)[/tex] is:
[tex]\[
3x^3 - 15x^2 + 18x
\][/tex]
