Question

Expand the expression to a polynomial in standard form:
left parenthesis, 3, x, minus, 5, right parenthesis, left parenthesis, x, squared, plus, x, plus, 5, right parenthesis
(3x−5)(x
2
+x+5)

Answer 1

To expand the expression \((3x - 5)(x^2 + x + 5)\), we can use the distributive property (also known as the FOIL method for binomials).

1. Distribute \(3x\) to each term in \((x^2 + x + 5)\):
\[
3x \cdot x^2 = 3x^3
\]
\[
3x \cdot x = 3x^2
\]
\[
3x \cdot 5 = 15x
\]

2. Now distribute \(-5\) to each term in \((x^2 + x + 5)\):
\[
-5 \cdot x^2 = -5x^2
\]
\[
-5 \cdot x = -5x
\]
\[
-5 \cdot 5 = -25
\]

3. Combine all these results:
\[
3x^3 + 3x^2 + 15x - 5x^2 - 5x - 25
\]

4. Now combine like terms:
- The \(x^2\) terms: \(3x^2 - 5x^2 = -2x^2\)
- The \(x\) terms: \(15x - 5x = 10x\)

5. Write the final expression in standard form:
\[
3x^3 - 2x^2 + 10x - 25
\]

Thus, the expanded expression in standard form is:
\[
\boxed{3x^3 - 2x^2 + 10x - 25}
\]