Question

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

Answer 1

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

1. Distribute \(2x\) to each term in the second polynomial:
\[
2x \cdot 2x^2 = 4x^3
\]
\[
2x \cdot x = 2x^2
\]
\[
2x \cdot (-3) = -6x
\]

2. Now distribute \(5\) to each term in the second polynomial:
\[
5 \cdot 2x^2 = 10x^2
\]
\[
5 \cdot x = 5x
\]
\[
5 \cdot (-3) = -15
\]

3. Now combine all these results:
\[
4x^3 + 2x^2 - 6x + 10x^2 + 5x - 15
\]

4. Combine like terms:
- For \(x^2\): \(2x^2 + 10x^2 = 12x^2\)
- For \(x\): \(-6x + 5x = -x\)

5. So we can now write the polynomial in standard form, combining all the like terms:
\[
4x^3 + 12x^2 - x - 15
\]

Thus, the expanded polynomial in standard form is:
\[
\boxed{4x^3 + 12x^2 - x - 15}
\]