Question

iliana multiplied 3p - 7 and 2p² - 3p - 4. her work is shown in the table.
(3p - 7)(2p² - 3p - 4)
table with rows 3p, -7 and columns 2p², -3p, -4; cells: 3p×2p²=6p³, 3p×(-3p)=-9p², 3p×(-4)=-12p; -7×2p²=-14p², -7×(-3p)=21p, -7×(-4)=28
which is the product?
options: 6p³ + 23p² + 9p + 28; 6p³ - 23p² - 9p + 28; 6p³ - 23p² + 9p + 28; 6p³ + 23p² - 9p + 28

Explanation:

Step1: Identify terms to add

We need to sum the products from the table: \(6p^3\), \(-9p^2\), \(-12p\), \(-14p^2\), \(21p\), and \(28\).

Step2: Combine like terms for \(p^3\)

Only \(6p^3\), so it remains \(6p^3\).

Step3: Combine like terms for \(p^2\)

\(-9p^2 - 14p^2 = -23p^2\).

Step4: Combine like terms for \(p\)

\(-12p + 21p = 9p\).

Step5: Constant term

The constant term is \(28\).

Step6: Form the polynomial

Putting it all together: \(6p^3 - 23p^2 + 9p + 28\).

Answer:

\(6p^3 - 23p^2 + 9p + 28\) (corresponding to the third option: \(6p^3 - 23p^2 + 9p + 28\))