Question

Match the equations to its equivalent in the options:

y = x^2 - 1x - 20

y = (x + 8) (x + 11)

Options:

y = x^2 + 8x + 11

y = x^2 + 19x + 88

Answer 1

Let's start by analyzing the first equation given:

1. **Equation to match**:
\[
y = x^2 - 1x - 20
\]

2. **Factored form**:
\[
y = (x + 8)(x + 11)
\]

Now we will expand the factored form \(y = (x + 8)(x + 11)\):

\[
y = x^2 + 11x + 8x + 88
\]
\[
y = x^2 + 19x + 88
\]

Next, we can simplify the original equation \(y = x^2 - 1x - 20\) to confirm if it is equivalent to the expanded terms.

Let's set the right-hand side of the original equation equal to zero and factor it:

To factor \(x^2 - 1x - 20\), we look for two numbers that multiply to \(-20\) (the constant term) and add to \(-1\) (the coefficient of \(x\)). These numbers are \(4\) and \(-5\):

\[
y = (x - 5)(x + 4)
\]

However, this does not match with the original factored form \(y = (x + 8)(x + 11)\).

So we can also calculate both polynomial forms.

Comparing both:

The right expanded form of \( (x + 8)(x + 11) = x^2 + 19x + 88 \) matches one of the options.

In summary:

- The equivalent of \(y = (x + 8)(x + 11)\) is:
\[
y = x^2 + 19x + 88
\]

Thus, the match is:

\[
y = x^2 - 1x - 20 \text{ does not match any of the options.}
\]
\[
y = (x + 8)(x + 11) \text{ matches with } y = x^2 + 19x + 88.
\]

So the only matched option is:
\[
y = x^2 + 19x + 88
\]