Multiple choice question asking which expression equals the product of (x + 2)(x - 3).
The expression (x + 2)(x - 3) is shown, with options for its expanded form: -x - 6, +x - 6, -5x - 6, and -6.
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Show Answer Key & Explanations
Step-by-step solution for: Integrated math 2 | Khan Academy
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Show Answer Key & Explanations
Step-by-step solution for: Integrated math 2 | Khan Academy
Let's solve the problem step by step.
We are given the expression:
$$
(x + 2)(x - 3)
$$
We need to expand this product and simplify it.
FOIL stands for:
- First: $x \cdot x = x^2$
- Outside: $x \cdot (-3) = -3x$
- Inside: $2 \cdot x = 2x$
- Last: $2 \cdot (-3) = -6$
Now add them all together:
$$
x^2 - 3x + 2x - 6
$$
$$
x^2 - x - 6
$$
So, the expanded form of $(x + 2)(x - 3)$ is:
$$
x^2 - x - 6
$$
But wait — the options given in your question are:
- $-x - 6$
- $+x - 6$
- $-5x - 6$
- $-6$
These are linear expressions, but our result is a quadratic: $x^2 - x - 6$. That means none of the listed options match the full expansion.
However, perhaps there was a typo or misunderstanding. Let’s double-check: maybe the original problem was asking for something else?
Wait — perhaps the expression was meant to be simplified without the $x^2$ term, or maybe the question was miswritten.
Alternatively, could the question have been asking for the constant term or value at a specific point? But based on what's written, we're asked:
> "Which expression is equal to the product below?"
And the product is $(x+2)(x-3)$, which expands to $x^2 - x - 6$.
But none of the choices match that.
Let’s check if any of the options might be related.
Looking at the options:
- $-x - 6$: This is similar to the linear part of the expansion.
- $+x - 6$: Not matching.
- $-5x - 6$: No.
- $-6$: Just the constant.
But again, none of these are equal to $(x+2)(x-3)$ as a whole.
The correct expansion is:
$$
(x + 2)(x - 3) = x^2 - x - 6
$$
But none of the given options match this.
However, if the question had a typo and was actually asking for the value of the expression when $x = 0$, then:
$$
(0 + 2)(0 - 3) = (2)(-3) = -6
$$
Then the answer would be $-6$, which is one of the options.
Alternatively, if the expression was supposed to be linear, maybe it was meant to be:
$$
(x + 2) + (x - 3) = 2x - 1
$$
But that's not the case.
Or perhaps it was meant to be a difference or simplification of something else.
But based on the current information:
> The product $(x+2)(x-3)$ equals $x^2 - x - 6$
So unless the question is asking for something else (like the constant term), none of the options are correct.
But since $-6$ is an option, and if the question was asking for the value of the expression when $x = 0$, then:
$$
(0 + 2)(0 - 3) = 2 \cdot (-3) = -6
$$
So the answer would be: $-6$
But that depends on context.
---
If the question is asking for the constant term or the value at $x = 0$, then:
$$
\boxed{-6}
$$
Otherwise, the correct algebraic expansion is $x^2 - x - 6$, which is not among the options.
Please confirm if there was a typo or missing context. But based on the choices, the only plausible match is:
$$
\boxed{-6}
$$
(assuming evaluation at $x = 0$)
We are given the expression:
$$
(x + 2)(x - 3)
$$
We need to expand this product and simplify it.
Step 1: Use the distributive property (FOIL method)
FOIL stands for:
- First: $x \cdot x = x^2$
- Outside: $x \cdot (-3) = -3x$
- Inside: $2 \cdot x = 2x$
- Last: $2 \cdot (-3) = -6$
Now add them all together:
$$
x^2 - 3x + 2x - 6
$$
Step 2: Combine like terms
$$
x^2 - x - 6
$$
So, the expanded form of $(x + 2)(x - 3)$ is:
$$
x^2 - x - 6
$$
But wait — the options given in your question are:
- $-x - 6$
- $+x - 6$
- $-5x - 6$
- $-6$
These are linear expressions, but our result is a quadratic: $x^2 - x - 6$. That means none of the listed options match the full expansion.
However, perhaps there was a typo or misunderstanding. Let’s double-check: maybe the original problem was asking for something else?
Wait — perhaps the expression was meant to be simplified without the $x^2$ term, or maybe the question was miswritten.
Alternatively, could the question have been asking for the constant term or value at a specific point? But based on what's written, we're asked:
> "Which expression is equal to the product below?"
And the product is $(x+2)(x-3)$, which expands to $x^2 - x - 6$.
But none of the choices match that.
Let’s check if any of the options might be related.
Looking at the options:
- $-x - 6$: This is similar to the linear part of the expansion.
- $+x - 6$: Not matching.
- $-5x - 6$: No.
- $-6$: Just the constant.
But again, none of these are equal to $(x+2)(x-3)$ as a whole.
Conclusion:
The correct expansion is:
$$
(x + 2)(x - 3) = x^2 - x - 6
$$
But none of the given options match this.
However, if the question had a typo and was actually asking for the value of the expression when $x = 0$, then:
$$
(0 + 2)(0 - 3) = (2)(-3) = -6
$$
Then the answer would be $-6$, which is one of the options.
Alternatively, if the expression was supposed to be linear, maybe it was meant to be:
$$
(x + 2) + (x - 3) = 2x - 1
$$
But that's not the case.
Or perhaps it was meant to be a difference or simplification of something else.
But based on the current information:
> The product $(x+2)(x-3)$ equals $x^2 - x - 6$
So unless the question is asking for something else (like the constant term), none of the options are correct.
But since $-6$ is an option, and if the question was asking for the value of the expression when $x = 0$, then:
$$
(0 + 2)(0 - 3) = 2 \cdot (-3) = -6
$$
So the answer would be: $-6$
But that depends on context.
---
Final Answer (assuming the question is asking for the value at $x=0$, or possibly a typo):
If the question is asking for the constant term or the value at $x = 0$, then:
$$
\boxed{-6}
$$
Otherwise, the correct algebraic expansion is $x^2 - x - 6$, which is not among the options.
Please confirm if there was a typo or missing context. But based on the choices, the only plausible match is:
$$
\boxed{-6}
$$
(assuming evaluation at $x = 0$)
Parent Tip: Review the logic above to help your child master the concept of integrated math 2 worksheet.