Transform f(x)=(x+3)(-x-4) to Standard Polynomial Form

Q: Why is the x² term negative in the final answer?

Because x times (-x) equals -x²! The first term of the second factor is negative, so when you multiply x by (-x), you get a negative quadratic term.

Q: How do I keep track of all the negative signs?

Write each multiplication step separately: x(-x), x(-4), 3(-x), 3(-4). Remember that positive × negative = negative in every case.

Q: What if I get a positive x² term instead?

Check your signs! The most common error is writing $ x \cdot (-x) = x^2 $ instead of $ x \cdot (-x) = -x^2 $. Always multiply signs first.

Q: Can I use a different method besides FOIL?

Yes! You can use the distributive property: distribute (x+3) to both terms in (-x-4). Either method works as long as you handle the signs correctly.

Q: How do I combine like terms at the end?

Group terms with the same variable power: -4x and -3x are both x terms, so -4x + (-3x) = -7x. The constant term -12 stands alone.

Polynomial Expansion with Negative Coefficients

Find the standard representation of the following function

$f(x)=(x+3)(-x-4)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify to the standard representation of the function

00:04 Open parentheses properly, multiply each factor by each factor

00:17 Group the factors

00:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the standard representation of the following function

$f(x)=(x+3)(-x-4)$

Step-by-step solution

To find the standard form of the given quadratic function $f(x) = (x+3)(-x-4)$ , we will expand it using the distributive property.

Step 1: Expand the product.
Using the distributive property (or FOIL method):

$f(x) = (x+3)(-x-4)$

Apply distribution:
First: $x \cdot -x = -x^2$
Outside: $x \cdot -4 = -4x$
Inside: $3 \cdot -x = -3x$
Last: $3 \cdot -4 = -12$

Step 2: Combine all terms together:

$f(x) = -x^2 - 4x - 3x - 12$

Step 3: Simplify by combining like terms:
Combine the $x$ terms:

$f(x) = -x^2 - 7x - 12$

Therefore, the standard representation of the function is $f(x) = -x^2 - 7x - 12$ .

The correct choice from the given options is choice 4.

$f(x)=-x^2-7x-12$

Final Answer

$f(x)=-x^2-7x-12$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Apply FOIL to multiply each term systematically
Technique: x(-x) = -x², x(-4) = -4x, 3(-x) = -3x, 3(-4) = -12
Check: Verify by substituting x = 0: (0+3)(-0-4) = 3(-4) = -12 ✓

Common Mistakes

Avoid these frequent errors

Incorrectly handling negative signs during multiplication
Don't forget that x × (-x) = -x² and positive × negative = negative! Missing or flipping signs leads to completely wrong coefficients. Always track each sign carefully through every multiplication step.

Practice Quiz

Test your knowledge with interactive questions

Create an algebraic expression based on the following parameters:

$$ a=3,b=0,c=-3 $$

FAQ

Everything you need to know about this question

Why is the x² term negative in the final answer?

Because x times (-x) equals -x²! The first term of the second factor is negative, so when you multiply x by (-x), you get a negative quadratic term.

How do I keep track of all the negative signs?

Write each multiplication step separately: x(-x), x(-4), 3(-x), 3(-4). Remember that positive × negative = negative in every case.

What if I get a positive x² term instead?

Check your signs! The most common error is writing $x \cdot (-x) = x^2$ instead of $x \cdot (-x) = -x^2$ . Always multiply signs first.

Can I use a different method besides FOIL?

Yes! You can use the distributive property: distribute (x+3) to both terms in (-x-4). Either method works as long as you handle the signs correctly.

How do I combine like terms at the end?

Group terms with the same variable power: -4x and -3x are both x terms, so -4x + (-3x) = -7x. The constant term -12 stands alone.

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Transform f(x)=(x+3)(-x-4) to Standard Polynomial Form

Polynomial Expansion with Negative Coefficients

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is the x² term negative in the final answer?

How do I keep track of all the negative signs?

What if I get a positive x² term instead?

Can I use a different method besides FOIL?

How do I combine like terms at the end?

🌟 Unlock Your Math Potential

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