Find the Coefficient of x in y=3x²+10-x: Identifying Linear Terms

Q: Why do I need to rearrange the equation first?

The standard form $ ax^2 + bx + c $ makes it easier to identify coefficients. When terms are mixed up like $ 3x^2 + 10 - x $, you might miss the negative sign!

Q: What if there's no x term in the equation?

If there's no $ x $ term, then b = 0. For example, in $ y = 2x^2 + 5 $, we have $ a = 2 $, $ b = 0 $, and $ c = 5 $.

Q: How do I handle terms like -x versus -1x?

They're the same thing! When you see -x, it's the same as -1x. The coefficient is -1, not 1. Don't forget that invisible coefficient!

Q: What's the difference between the coefficient and the term?

The term is the whole expression like $ -x $, while the coefficient is just the number part: -1. Think of it as the number that multiplies the variable.

Q: Can I check my answer somehow?

Yes! Substitute a simple value like $ x = 1 $ into both the original equation $ 3x^2 + 10 - x $ and the rearranged form $ 3x^2 - x + 10 $. You should get the same result!

Quadratic Coefficients with Negative Linear Terms

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $b$ in the equation

$y=3x^2+10-x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's find the coefficient B.

00:10 We're going to use the quadratic formula for this.

00:20 Remember, B is the coefficient of the X term.

00:26 First, let's arrange our equation to fit the formula.

00:30 Now, compare the formula with our equation to find the coefficients.

00:41 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $b$ in the equation

$y=3x^2+10-x$

Step-by-step solution

To solve this problem, we need to identify the coefficient of $x$ in the given quadratic equation. The equation given is $y = 3x^2 + 10 - x$ . Let’s rearrange this equation to match the standard form of a quadratic equation $ax^2 + bx + c$ .

The given equation can be rewritten as:

$y = 3x^2 - x + 10$

Here, we can identify the coefficients:

$a = 3$ (for $x^2$ )
$b = -1$ (for $x$ )
$c = 10$ (the constant term)

Therefore, the value of $b$ , the coefficient of $x$ , is $-1$ .

Final Answer

$b=-1$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Rearrange equation to $ax^2 + bx + c$ order
Technique: Rewrite $3x^2 + 10 - x$ as $3x^2 - x + 10$
Check: Count terms: $a = 3$ , $b = -1$ , $c = 10$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign when identifying coefficients
Don't read -x as having coefficient +1 = wrong answer b = 1! The minus sign belongs to the coefficient, not as a separate operation. Always include the sign when identifying coefficients: -x means b = -1.

Practice Quiz

Test your knowledge with interactive questions

Solve the following equation:

$$ 2x^2-10x-12=0 $$

FAQ

Everything you need to know about this question

Why do I need to rearrange the equation first?

The standard form $ax^2 + bx + c$ makes it easier to identify coefficients. When terms are mixed up like $3x^2 + 10 - x$ , you might miss the negative sign!

What if there's no x term in the equation?

If there's no $x$ term, then b = 0. For example, in $y = 2x^2 + 5$ , we have $a = 2$ , $b = 0$ , and $c = 5$ .

How do I handle terms like -x versus -1x?

They're the same thing! When you see -x, it's the same as -1x. The coefficient is -1, not 1. Don't forget that invisible coefficient!

What's the difference between the coefficient and the term?

The term is the whole expression like $-x$ , while the coefficient is just the number part: -1. Think of it as the number that multiplies the variable.

Can I check my answer somehow?

Yes! Substitute a simple value like $x = 1$ into both the original equation $3x^2 + 10 - x$ and the rearranged form $3x^2 - x + 10$ . You should get the same result!

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