Find the Common Factor in 5y²+9y: Basic Term Analysis

Q: Why isn't 5 the common factor if it's in the first term?

A common factor must appear in all terms. Since 5 only appears in $ 5y^2 $ but not in $ 9y $, it's not common to both terms.

Q: What if there are numbers and variables as common factors?

Factor out both! For example, in $ 6x^2 + 12x $, the common factor is $ 6x $ because both 6 and x appear in every term.

Q: Can I factor out 1 as a common factor?

Technically yes, but it's not helpful! Since 1 × anything = that thing, factoring out 1 doesn't simplify the expression. Look for more meaningful common factors.

Q: What if the expression has no common factors?

Some expressions are already in simplest form! For example, $ 3x + 7y $ has no common factors, so it cannot be factored further.

Common Factor Identification with Polynomial Terms

We factored the expression

$5y^2+9y$ into its basic terms:

$5\cdot y\cdot y+9\cdot y$

What common factor can be found in these terms?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

We factored the expression

$5y^2+9y$ into its basic terms:

$5\cdot y\cdot y+9\cdot y$

What common factor can be found in these terms?

Step-by-step solution

To factor the expression $5y^2+9y$ , we first write each term as a product of factors:

$5y^2 = 5 \cdot y \cdot \orange y$ and $9y=9\cdot \orange y$ .

We notice that both terms include the factor $y$ . Thus, the common factor is $y$ .

Final Answer

$y$

Key Points to Remember

Essential concepts to master this topic

Factor Rule: Look for variables or numbers appearing in all terms
Technique: Write $5y^2 = 5 \cdot y \cdot y$ and $9y = 9 \cdot y$
Check: Factor out y: $y(5y + 9)$ expands back to original ✓

Common Mistakes

Avoid these frequent errors

Looking for the largest coefficient as common factor
Don't assume the biggest number like 9 is the common factor = wrong factorization! Coefficients 5 and 9 share no common factors except 1. Always look for variables that appear in every term first.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

$$ 4x^2 + 6x $$

FAQ

Everything you need to know about this question

Why isn't 5 the common factor if it's in the first term?

A common factor must appear in all terms. Since 5 only appears in $5y^2$ but not in $9y$ , it's not common to both terms.

What if there are numbers and variables as common factors?

Factor out both! For example, in $6x^2 + 12x$ , the common factor is $6x$ because both 6 and x appear in every term.

How do I know if I found all the common factors?

After factoring, the remaining terms inside the parentheses should have no more common factors. In $y(5y + 9)$ , the terms 5y and 9 share no common factors.

Can I factor out 1 as a common factor?

Technically yes, but it's not helpful! Since 1 × anything = that thing, factoring out 1 doesn't simplify the expression. Look for more meaningful common factors.

What if the expression has no common factors?

Some expressions are already in simplest form! For example, $3x + 7y$ has no common factors, so it cannot be factored further.

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