When and How to Use Each Expression?

Get a sense of when and how each expression can be used through the following examples!

To factor (Infinitive)

Purpose or Intention: Use the infinitive "to factor" when you want to express a purpose, intention, desire, or potential action

Example

I need to factor in all the variables to solve this equation.

Factoring (Gerund)

Activity or Experience: Use the gerund "factoring" when you want to refer to the activity itself or the experience as a noun.

Example

Factoring can simplify complex algebraic expressions.

Where can infinitives/gerunds be placed in a sentence?

To factor (Infinitive)

1Subject
To factor is an important step in solving quadratic equations.
To factor is an important step in solving quadratic equations.
- "*To factor*" serves as the subject of the sentence.
- Infinitive phrase (subject) + verb (is) + noun phrase (an important step in solving quadratic equations).
2Object
She wants me to factor in the cost of materials.
She wants me to factor in the cost of materials.
- "Me *to factor* in the cost of materials" is the object of the verb "wants."
- Noun (She) + verb (wants) + noun phrase (me *to factor* in the cost of materials).
3Adjective Modifier
We need a calculator to factor large numbers.
We need a calculator to factor large numbers.
- "*To factor* large numbers" modifies the noun "calculator."
- Noun (We) + verb (need) + noun phrase (a calculator *to factor* large numbers).

Factoring (Gerund)

1Subject
Factoring is an essential skill in algebra.
Factoring is an essential skill in algebra.
- "*Factoring*" is the subject of the sentence.
- Gerund (subject) + verb (is) + noun phrase (an essential skill in algebra).
2Object
I enjoy factoring polynomials in my spare time.
I enjoy factoring polynomials in my spare time.
- "*Factoring* polynomials" is the object of the verb "enjoy."
- Noun (I) + verb (enjoy) + gerund (*factoring* polynomials).
3Object of Preposition
She has a talent for factoring complex equations.
She has a talent for factoring complex equations.
- "For *factoring* complex equations" is the object of the preposition "for."
- Noun phrase (She) + verb (has) + noun phrase (a talent for *factoring* complex equations).

The following are verbs that can take only the base form of the verb (infinitive), only the -ing form (gerund), or both.

Verbs Taking Infinitives as Objects

Example

He plans to factor in the exchange rate when making international investments.

We decided to factor in the time it takes to complete the project.

They hope to factor in the impact of climate change on their business strategy.

She wants to factor in the opinions of all team members before making a decision.

He refuses to factor in any shortcuts or compromises in his work.

Verbs Taking Gerunds as Objects

Example

Math teachers often recommend factoring as a problem-solving technique.

Students should avoid rushing through the process of factoring.

Can you imagine factoring without a calculator?

They consider factoring as a fundamental skill for success in higher-level math courses.

You need to practice factoring different types of equations to improve your skills.

Verbs Taking Both Infinitives and Gerunds as Objects

Example

I like to factor in real-life scenarios when teaching math. I like factoring complex equations.

I like to factor in real-life scenarios when teaching math.

She started to factor at an early age. She started factoring algebraic expressions at an early age.

She started to factor at an early age.

We began to factor quadratic equations in class. We began factoring quadratic equations in class.

We began to factor quadratic equations in class.