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To Factor vs Factoring Infinitives & Gerunds

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Notes from a Native English Speaker

Infinitives: An infinitive is the base form of a verb, usually preceded by the word "to" (e.g., to swim, to eat, to learn). It can function as a noun, adjective, or adverb in a sentence. Infinitives are often used to express intentions, purposes, desires, or potential actions. Gerunds: A gerund is the -ing form of a verb (e.g., swimming, eating, learning). It’s different from a “present participle” which functions as a verb tense. A gerund can be the subject, object, or complement of a sentence.

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.

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.

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).

Verbs Taking Infinitives/Gerunds as Objects

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.

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.

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.

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.

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.

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.

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

Students should avoid rushing through the process of factoring.

Students should avoid rushing through the process of factoring.

Can you imagine factoring without a calculator?

Can you imagine factoring without a calculator?

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

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.

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.

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