Below you will find example sentences with "leading coefficient". The examples show how this phrase is used in natural context and which words often surround it.

Leading Coefficient in a sentence

Corpus data

  • Displayed example sentences: 7
  • Discovered as a combination around: leading
  • Corpus frequency in the collocation scan: 6
  • Phrase length: 2 words
  • Average sentence length: 27.3 words

Words in this phrase

leading coefficient

Meanings of words in this phrase

  • leading can mean: present participle and gerund of lead Common word
  • coefficient can mean: Cooperating. Less frequent word

Sentence profile

  • Phrase position: 2 start, 3 middle, 2 end
  • Sentence types: 7 statements, 0 questions, 0 exclamations

Usage patterns

These patterns show short text windows around the phrase in the example sentences:

is the leading coefficient of the 2× by its leading coefficient we get 1× by the leading coefficient one substitutes 1× called the leading coefficient of the 1× called the leading coefficient or pivot 1× have a leading coefficient 1× is the leading coefficient and are 1× substitutes the leading coefficient by 1 1×

Sentence openings and endings

Common sentence openings:

definition in terms 1× dividing by its 1× echelon form main 1× for the largest 1× reduced quadratic equation 1× the leading coefficient 1×

Common sentence endings:

a leading coefficient 1× coefficient is one 1× of that row 1× of the determinant 1× of the polynomial 1× some splitting field 1×

Context words

These words often appear near this phrase in the example sentences:

row 7× roots 4× polynomial 3× first 2× dividing 2× determinant 2× quadratic 2× equation 2× third 1× last 1× division 1× defined 1×

Related phrases

leading provider leading cause

Phrases around this combination

Other phrases discovered around leading:

leading cause 7×

Just before it in the phrase index:

leading cause leadership team leadership skills leadership roles leader sir leader rachel

Just after it in the phrase index:

leading provider league baseball league champions league cup league opener league soccer

Other phrases with the same pattern

Same start:

leading provider leading cause

Corpus analysis

  • The phrase "leading coefficient" has 2 words and usually appears in the middle in these examples. The average sentence has 27.3 words and is mostly made up of statements.
  • Around this phrase, patterns and context words such as is the leading coefficient of the, by its leading coefficient we get, row, roots and polynomial stand out.
  • In the phrase index, this combination connects with leading provider, leading cause and leading cause, linking the page to nearby combinations.

Example types with leading coefficient

This selection groups the examples by length and sentence type, making usage of the full phrase easier to scan:

Short example sentences

For the largest with (if any), is called the leading coefficient of the polynomial. (14 words)

Reduced quadratic equation It is sometimes convenient to reduce a quadratic equation so that its leading coefficient is one. (19 words)

Dividing by its leading coefficient, we get another polynomial q(x) which has roots if and only if p(x) has roots. (22 words)

Longer example sentences

The leading coefficient of the first row is 1; 2 is the leading coefficient of the second row; 4 is the leading coefficient of the third row, and the last row does not have a leading coefficient. (37 words)

However, as the division is not always defined in such a ring, instead of dividing the determinant by the leading coefficient, one substitutes the leading coefficient by 1 in the first column of the determinant. (35 words)

Echelon form main For each row in a matrix, if the row does not consist of only zeros, then the left-most non-zero entry is called the leading coefficient (or pivot) of that row. (35 words)

Example sentences (7)

The leading coefficient of the first row is 1; 2 is the leading coefficient of the second row; 4 is the leading coefficient of the third row, and the last row does not have a leading coefficient.

However, as the division is not always defined in such a ring, instead of dividing the determinant by the leading coefficient, one substitutes the leading coefficient by 1 in the first column of the determinant.

Definition In terms of the roots, the discriminant is given by : where is the leading coefficient and are the roots (counting multiplicity ) of the polynomial in some splitting field.

Dividing by its leading coefficient, we get another polynomial q(x) which has roots if and only if p(x) has roots.

Echelon form main For each row in a matrix, if the row does not consist of only zeros, then the left-most non-zero entry is called the leading coefficient (or pivot) of that row.

For the largest with (if any), is called the leading coefficient of the polynomial.

Reduced quadratic equation It is sometimes convenient to reduce a quadratic equation so that its leading coefficient is one.