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Lesson · Grade 9 · Mathematics

Polynomials: Terms, Coefficients, Constants and Degree

  • Grade 9
  • Mathematics
  • 1 min 58 s
  • British Columbia
  • BC9-MA-10

Using 3x² − 5x + 7, the video splits the polynomial into its three terms, keeping each sign with its term, and builds each term from algebra tiles: big squares, pink negative rectangles and small squares. It then names the coefficients 3 and −5, the constant term 7, and the term degrees 2, 1 and 0, so the polynomial has degree 2. It warns against dropping the sign of −5, sorts monomials, binomials and trinomials, and ends on a one-line recap.

Concept: Polynomials: terms, degree, coefficients and constants

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In one sentence

The question this lesson answers

What are the parts of three x squared minus five x plus seven? Let us name each one.

A polynomial is a sum of terms. A term is a number, or a number times a power of x.

Transcript

What the lesson says

What are the parts of three x squared minus five x plus seven? Let us name each one.

A polynomial is a sum of terms. A term is a number, or a number times a power of x.

Split it before each plus or minus sign, and keep the sign with its term: three x squared, negative five x, and seven.

In algebra tiles, a big square is x by x, so it means x squared. Three x squared is three big squares.

A rectangle is x by one, so it means x. Negative five x is five rectangles in the negative colour.

A small square is one by one, so it means one. Seven is seven small squares.

A coefficient is the number that multiplies a variable. Here the coefficients are three and negative five.

A term with no variable is the constant term. Here the constant term is seven.

The degree of a term is the exponent on its variable. Three x squared has degree two. Negative five x has degree one, since x is x to the power one. Seven has no x, so its degree is zero.

The degree of the polynomial is the highest of these, so it has degree two.

A common mistake is dropping the sign. The coefficient of x is negative five, not five.

A monomial has one term, like five x squared. A binomial has two, like x plus four. A trinomial has three, like ours.

So our polynomial is a trinomial of degree two, with coefficients three and negative five, and constant term seven.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Patterns and algebra: operations with polynomials, of degree less than or equal to 2BC9-MA-10

Next: Adding Polynomials by Collecting Like Terms

The outcomes and strands follow the British Columbia curriculum.

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