9th grade · Math · Unit 10 of 16
Polynomials
Add, subtract, expand and evaluate
What your child practices
Naming polynomials by terms and degree, combining like terms, subtracting polynomials, multiplying and dividing by a constant, and substituting values for x.
Texas Essential Knowledge and Skills (TEKS) teks student expectation: A.10(A); A.10(B) · adding, subtracting and multiplying polynomials
How we explain it
Children can open this short lesson before they practice.
- Like terms have the same variable and exponent. Only combine those.
- To add polynomials, combine like terms.
- To expand, multiply each term inside the brackets: a(b + c) = ab + ac.
Example: (3x + 2) + (x − 5) = ? Combine the x terms: 3x + x = 4x. Combine the numbers: 2 − 5 = −3. Answer: 4x − 3
Polynomials in Texas
In the Texas Essential Knowledge and Skills (TEKS), this is unit 10 of 16 in 9th grade Math, after Two-Way Tables & Causation and before Expressions.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Source: Texas Education Agency (TEA)
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Classify the polynomial 3x² + 5x + 8 by its number of terms.
- trinomial
- binomial
- monomial
- quadrinomial
trinomial
Hint: Count the terms: 3x² + 5x + 8 has 3. One term is a monomial, two a binomial, three a trinomial.
Question 2
What is the degree of −7x² + 4x + 6?
answer box
2
Hint: The degree is the highest exponent on the variable.
Question 3
Add: (−6x² + 5x + 2) + (−4x² − 5x − 1)
- −8x² + 1
- −10x² − 2x + 1
- −10x² + 1
- −9x² + 1
- −10x² + 2x + 1
−10x² + 1
Hint: Add the like terms: -6 + (−4) = -10, 5 + (−5) = 0, 2 + (−1) = 1. The result is −10x² + 1.
Question 4
Subtract: (−x² + 7x + 1) − (4x² − 9x + 5)
- −4x² + 16x − 4
- −5x² + 16x − 4
- 3x² − 2x + 6
- −5x² − 2x + 6
- −7x² + 16x − 4
−5x² + 16x − 4
Hint: Subtracting a polynomial changes the sign of every term in it: −x² + 7x + 1 + (−4x² + 9x − 5). Then combine like terms to get −5x² + 16x − 4.
Question 5
Expand: −6(−5x² − 2x + 5)
- 30x² − 2x + 5
- 30x² + 12x + 5
- 30x² + 12x − 30
- −11x² − 8x − 1
- 30x² − 13x − 30
30x² + 12x − 30
Hint: Multiply every term inside the brackets by −6: 30x² + 12x − 30.
Question 6
Divide: (−9x² + 18x − 18) ÷ 3
- 2x² + 6x − 6
- −9x² + 18x − 6
- −3x² + 6x − 6
- −3x² + 18x − 18
- −3x² + 6x − 7
−3x² + 6x − 6
Hint: Divide every term by 3: -18, 18, -9 ÷ 3. The result is −3x² + 6x − 6.