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Grade 9 · unit review

Review: Algebra1: Polynomial Expressions

Polynomials combine terms with nonnegative integer variable powers. Their degree describes the highest power, while addition, multiplication and factoring preserve equivalent expressions that can be checked by expansion or substitution.

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Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. What is the degree of 7x^9−8x²+11?
Need a hint?
  • Degree is determined by the greatest variable exponent attached to a nonzero coefficient.
  • The number of terms is not the degree.
2. Add (7x²+3x−1)+(8x²−x+4).
Need a hint?
  • Polynomial addition combines coefficients of identical powers separately.
  • Adding terms does not add their exponents.
3. Expand (x+7)(x+8).
Need a hint?
  • Multiplying binomials requires multiplying each term of one factor by each term of the other.
  • The middle terms usually do not vanish.
4. Factor x²−49.
Need a hint?
  • Opposite middle terms cancel in (u−v)(u+v), leaving u²−v².
  • A difference of squares differs from the square of a difference.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. What is the degree of 9x^11−10x²+13? Candidate answers: (A) 11 (B) 2 (C) 3 (D) 9. 2. Add (9x²+3x−1)+(10x²−x+4). Candidate answers: (A) 19x²+2x+3 (B) 19x²+2x−5 (C) 19x²+4x+3 (D) 19x⁴+2x+3. 3. Expand (x+9)(x+10). Candidate answers: (A) 2x+19 (B) x²+19x+90 (C) x²+90 (D) x²+90x+19. 4. Factor x²−81. Candidate answers: (A) (x−81)(x+1) (B) (x−9)(x+9) (C) (x−9)² (D) x(x−81).

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. 11. The largest exponent with a nonzero coefficient is 11. Coefficient size and the number of terms do not determine degree. 2. 19x²+2x+3. Combine terms with matching powers: (9+10)x²+(3−1)x+(−1+4)=19x²+2x+3. 3. x²+19x+90. Distribute each term: x²+10x+9x+90. Combining the middle terms gives x²+19x+90. 4. (x−9)(x+9). Use u²−v²=(u−v)(u+v) with u=x and v=9. The opposite middle terms cancel when the factors are multiplied.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.