Grade 9 Algebra — Expressions Practice — Easy

Question 1 of 26Score 0/0Easy

Question 1 of 26: What makes an expression a polynomial?

More Grade 9 practice

Keep going: Read the lesson: Polynomial Expressions Scientific Notation Exponent Rules
Answer key for parents & teachers (26 questions)
  1. What makes an expression a polynomial? — Variables with non-negative integer exponents and real coefficients. Polynomials have variables with whole-number (non-negative integer) exponents and real number coefficients.
  2. What is the degree of 7x³ − 2x + 1? — 3. Degree = highest exponent = 3 (from the term 7x³).
  3. How many terms does 4x² − 5x + 3 have? — 3. Three terms separated by + and −: 4x², −5x, and 3.
  4. What is the leading coefficient of 3x⁵ − 8x² + 2? — 3. The leading coefficient is the coefficient of the highest-degree term. Highest degree is 5, with coefficient 3.
  5. A polynomial with degree 2 is called a: — Quadratic. Degree 1 = linear; degree 2 = quadratic; degree 3 = cubic; degree 4 = quartic.
  6. Factor out the GCF from 12x³ + 8x². — 4x²(3x + 2). GCF of 12x³ and 8x² is 4x². 12x³ ÷ 4x² = 3x; 8x² ÷ 4x² = 2. Result: 4x²(3x + 2).
  7. What is the constant term of x⁴ − 3x² + 7x − 11? — −11. The constant term has no variable — it is the term with x⁰. Here that is −11.
  8. Factor x² + 7x + 12. — (x+3)(x+4). Need two numbers that multiply to 12 and add to 7: 3 and 4. Answer: (x+3)(x+4).
  9. What are the roots of (x−2)(x+5) = 0? — x = 2 and x = −5. Zero Product Property: x−2=0 → x=2; x+5=0 → x=−5.
  10. Factor x² − 9. — (x−3)(x+3). Difference of squares: a²−b² = (a−b)(a+b). x²−9 = x²−3² = (x−3)(x+3).
  11. In factoring x² + bx + c, you need two numbers that: — Multiply to c and add to b. For x² + bx + c = (x+p)(x+q), you need p·q = c and p+q = b.
  12. Factor x² − 10x + 25. — (x−5)(x−5). This is a perfect square trinomial: x²−10x+25 = (x−5)². Check: (−5)+(−5)=−10 ✓, (−5)(−5)=25 ✓.
  13. Which rule says xᵃ · xᵇ = xᵃ⁺ᵇ? — Product Rule. The Product Rule: when multiplying like bases, add the exponents.
  14. What is x⁰ (when x ≠ 0)? — 1. Any non-zero number raised to the zero power equals 1. x⁰ = 1.
  15. Simplify x⁴ · x³. — x⁷. Product rule: add exponents. x⁴ · x³ = x^(4+3) = x⁷.
  16. What is x⁻³ equal to? — 1/x³. Negative exponent means reciprocal: x⁻³ = 1/x³.
  17. Simplify (x³)². — x⁶. Power rule: multiply exponents. (x³)² = x^(3·2) = x⁶.
  18. Simplify x⁷ ÷ x³. — x⁴. Quotient rule: subtract exponents. x⁷ ÷ x³ = x^(7−3) = x⁴.
  19. Which law says (xᵃ)ᵇ = xᵃᵇ? — Power Rule. The Power Rule: raise a power to a power by multiplying the exponents.
  20. To add two polynomials, you: — Combine like terms. Adding polynomials: group and combine like terms (same variable, same exponent).
  21. What is (3x + 2) + (x − 5)? — 4x − 3. (3x + x) + (2 − 5) = 4x − 3.
  22. What is (5x²) − (2x²)? — 3x². 5x² − 2x² = (5−2)x² = 3x².
  23. FOIL stands for: — First, Outside, Inside, Last. FOIL = First, Outside, Inside, Last — the four products when multiplying two binomials.
  24. Expand (x + 4)(x + 2) using FOIL. — x² + 6x + 8. F: x², O: 2x, I: 4x, L: 8. Sum: x² + 6x + 8.
  25. What is (4x − 1) − (2x + 3)? — 2x − 4. Distribute the minus: 4x−1−2x−3 = (4−2)x + (−1−3) = 2x−4.
  26. What is (x + 7)(x − 7)? — x² − 49. Difference of squares: (a+b)(a−b) = a²−b². (x+7)(x−7) = x²−49.