1. The term with number without variable is called the **Constant Term**. 2. The function $y = x^4 + 1$ is a **Quartic Function** because the highest power of $x$ is 4. 3. The NOT polynomial function is the one with non-polynomial form; options A ($f(x) = ax + b$), C ($f(x) = ax^2 + bx + c$), and D ($P(x) = ax^4 + bx^3 + cx^4 + dx + e$) are polynomials, but B ($(x) = (x)q(x)$) does not specify polynomial form clearly and may not be a polynomial, so **B** is NOT polynomial. 4. Given $f(x) = x - 3n + 2x^2$, to make $f$ degree 4, the term with $x^4$ must appear which is absent, so we assign $n$ so that the polynomial forms degree 4. The answer is **C. 43** (assuming typo indicates this option relates to degree 4 formation). 5. For $f(x) = 5x^3 + x^2 + 3x + 15$: 1) Leading coefficient is coefficient of highest degree term $5x^3$ which is **5**. 6) Constant term is the number without variable, here **15**. 7) Degree of the function is the highest power of $x$, which is **3**. 8) Coefficients are 5, 1, 3; number not a coefficient is **15**. 9. $f(x) = 5x^3 + x^2 + 15$ is a **Cubic Polynomial Function** (highest degree 3). 10. $f(x) = (x + 2)(2x - 8) = 2x^2 - 8x + 4x - 16 = 2x^2 - 4x -16$, degree 2, so **Quadratic Polynomial Function**. 11. For $f(x) = x^n$ to be polynomial, $n$ must be a **positive integer**. 12. Standard form means decreasing order of powers: $f(x) = x^4 - 10x^2 + 9$ is **D**. 13. $f(x) = -2x^4 + 3x^2 + 7x^6 + x + 1$ highest degree is 6, so degree is **6**. 14. $f(x) = x(x - 2)(x + 1)(x + 3)$ zeros are $x=0, 2, -1, -3$, so x-intercepts are **-3, -1, 0, 2**. 15. $f(x) = (x + 4)(x - 1)(x - 5)$ y-intercept at $x=0$ is $(0+4)(0-1)(0-5) = 4 imes (-1) imes (-5) = 20$. 16. Missing text for options to evaluate. 17. Missing function to determine leading coefficient. 18-20. Missing functions to determine degree and standard form. 21. Missing expressions specify $k$ for division remainder problem. 22. Missing condition to evaluate. 23. The measure of intercepted arc is **Twice** the measure of inscribed angle. 24. An inscribed angle intercepting a diameter is a **Right angle**. 25. Inscribed angle is **One-half** the measure of central angle. 26. A line touching circumference at one point is a **Tangent**. 27. Line segment joining two points on circumference is a **Chord**. 28. At a given point on circle, only **One** tangent line. 29. Region bounded by arc and two radii is a **Sector**. 30. TRUE: A secant intersects circle at two points. 31. Region bounded by arc and segment is a **Segment**. 32. Angles $ ext{BTU}$ and $ ext{BEU}$ intercept same arc, so they are **Congruent**. 33. If $ ext{m} ext{∠BTU} = 45^ ext{o}$, then $ ext{m} ext{∠BEU} = 45^ ext{o}$. 34. If $ ext{m} ext{∠BEU} = 20^ ext{o}$, $ ext{m} ext{∠BAU} = 20^ ext{o}$. 35. In circle I, if $ ext{m}∠KIE = 60^ ext{o}$, $ ext{m}$ is **30^ ext{o}** (assuming half-angle or corresponding angle). 36. $ ext{m} ∠KTE = 60^ ext{o}$ 37. Sum of $ ext{m} ∠KTE$ and $ ext{m} ∠KIE$ is **120°**. 38. $ ext{m}$ is **120^ ext{o}**. 39. Inscribed angle 55°, intercepted arc is **110°**. 40. Intercepted arc 140°, inscribed angle is **70°**. 41. Intercepted arc is **2 × (inscribed angle)**. 42. Inscribed angle is **½ × (intercepted arc)**. 43. Sum of inscribed angle and intercepted arc equals 150° when inscribed angle is **50°**. 44. Given $m ext{XŶ} = 150^ ext{o}$ and $m ext{MN̂} = 30^ ext{o}$, $m ext{XPŶ} = 60^ ext{o}$. 45. Arc AB = 60°, radius = 6 cm, area of sector = $(60/360) imes frac{22}{7} imes 6^2 = 6oldsymbol{ imes}oldsymbol{ ext{pi}}$ cm$^2$. 46. Missing figure data for vertex A. 47. Missing figure data for quadrilateral naming. 48. Diameter endpoints $L(-3,-2)$ and $G(9,-6)$ distance is $$ ext{length} = rac{ ext{distance}}{2} = rac{rac{ ext{d}}{2}}{}$$ where distance $d = \\sqrt{(9 - (-3))^2 + (-6 - (-2))^2} = \\sqrt{12^2 + (-4)^2} = \\sqrt{144 + 16} = \\sqrt{160} = 4\\sqrt{10}$, radius $= rac{4 \\sqrt{10}}{2} = 2 \\sqrt{10}$; approximate 6.32. Thus radius length is close to option with value 2 if options given as 2,4, etc., but actual correct radius length is $2\\sqrt{10}$.