QuestionAugust 24, 2025

2x^2+11x+5 18x^2-18x+4 4x^3-20x^2+9x-45

2x^2+11x+5 18x^2-18x+4 4x^3-20x^2+9x-45
2x^2+11x+5 18x^2-18x+4 4x^3-20x^2+9x-45

Solution
3.1(310 votes)

Answer

(2x + 1)(x + 5); 2(3x - 1)(3x - 2); (x - 5)(4x^2 + 9) Explanation 1. Factor the first polynomial Factor 2x^2 + 11x + 5 using trial and error or the quadratic formula. The factors are (2x + 1)(x + 5). 2. Factor the second polynomial Factor 18x^2 - 18x + 4. First, factor out the greatest common factor, which is 2: 2(9x^2 - 9x + 2). Then factor 9x^2 - 9x + 2 to get (3x - 1)(3x - 2). 3. Factor the third polynomial Factor 4x^3 - 20x^2 + 9x - 45. Use grouping: (4x^3 - 20x^2) + (9x - 45). Factor each group: 4x^2(x - 5) + 9(x - 5). Combine to get (x - 5)(4x^2 + 9).

Explanation

1. Factor the first polynomial<br /> Factor $2x^2 + 11x + 5$ using trial and error or the quadratic formula. The factors are $(2x + 1)(x + 5)$.<br /><br />2. Factor the second polynomial<br /> Factor $18x^2 - 18x + 4$. First, factor out the greatest common factor, which is 2: $2(9x^2 - 9x + 2)$. Then factor $9x^2 - 9x + 2$ to get $(3x - 1)(3x - 2)$.<br /><br />3. Factor the third polynomial<br /> Factor $4x^3 - 20x^2 + 9x - 45$. Use grouping: $(4x^3 - 20x^2) + (9x - 45)$. Factor each group: $4x^2(x - 5) + 9(x - 5)$. Combine to get $(x - 5)(4x^2 + 9)$.
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