1.) (x² + 3x + 10) = (x+2)2.)(5x²-2x+1)=(x+2)3२3.) (׳² + 4x² -×-25) ÷ (x+5)24.) (׳+ 35+9x²+ 13×) = (x-5)435.) (2x-9׳ +9x²+5x-1)= (2x+1)
Answer (1)
Answer:I hope it helpsStep-by-step explanation:Here are the solutions using the long division method for each problem: 1) (x² + 3x + 10) ÷ (x + 2) plaintext
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x + 1 x + 2 | x² + 3x + 10 -(x² + 2x) ---------------- x + 10 -(x + 2) ---------------- 8 Therefore, (x² + 3x + 10) ÷ (x + 2) = x + 1 with a remainder of 8. 2) (5x² - 2x + 1) ÷ (x + 2) plaintext
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5x - 12x + 2 | 5x² - 2x + 1 -(5x² + 10x) ---------------- -12x + 1 -(-12x - 24) ---------------- 25 Therefore, (5x² - 2x + 1) ÷ (x + 2) = 5x - 12 with a remainder of 25. 3) (x³ + 4x² - x - 25) ÷ (x + 5) plaintext
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x² - x + 4x + 5 | x³ + 4x² - x - 25 -(x³ + 5x²) ---------------- -x² - x -(-x² - 5x) ---------------- 4x - 25 -(4x + 20) ---------------- -45 Therefore, (x³ + 4x² - x - 25) ÷ (x + 5) = x² - x + 4 with a remainder of -45. 4) (x³ + 35 + 9x² + 13x) ÷ (x - 5) - Rearrange the terms in descending order of exponents:(x³ + 9x² + 13x + 35) ÷ (x - 5) plaintext
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x² + 14x + 87x - 5 | x³ + 9x² + 13x + 35 -(x³ - 5x²) ---------------- 14x² + 13x -(14x² - 70x) ---------------- 83x + 35 -(83x - 415) ---------------- 450 Therefore, (x³ + 35 + 9x² + 13x) ÷ (x - 5) = x² + 14x + 87 with a remainder of 450. 5) (2x⁴ - 9x³ + 9x² + 5x - 1) ÷ (2x + 1) plaintext
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x³ - 5x² + 7x - 12x + 1 | 2x⁴ - 9x³ + 9x² + 5x - 1 -(2x⁴ + x³) ---------------- -10x³ + 9x² -(-10x³ - 5x²) ---------------- 14x² + 5x -(14x² + 7x) ---------------- -2x - 1 -(-2x - 1) ---------------- 0 Therefore, (2x⁴ - 9x³ + 9x² + 5x - 1) ÷ (2x + 1) = x³ - 5x² + 7x - 1 with a remainder of 0.
