Mathematics 2010 JAMB Past Questions - Question 15: Factorize completely x³ + 3x² - 10x/2x² -8

Correct Answer

B

Explanation

x³ + 3x² - 10x/2x² -8= x(x² - 3x -10 )/2(x² - 2²) = x(x-5)(x+2)/2(x-2)(x+2)= x(x -5)/2(x – 2) To factorize the expression x³ + 3x² - 10x / 2x² - 8, we can start by factoring the numerator and denominator separately.Numerator: x³ + 3x² - 10xWe can factor out an x from each term:x(x² + 3x - 10)Now, we can factor the quadratic expression inside the parentheses:x(x + 5)(x - 2)Denominator: 2x² - 8We can factor out a 2 from each term:2(x² - 4)Now, we can factor the quadratic expression inside the parentheses as the difference of squares:2(x + 2)(x - 2)Putting it all together, the expression can be fully factorized as:(x(x + 5)(x - 2)) / (2(x + 2)(x - 2))Notice that (x - 2) appears in both the numerator and denominator, so it can be canceled out:(x(x + 5)) / (2(x + 2))Therefore, the fully factorized form of the expression x³ + 3x² - 10x / 2x² - 8 is (x(x + 5)) / (2(x + 2)).