Mathematics 2014 JAMB Past Questions - Question 13: Factorise 2y² -15xy+18x².

Correct Answer

C

Explanation

2ysup2 - 15xy + 18xsup22ysup2 - 12xy - 3xy + 18xsup22y (y-6x) -3x (y-6x)To factorize the expression 2y² - 15xy + 18x², we can look for two binomial factors that, when multiplied, give us the original expression. The general form of the expression is:ay² + bxy + cx²In this case, a = 2, b = -15, and c = 18. We need to find two binomial factors in the form of (dy + ex) that satisfy the equation:(2y² - 15xy + 18x²) = (dy + ex)(fy + gx)To factorize the expression, we need to find the values of d, e, f, and g. Let's proceed:The product of the first terms in each binomial is dfy², which should be equal to 2y². Therefore, d * f = 2.The product of the last terms in each binomial is egx², which should be equal to 18x². Therefore, e * g = 18.Now, let's consider the middle term, -15xy. It can be obtained by adding the cross products of the outer and inner terms:Outer terms: d * gx * y = dgyInner terms: e * fy * x = efxyThe sum of these two terms should be equal to -15xy. Therefore, dg + ef = -15.Now, let's find the values of d, e, f, and g that satisfy these equations:From the equation d * f = 2, the possible values for d and f are (1, 2) or (2, 1).From the equation e * g = 18, the possible values for e and g are (1, 18), (2, 9), (3, 6), or (6, 3).Now, let's check the equation dg + ef = -15 for each combination of values:For d = 1 and f = 2:1g + e2 = -15g + 2e = -15By trying different values for e and g, we find that e = -3 and g = -9 satisfy the equation.Therefore, the binomial factors are (y - 3x) and (2y - 9x).Hence, the factored form of 2y² - 15xy + 18x² is:(2y - 9x)(y - 2x)(2y-3x) (y-6x)