Past papers › JAMB 2010 · UTME › Question 15 Question JAMB General Maths 2010 Objective Expressions, formulae & change of subject Quadratics & their graphs Expressions, formulae & change of subject, Quadratics & their graphs
Factorize completely x 3 + 3 x 2 − 10 x 2 x 2 − 8 \dfrac{x^3 + 3x^2 - 10x}{2x^2 - 8} 2 x 2 − 8 x 3 + 3 x 2 − 10 x
A x 2 + 5 2 x + 4 \dfrac{x^2 + 5}{2x + 4} 2 x + 4 x 2 + 5 B x ( x + 5 ) 2 ( x + 2 ) \dfrac{x(x + 5)}{2(x + 2)} 2 ( x + 2 ) x ( x + 5 ) C x ( x − 5 ) 2 ( x + 2 ) \dfrac{x(x - 5)}{2(x + 2)} 2 ( x + 2 ) x ( x − 5 ) D x ( x − 5 ) 2 ( x − 2 ) \dfrac{x(x - 5)}{2(x - 2)} 2 ( x − 2 ) x ( x − 5 )
Worked solution (try it first) Take out the common factor
x x x on top and factorise the quadratic:
x 3 + 3 x 2 − 10 x = x ( x + 5 ) ( x − 2 ) x^3 + 3x^2 - 10x = x(x + 5)(x - 2) x 3 + 3 x 2 − 10 x = x ( x + 5 ) ( x − 2 ) .
Take out 2 on the bottom and use the difference of two squares:
2 x 2 − 8 = 2 ( x − 2 ) ( x + 2 ) 2x^2 - 8 = 2(x - 2)(x + 2) 2 x 2 − 8 = 2 ( x − 2 ) ( x + 2 ) .
Cancel the common bracket
x − 2 x - 2 x − 2 :
x ( x + 5 ) 2 ( x + 2 ) \dfrac{x(x + 5)}{2(x + 2)} 2 ( x + 2 ) x ( x + 5 ) , option B.
Watch out
x 2 + 3 x − 10 x^2 + 3x - 10 x 2 + 3 x − 10 − 10 -10 − 10 + 3 +3 + 3 + 5 +5 + 5 − 2 -2 − 2 − 5 -5 − 5 + 2 +2 + 2 ( x − 5 ) ( x + 2 ) (x - 5)(x + 2) ( x − 5 ) ( x + 2 ) Report a problem with this question