Past papers › JAMB 1989 · UME › Question 18 Question JAMB General Maths 1989 Objective Quadratics & their graphs Expressions, formulae & change of subject Quadratics & their graphs, Expressions, formulae & change of subject
Simplify 324 − 4 x 2 2 x + 18 \frac{324 - 4x^2}{2x + 18} 2 x + 18 324 − 4 x 2
A 2 ( x − 9 ) 2(x - 9) 2 ( x − 9 ) B 2 ( 9 + x ) 2(9 + x) 2 ( 9 + x ) C 81 − x 2 81 - x^2 81 − x 2 D − 2 ( x − 9 ) -2(x - 9) − 2 ( x − 9 )
Worked solution (try it first) Take out 4 from the top:
324 − 4 x 2 = 4 ( 81 − x 2 ) 324 - 4x^2 = 4(81 - x^2) 324 − 4 x 2 = 4 ( 81 − x 2 ) .
Difference of two squares:
81 − x 2 = ( 9 − x ) ( 9 + x ) 81 - x^2 = (9 - x)(9 + x) 81 − x 2 = ( 9 − x ) ( 9 + x ) .
The bottom is
2 x + 18 = 2 ( x + 9 ) 2x + 18 = 2(x + 9) 2 x + 18 = 2 ( x + 9 ) .
Cancel
2 ( x + 9 ) 2(x + 9) 2 ( x + 9 ) to leave
2 ( 9 − x ) 2(9 - x) 2 ( 9 − x ) .
Since
9 − x = − ( x − 9 ) 9 - x = -(x - 9) 9 − x = − ( x − 9 ) , this is
− 2 ( x − 9 ) -2(x - 9) − 2 ( x − 9 ) , option D.
Watch out
9 − x 9 - x 9 − x x − 9 x - 9 x − 9 2 ( 9 − x ) 2(9 - x) 2 ( 9 − x ) 2 ( x − 9 ) 2(x - 9) 2 ( x − 9 ) Report a problem with this question