Question

(i) Express 2x² +8x-10 in the form a(x+b)² + c

Help

Answer 1

2(x+2)² - 18

Explanation:

Given

2x² +8x-10

express in the form a(x + b)² + c

Take out common factor 2 from 2x² +8x-10 ==> 2(x² + 4x -5)

x² + 4x - 5 can be converted to the form (x + b)² + c as follows using complete the square technique

(x + b)² = x² +2bx + b²

Comparing x² +2bx + b² and x² + 4x - 5 we can see that b = 2

So the expression becomes
x² + 4x - 5 = (x+2)³ + c
= x² + 4x + 4 + c

Therefore -5 = 4 - c

c = -5 -4 = -9

Therefore
x² + 4x - 5 = (x+2)³ -9

2(x² + 4x -5) = 2[(x+2)³ -9]

=2(x+2)² -18

ANSWER

Verify

2(x+2)² -18 = 2(x² +4x + 4) - 18 = 2x²+8x +8 - 18 = 2x² + 8x - 10
Thus verified