Answer:
a = –2
b = –13
Explanation:
(3x + a )(2x – 3) = 6x² + bx + 6
The value of a and b can be obtained as follow:
(3x + a )(2x – 3)
Expand
3x(2x – 3) + a(2x – 3)
6x² – 9x + 2ax – 3a
6x² – (9 – 2a)x – 3a
But:
(3x + a )(2x – 3) = 6x² + bx + 6
Therefore,
6x² – (9 – 2a)x – 3a = 6x² + bx + 6
From the above,
–3a = 6
Divide both side by –3
a = 6/–3
a = –2
b = –(9 – 2a)
But
a = –2
b = –(9 – 2×–2)
b = –(9 + 4)
b = –(13)
b = –13
SUMMARY:
a = –2
b = –13
