If ax + 3x² + bx – 3 has a factor (2x + 3) and leaves remainder “-3” when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression f(x)+g(x)+4x²+7x About the author Kaylee
Hi mate , here’s ur solution, Since (x-2) is a factor of 2x³+ax²+bx-14 => 2(2)³ + a(2)² + b(2)-14=0 =>16+4a+2b-14=0 =>4a+2b=-2 =>2a+b=-1 Also when 2x³+ax²+bx-14 is divided by by x-3,it leaves remainder 52. => 2(3)³+a(3)²+b(3)-14=52 =>54+9a+3b=52+14 =>9a+3b=12 =>3a+b=4 Subtract i) from ii) we have, a=5. From i) we have , =>2(5)+b=-1 =>b=-11 Hence, the required value of a and b are 5 and -11 respectively!!!!! Thanks! Reply
Hi mate , here’s ur solution, Since (x-2) is a factor of 2x³+ax²+bx-14 => 2(2)³ + a(2)² + b(2)-14=0 =>16+4a+2b-14=0 =>4a+2b=-2 =>2a+b=-1 Also when 2x³+ax²+bx-14 is divided by by x-3,it leaves remainder 52. => 2(3)³+a(3)²+b(3)-14=52 =>54+9a+3b=52+14 =>9a+3b=12 =>3a+b=4 Subtract i) from ii) we have, a=5. From i) we have , =>2(5)+b=-1 =>b=-11 Hence, the required value of a and b are 5 and -11 respectively!!!!! Thanks! Reply
Hi mate , here’s ur solution,
Since (x-2) is a factor of 2x³+ax²+bx-14
=> 2(2)³ + a(2)² + b(2)-14=0
=>16+4a+2b-14=0
=>4a+2b=-2
=>2a+b=-1
Also when 2x³+ax²+bx-14 is divided by by x-3,it leaves remainder 52.
=> 2(3)³+a(3)²+b(3)-14=52
=>54+9a+3b=52+14
=>9a+3b=12
=>3a+b=4
Subtract i) from ii) we have,
a=5.
From i) we have ,
=>2(5)+b=-1
=>b=-11
Hence, the required value of a and b are 5 and -11 respectively!!!!!
Thanks!
Hi mate , here’s ur solution,
Since (x-2) is a factor of 2x³+ax²+bx-14
=> 2(2)³ + a(2)² + b(2)-14=0
=>16+4a+2b-14=0
=>4a+2b=-2
=>2a+b=-1
Also when 2x³+ax²+bx-14 is divided by by x-3,it leaves remainder 52.
=> 2(3)³+a(3)²+b(3)-14=52
=>54+9a+3b=52+14
=>9a+3b=12
=>3a+b=4
Subtract i) from ii) we have,
a=5.
From i) we have ,
=>2(5)+b=-1
=>b=-11
Hence, the required value of a and b are 5 and -11 respectively!!!!!
Thanks!