Question

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
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Answer 1

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!

Answer 2

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!