Question

p(x) = 2x³- 11x²- 4x+ 3; g(x) = 2x + 3. Check whether p(x) is a multiple of g(x) or not.

Answer 1

First we have to find the 0 of the polynomial...

2x + 3 = 0
2x = 0-3
x = -3/2

So, we have found the zero of the polynomial...

and then---

we have to put the value of gx into px----

2×(-3/2)^3 - 11×(-3/2)^2 - 4×(-3/2) + 3


And you have to solve it...

And if answer is 0,, then px is the multiple of gx..






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Answer 2

Hi ,

It is given that ,

p(x) = 2x³- 11x² - 4x + 3 ,

g(x) = 2x + 3 ,

We have to check whether g(x) is a

factor of p(x) ,

Replace x , by the zero of 2x + 3 ,

i.e 2x + 3 = 0

=> x = -3/2

p(-3/2)=2(-3/2)³-11(-3/2)²-4(-3/2)+3

= 2×(-27/8)-11×(9/4)+6+3

= -27/4 - 99/4 + 9

= ( -27 - 99 + 36 )/4

= -90/4

= -45/2

As the remainder is not Equal to zero,

the g(x) is not a factor of p(x).

Therefore ,

p(x) is not a multiple of g(x).

I hope this helps you.

: )