Please help me with this problem

Question

If x-2 is a factor of 2x^2+bx-10 , what is the value of b ?

Answer 1

We can use synthetic division.

 

2 |  2                b              -10

                       4               2b+8

____________________________

      2            (b+4)              0

 

 

 

Solve the equation

 

-10 + 2b + 8 = 0

Answer 2

If x-2 is a factor of 2x^2+bx-10 , what is the value of b ?

 

An alternative approach to solving this problem is to use the Remainder Factor theorem.

If x-2 is a factor, then the remainder is P(2).

P(2) = 2(2)² - b(2) -10 = 0

⇒8 -2b -10 =0

⇒ 2b = 2     or b =1

I just realized that this is the same approach Arthur used.

Answer 3

2x^2+bx-10

x-2 is a factor

2x^2+bx-10=0

x-2=0

x=2

2(2^2)+b(2)-10=0

2*4+2b-10=0

8+2b-10=0

2b-2==0

2b=2

b=1

check:

(x-2)(2x+5)=2x^2-4x+5x-10=2x^2+x-10