Question

without actual division show that x^2 + 3x+2 is a factor of 2x^4 -6x^3 + 3x^2 + 3x - 2​

Answer 1

Step-by-step explanation:

put x^2+3x+2=0

x^2+2x+x+2=0

x(x+2)+1(x+2)

(x+2)(x+1) therefore x=-2,-1

f(x)=2x^4-6x^3+3x^2+3x-2

put x=-2

f(x)=2×-2^4-6×-2^3+3×-2^2+3×-2-2

f(x)=2×16-6×-8+3×4-6-2

f(x)=32+48+12-2

f(x)=80+10=90

x=-2 is not a factor

put x=-1

2×-1^4-6×-1^3+3×-1^2+3×-1-2

2×1-6×-1+3×1+3×-1-2

2+6+3-3-2

8-2

6

x=-1is also not a factor