Question

Someone please help! I asked earlier but they just stole the points...

(12-15) Q(x) = 2x^4 - 7x^3 + 6x^2 + x -2
1. Use synthetic division to determine whether (x-1) is a factor of Q(x).

2. Use synthetic division in to find Q(-2)

3. List all of the possible rational roots of Q(x) = 0

4. Find all of the real roots Q(x) =0

Answer 1

1)
`Q(x)=2x^(4)-7x^(3)+6x^(2) +x-2\\\\=(x-1)^(2)(x-2)(2x+1)\\`

2) Q(-2) = (-2-1)².(-2-2).(2.-2+1)

= (-3)².(-4).(-3)

= 108

3) Q(x) = 0

=> (x-1)²(x-2)(2x+1) = 0

⇔ x - 1 = 0 or x - 2 = 0 or 2x +1 = 0

4) x-1 = 0 or x - 2 = 0 or 2x + 1 = 0

⇔ x = 1 or x = 2 or x = -1/2

Explanation: