Question

Help me please fast

Given (x² − x + 2)(x − 1) = Ax³ + Bx² + Cx + D what is the value of A + D

Answer 1

-1

Explanation:

Expanding (x² − x + 2)(x − 1) we get
`x^(3) -x^(2) -x^(2) +x+2x-2`. When we simplify that, we get
`x^(3) -2x^(2) +3x-2` which fits the form Ax³ + Bx² + Cx + D.

We can see that A = 1, B = -2, C = 3, D = -2. Thus A + D = 1 - 2 = -1.

Therefore your answer is -1

Answer 2

A + D = -1

Explanation:

Given: (x² − x + 2)(x − 1) = Ax³ + Bx² + Cx + D

Step 1: Simplify using the Distributive Property.

`\\\implies (x^2 - x + 2)(x - 1) \\\\\implies x(x^2 - x + 2) + -1(x^2 - x + 2)\\\\\implies x^3 - x^2 + 2x - x^2 + x - 2\\\\\implies \bold{1}x^3 -\bold{2}x^2 + \bold{3}x - \bold{2}`

Step 2: Determine the value of the coefficients.

`\implies {\sf A} = 1, {\sf B} = -2, {\sf C} = 3, {\sf D} = -2`

Step 3: Find the value of A + D.

`\implies {\sf A} + {\sf D} \Rightarrow 1 - 2 = \boxed{-1}`