Given that (ax^2 + bx + 3) (x+d) = x^3 + 6x^2 + 11x + 12, it asks a + 2b - d = ?

a+2b-d=1, 3, 5, 7

Step-by-step explanation:

(ax^2+bx+3)(x+d)

ax^3+bx^2+3x+adx^2+bdx+3d

ax^3+bx^2+adx^2+3x+bdx+3d=x^3+6x^2+11x+12

ax^3=x^3, a=1

bx^2+adx^2=6x^2

x^2(b+ad)=6x^2

b+ad=6

b+(1)d=6

b+d=6

3x+bdx=11x

x(3+bd)=11x

3+bd=11

b=6-d

3+(6-d)d=11

3+6d-d^2=11

3-11+6d-d^2=0

-8+6d-d^2=0

d^2-6d+8=0

factor out,

(d-4)(d-2)=0

zero property,

d-4=0, d-2=0

d=0+4=4,

d=0+2=2

b=6-4=2,

b=6-2=4.

a+2b-d=1+2(2)-2=1+4-2=5-2=3

a+2(4)-4=1+8-4=9-4=5

a+2(2)-4=1+4-4=5-4=1

a+2(4)-2=1+8-2=9-2=7

Step-by-step explanation:

We are given that:

And we want to determine:

So, we will determine our unknowns first.

We can distribute our expression:

Distribute:

Rearranging gives:

Factoring out the variable yields:

Since we know that our expression equals:

This means that each of the unknown terms in front of each variable corresponds with the coefficient of the resulting equation. Therefore:

Solving the first and fourth equation yields that:

Then the second and third equations become:

And solving for b now yields that:

Therefore, we know that:

For the equation:

Then the expression:

Can be evaluated as:

Evaluate:

Hence, our final answer is 1.

irrational, cannot

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116