Question

Let a= x^2 +4. Rewrite the following equation in terms of a and set it equal to zero.

(x^2+4)^2+32=12x^2+48

In resulting equation what is the coefficient of the a term?

In the resulting equation, what is the constant?

Answer 1

coefficient: -12
Constant:32

Answer 2

If:

`a=x^(2)+4` (1)

And we have to rewrite the following expresion in terms of
`a`:

`{(x^(2)+4)}^(2)+32=12x^(2)+48` (2)

Firstly we have to rearrange the right side of equation (2) in terms of
`x^(2)+4`, factorizing by the common factor:

`{(x^(2)+4)}^(2)+32=12(x^(2)+4)`

Then, we can substitute
`x^(2)+4` by
`a`:

`a^(2)+32=12a`

And set it equal to zero:

`a^(2)-12a+32=0`>>>>This is the resulting equation

Now, each term of an algebraic expresion (like the equation above) is composed of sign, coefficient, variable and exponent. The terms are separated from each other by the plus sign (+) or the minus sign (-).

In this case, the variable is
`a` and the number that multiplies the variable (the coefficient) is
`-12`, whereas the constant (which is the term with no variable) is
`32`