Question

select the correct answer. which expression is equivalent to this polynomial? 9x2 4 a. (3x 2i)(3x − 2i) b. (3x 2)(3x − 2) c. (3x 2i)2 d. (3x 2)2

Answer 1

The polynomial 9x^2 + 4 is equivalent to (3x+2i)(3x-2i). The answer is A.

Polynomials are algebraic expressions that consist of variables and coefficients where arithmetic operations can be performed.

A polynomial is expanded if no variable appears within parentheses and all like terms have been combined.

To expand a polynomial, multiply its factors (often by using the distributive property) or perform the indicated operations.  Then combine all like terms.

Expanding each of the options provided using FOIL method:

a) (3x+2i)(3x-2i)

= 9x^2 - 2ix + 2ix - 4i^2

= 9x^2 - 4i^2            *(i^2 = -1) note that i is an imaginary number and i squared is equal to -1

= 9x^2 - 4(-1)

= 9x^2 + 4

b) (3x+2)(3x-2)

= 9x^2 + 6x - 6x - 4

= 9x^2 - 4

c) (3x + 2i)^2

= 9x^2 + 6ix + 6ix + 4i^2          *(i^2 = -1)

= 9x^2 + 12ix - 4

d) (3x + 2)^2

= 9x^2 + 6x + 6x + 4

= 9x^2 + 12x + 4

Hence, the polynomial 9x^2 + 4 is equivalent to (3x+2i)(3x-2i). The answer is A.

To learn more about polynomials: brainly.com/question/1218464

#SPJ4