Which polynomials are prime? Check all that apply. 15x ^ 2 + 10x - 9x + 7 20x ^ 2 - 12x + 30x - 18 6x ^ 3 + 14x ^ 2 - 12x - 28 8x ^ 3 + 20x ^ 2 + 3x + 12 11x ^ 4 + 4x ^ 2 - 6x ^ 2 - 16

Answer:

15x2+10x-9x+7

8x3+20x2+3x+12

11x4+4x2-6x2-16

Step-by-step explanation:

The prime polynomials are;

⇒ 15x² + 10x – 9x + 7

⇒ 8x³ + 20x² + 3x + 12

⇒ 11x⁴ + 4x² – 6x² – 16

What is an expression?

Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

There are some polynomials.

Now,

Evaluate all options in order to check that the polynomials are prime or not as;

Since, The polynomial is called a prime polynomial if the polynomial has not lower degree factors.

1). 15x² + 10x – 9x + 7

15x² + 10x – 9x + 7 = 5x(3x + 2) - (9x - 7)

Thus, This polynomial can not be factored into lower degree polynomial. Hence, it is a prime polynomial.

2). 20x² - 12x + 30x - 18

20x² - 12x + 30x - 18 = 4x (5x - 3) + 6 (5x - 3)

                                = (4x + 6) (5x - 3)

Thus, This polynomial is converted into a lower degree polynomial. Therefore, it is not a prime polynomial.

3). 6x³ + 14x² - 12x - 28

6x³ + 14x² - 12x - 28 = 2x² (3x + 7) - 4(3x + 7)

                               = (2x² - 4) (3x + 7)

Thus, This polynomial is converted into a lower degree polynomial. Therefore, it is not a prime polynomial.

4). 8x³ + 20x² + 3x + 12

8x³ + 20x² + 3x + 12 = 4x² (2x + 5) + 3 (x + 4)

                                = (4x² + 3) (2x + 5)

Thus, This polynomial can not be factored into lower degree polynomial. Therefore, it is a prime polynomial.

5). 11x⁴ + 4x² – 6x² – 16

11x⁴ + 4x² – 6x² – 16 = x² (11x² + 4) - 2 (x² + 8)

Thus, This polynomial can not be factored into lower degree polynomial. Therefore, it is a prime polynomial.

Therefore, The prime polynomials are;

⇒ 15x² + 10x – 9x + 7

⇒ 8x³ + 20x² + 3x + 12

⇒ 11x⁴ + 4x² – 6x² – 16

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