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

To determine which polynomials are prime, we need to check if they can be factored into simpler polynomials with lower degrees. Let's analyze each polynomial one by one.<br /><br />1. $15x^{2}+10x-9x+7$<br /><br />This polynomial can be simplified by combining like terms:<br />$15x^{2}+(10x-9x)+7$<br />$15x^{2}+x+7$<br /><br />This polynomial cannot be factored further, so it is prime.<br /><br />2. $20x^{2}-12x+30x-18$<br /><br />This polynomial can be simplified by combining like terms:<br />$20x^{2}+(30x-12x)-18$<br />$20x^{2}+18x-18$<br /><br />This polynomial cannot be factored further, so it is prime.<br /><br />3. $6x^{3}+14x^{2}-12x-28$<br /><br />This polynomial can be simplified by factoring out the greatest common factor (GCF) from each term:<br />$2x(3x^{2}+7x-6)-28$<br /><br />This polynomial can be factored further, so it is not prime.<br /><br />4. $8x^{3}+20x^{2}+3x+12$<br /><br />This polynomial can be simplified by factoring out the greatest common factor (GCF) from each term:<br />$4x(2x^{2}+5x)+3x+12$<br /><br />This polynomial can be factored further, so it is not prime.<br /><br />5. $11x^{4}+4x^{2}-6x^{2}-16$<br /><br />This polynomial can be simplified by combining like terms:<br />$11x^{4}+(4x^{2}-6x^{2})-16$<br />$11x^{4}-2x^{2}-16$<br /><br />This polynomial cannot be factored further, so it is prime.<br /><br />Therefore, the prime polynomials are:<br />- $15x^{2}+x+7$<br />- $20x^{2}+18x-18$<br />- $11x^{4}-2x^{2}-16$