Find the product. (a2)(2a3)(a2 – 8a + 9) 2a7 – 16a6 + 18a5 2a7 – 16a6 – 18a5 2a8 – 16a7 + 18a6 2a12 – 16a7 + 18a6 consider the degree of each polynomial in the problem. the first factor has a degree of . the second factor has a degree of . the third factor has a degree of . the product has a degree of .

Answer: [tex]2x^7 -16a^6 +18a^5[/tex]
Step-by-step explanation: Given expression [tex](a^2)(2a^3)(a^2-8a + 9)[/tex].The first factor [tex](a^2)[/tex] has a degree of : 2 because power of a is 2.The second factor [tex](2a^3)[/tex] has a degree of : 3 because power of a is 3.The third factor [tex](a^2-8a + 9)[/tex] has a degree of : 2 because highest power of a is 2.Let us multiply them now:[tex](a^2)(2a^3)(a^2-8a + 9).[/tex]First we would multiply [tex](a^2)(2a^3)[/tex].According to product rule of exponents, we would add the powers of a.Therefore,[tex](a^2)(2a^3) = 2a^{2+3}= 2a^5[/tex]Now, we need to distribute [tex]2a^5[/tex] over [tex](a^2-8a + 9)[/tex]Therefore,[tex](2a^5)(a^2-8a + 9)= 2a^{5+2} -16a^{5+1}+18a^5[/tex]=[tex]2x^7 -16a^6 +18a^5[/tex]Highest power of resulting polynomial [tex]2x^7 -16a^6 +18a^5[/tex] is 7.Therefore, The product has a degree of 7.