Question

find the product.$(a^{2})(2a^{3})(a^{2}-8a + 9)LXB02a^{7}-16a^{6}-18a^{5}LXB12a^{12}-16a^{7}+18a^{6}$completeconsider the degree of each polynomial in the problem.the first factor has a degree ofthe second factor has a degree ofthe third factor has a degree ofthe product has a degree ofdone

Explanation:

Step1: Multiply first two factors

Multiply $a^2$ and $2a^3$:
$a^2 \times 2a^3 = 2a^{2+3} = 2a^5$

Step2: Distribute $2a^5$ to trinomial

Multiply $2a^5$ by each term in $a^2-8a+9$:
$2a^5 \times a^2 = 2a^{5+2} = 2a^7$
$2a^5 \times (-8a) = -16a^{5+1} = -16a^6$
$2a^5 \times 9 = 18a^5$

Step3: Sum the results

Combine the terms from Step2:
$2a^7 -16a^6 +18a^5$

Step4: Find degree of first factor

Degree of $a^2$ is the highest exponent: $2$

Step5: Find degree of second factor

Degree of $2a^3$ is the highest exponent: $3$

Step6: Find degree of third factor

Degree of $a^2-8a+9$ is highest exponent: $2$

Step7: Find degree of product

Degree of $2a^7-16a^6+18a^5$ is highest exponent: $7$

Answer:

Product: $2a^7 - 16a^6 + 18a^5$
First factor degree: $2$
Second factor degree: $3$
Third factor degree: $2$
Product degree: $7$