 # 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

Mathematics

## Question

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: $$2x^7 -16a^6 +18a^5$$

Step-by-step explanation: Given expression $$(a^2)(2a^3)(a^2-8a + 9)$$.

The first factor $$(a^2)$$ has a degree of : 2 because power of a is 2.

The second factor $$(2a^3)$$ has a degree of : 3 because power of a is 3.

The third factor $$(a^2-8a + 9)$$ has a degree of : 2 because highest power of a is 2.

Let us multiply them now:

$$(a^2)(2a^3)(a^2-8a + 9).$$

First we would multiply $$(a^2)(2a^3)$$.

According to product rule of exponents, we would add the powers of a.

Therefore,

$$(a^2)(2a^3) = 2a^{2+3}= 2a^5$$

Now, we need to distribute $$2a^5$$ over $$(a^2-8a + 9)$$

Therefore,

$$(2a^5)(a^2-8a + 9)= 2a^{5+2} -16a^{5+1}+18a^5$$

=$$2x^7 -16a^6 +18a^5$$

Highest power of resulting polynomial $$2x^7 -16a^6 +18a^5$$ is 7.

Therefore, The product has a degree of 7.