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 1

Explanation:

A

2a7 – 16a6 + 18a5

Answer 2

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.