Answer:
Part 1)
[tex]=12a^5-6a^4-5a^3-24a^2+12a-7[/tex]
Part 2)
[tex](2x^3-10x^2+5x+14)\div(x-2)=2x^2-6x-7[/tex]
Step-by-step explanation:
Part 1)
We would like to multiply:
[tex](3a^3-2a-7)(4a^2-2a+1)[/tex]
Distribute each term from the first group into the second group. So:
[tex]=3a^3(4a^2-2a+1)-2a(4a^2-2a+1)-7(4a^2-2a+1)[/tex]
Distribute further:
[tex]=(12a^5-6a^4+3a^3)+(-8a^3+4a^2-2a)+(-28a^2+14a-7)[/tex]
Combine like terms:
[tex]=(12a^5)+(-6a^4)+(3a^3-8a^3)+(-28a^2+4a^2)+(-2a+14a)+(-7)[/tex]
Simplify:
[tex]=12a^5-6a^4-5a^3-24a^2+12a-7[/tex]
Part 2)
We would like to divide:
[tex](2x^3-10x^2+5x+14)\div(x-2)[/tex]
Using long division.
Please refer to the attached document.
For the first step, x goes into 2x³ 2x² times. Hence, we multiply our divisor by 2x².
Next, x goes into -6x^2 -6x times. Hence, we multiply our divisor by -6x.
Finally, x goes into -7x -7 times. So, we multiply our divisor by -7 and we simplify.
Therefore:
[tex](2x^3-10x^2+5x+14)\div(x-2)=2x^2-6x-7[/tex]
