Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Given the expression that represents the length of the rectangle:
[tex]3x-4[/tex]And the expression that represents the area of the rectangle:
[tex]6x^4-8x^3+9x^2-3x-12[/tex]You need to remember that the formula for calculating the area of a rectangle is:
[tex]A=lw[/tex]Where "l" is the length and "w" is the width.
If you solve for the width, you get this formula:
[tex]w=\frac{A}{l}[/tex]Therefore, you can write this expression to represent the width of the given rectangle:
[tex]\frac{6x^4-8x^3+9x^2-3x-12}{3x-4}[/tex]In order to simplify it, you can follow these steps:
1. Rewrite this term in this form in the numerator:
[tex]3x=-12x+9x[/tex]Then:
[tex]=\frac{6x^4-8x^3+9x^2-12x+9x-12}{3x-4}[/tex]2. Group pair of terms in the numerator and factor the Greatest Common Factor (the largest factor each group has in common) out of the parentheses:
[tex]=\frac{(6x^4-8x^3)+(9x^2-12x)+(9x-12)}{3x-4}[/tex][tex]=\frac{2x^3(3x-4)+3x(3x-4)+3(3x-4)}{3x-4}[/tex]3. Factor this Greatest Common Factor out in the numerator:
[tex]3x-4[/tex]You get:
[tex]=\frac{(3x-4)(2x^3+3x+3)}{3x-4}[/tex]4. By definition:
[tex]\frac{a}{a}=1[/tex]Therefore, you get:
[tex]=2x^3+3x+3[/tex]Hence, the answer is:
[tex]2x^3+3x+3[/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
