SOLUTION: Find the degree of the following polynomial function: f(x) = 4(x + 3)(x- 2)2 a. 1 b. 2 c. 3 d. 4 e. None of the others

Algebra ->  Functions -> SOLUTION: Find the degree of the following polynomial function: f(x) = 4(x + 3)(x- 2)2 a. 1 b. 2 c. 3 d. 4 e. None of the others       Log On


   

Question 43155: Find the degree of the following polynomial function:
f(x) = 4(x + 3)(x- 2)2

a. 1
b. 2
c. 3
d. 4
e. None of the others
Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
We need to simplify it first:
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: 4%2A%28x%2B3%29%2A%28x-2%29%2A2 simplifies to 8%2Ax%5E2%2B8%2Ax-48
  • Text form: 4*(x+3)*(x-2)*2 simplifies to 8*x^2+8*x-48
  • Cartoon (animation) form: simplify_cartoon%28+4%2A%28x%2B3%29%2A%28x-2%29%2A2+%29
    For tutors: simplify_cartoon( 4*(x+3)*(x-2)*2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+4+%29%2A%28x%2B3%29%2A%28x-2%29%2Ahighlight_red%28+2+%29.
Multiplied numerator integers
It becomes highlight_green%28+8+%29%2A%28x%2B3%29%2A%28x-2%29.
Look at highlight_red%28+8%2A%28x%2B3%29%2A%28x-2%29+%29.
Expanded term 8%2A%28x-2%29 by using associative property on %28x%2B3%29
It becomes highlight_green%28+8%2A%28x-2%29%2Ax+%29%2Bhighlight_green%28+8%2A%28x-2%29%2A3+%29.
Look at 8%2A%28x-2%29%2Ax%2Bhighlight_red%28+8+%29%2A%28x-2%29%2Ahighlight_red%28+3+%29.
Multiplied numerator integers
It becomes 8%2A%28x-2%29%2Ax%2Bhighlight_green%28+24+%29%2A%28x-2%29.
Look at highlight_red%28+8%2A%28x-2%29%2Ax+%29%2B24%2A%28x-2%29.
Expanded term 8%2Ax by using associative property on %28x-2%29
It becomes highlight_green%28+8%2Ax%2Ax+%29-highlight_green%28+8%2Ax%2A2+%29%2B24%2A%28x-2%29.
Look at 8%2Ax%2Ax-highlight_red%28+8+%29%2Ax%2Ahighlight_red%28+2+%29%2B24%2A%28x-2%29.
Multiplied numerator integers
It becomes 8%2Ax%2Ax-highlight_green%28+16+%29%2Ax%2B24%2A%28x-2%29.
Look at 8%2Ahighlight_red%28+x+%29%2Ahighlight_red%28+x+%29-16%2Ax%2B24%2A%28x-2%29.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes 8%2Ahighlight_green%28+x%5E2+%29-16%2Ax%2B24%2A%28x-2%29.
Look at 8%2Ax%5E2-16%2Ax%2Bhighlight_red%28+24%2A%28x-2%29+%29.
Expanded term 24 by using associative property on %28x-2%29
It becomes 8%2Ax%5E2-16%2Ax%2Bhighlight_green%28+24%2Ax+%29-highlight_green%28+24%2A2+%29.
Look at 8%2Ax%5E2-16%2Ax%2B24%2Ax-highlight_red%28+24+%29%2Ahighlight_red%28+2+%29.
Multiplied numerator integers
It becomes 8%2Ax%5E2-16%2Ax%2B24%2Ax-highlight_green%28+48+%29.
Look at 8%2Ax%5E2-highlight_red%28+16%2Ax+%29%2Bhighlight_red%28+24%2Ax+%29-48.
Eliminated similar terms highlight_red%28+-16%2Ax+%29,highlight_red%28+24%2Ax+%29 replacing them with highlight_green%28+%28-16%2B24%29%2Ax+%29
It becomes 8%2Ax%5E2%2Bhighlight_green%28+%28-16%2B24%29%2Ax+%29-48.
Look at 8%2Ax%5E2%2B%28-highlight_red%28+16+%29%2Bhighlight_red%28+24+%29%29%2Ax-48.
Added fractions or integers together
It becomes 8%2Ax%5E2%2B%28highlight_green%28+8+%29%29%2Ax-48.
Look at 8%2Ax%5E2%2Bhighlight_red%28+%28highlight_red%28+8+%29%29%2Ax+%29-48.
Remove unneeded parentheses around factor highlight_red%28+8+%29
It becomes 8%2Ax%5E2%2Bhighlight_green%28+8+%29%2Ax-48.
Result: 8%2Ax%5E2%2B8%2Ax-48

Universal Simplifier and Solver


Done!


As the higher exponent is 2, in 8x%5E2, the answer is letter b.