document.write( "Question 43155: Find the degree of the following polynomial function:
\n" ); document.write( "f(x) = 4(x + 3)(x- 2)2\r
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\n" ); document.write( "\n" ); document.write( " a. 1
\n" ); document.write( " b. 2
\n" ); document.write( " c. 3
\n" ); document.write( " d. 4
\n" ); document.write( " e. None of the others \n" ); document.write( "

Algebra.Com's Answer #28178 by aaaaaaaa(138) $\"\"$ $\"About$

You can put this solution on YOUR website!
We need to simplify it first:\r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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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.

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DETAILED EXPLANATION

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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 $\"highlight_green%28+8+%29%2A%28x%2B3%29%2A%28x-2%29\"$ .
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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 $\"highlight_green%28+8%2A%28x-2%29%2Ax+%29%2Bhighlight_green%28+8%2A%28x-2%29%2A3+%29\"$ .
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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 $\"8%2A%28x-2%29%2Ax%2Bhighlight_green%28+24+%29%2A%28x-2%29\"$ .
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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 $\"highlight_green%28+8%2Ax%2Ax+%29-highlight_green%28+8%2Ax%2A2+%29%2B24%2A%28x-2%29\"$ .
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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 $\"8%2Ax%2Ax-highlight_green%28+16+%29%2Ax%2B24%2A%28x-2%29\"$ .
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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 $\"8%2Ahighlight_green%28+x%5E2+%29-16%2Ax%2B24%2A%28x-2%29\"$ .
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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 $\"8%2Ax%5E2-16%2Ax%2Bhighlight_green%28+24%2Ax+%29-highlight_green%28+24%2A2+%29\"$ .
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Look at $\"8%2Ax%5E2-16%2Ax%2B24%2Ax-highlight_red%28+24+%29%2Ahighlight_red%28+2+%29\"$ .
Multiplied numerator integers
It becomes $\"8%2Ax%5E2-16%2Ax%2B24%2Ax-highlight_green%28+48+%29\"$ .
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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 $\"8%2Ax%5E2%2Bhighlight_green%28+%28-16%2B24%29%2Ax+%29-48\"$ .
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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 $\"8%2Ax%5E2%2B%28highlight_green%28+8+%29%29%2Ax-48\"$ .
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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: $\"8%2Ax%5E2%2B8%2Ax-48\"$
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Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "As the higher exponent is 2, in $\"8x%5E2\"$ , the answer is letter b. \n" ); document.write( "

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