The correct answer is: [D]: " -3x⁶ − 4x⁵ + 2x² + 8x + 4 " .
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Explanation:
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Given:
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" ( 4x² + 3x + 4) + ( -3x⁶ − 4x⁵ − 2x² + 5x) " ;
Rewrite as:
" ( 4x² + 3x + 4) + 1( -3x⁶ − 4x⁵ − 2x² + 5x) " ;
Note: The "1" is implied — since "1", multiplied by any value, is equal to that same value.
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Note the "distributive property of multiplication" :
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a(b + c) = ab + ac ;
a(b − c) = ab − ac ;
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So, consider the following portion of the expression:
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" + 1 ( -3x⁶ − 4x⁵ − 2x² + 5x) " ;
= (+1 * -3x⁶) − (1 * 4x⁵) − (1 * 2x²) + (1 * 5x)
= − 3x⁶ − 4x⁵ − 2x² + 5x ;
Now, bring down the rest of the expression:
( 4x² + 3x + 4) − 3x⁶ − 4x⁵ − 2x² + 5x ;
= 4x² + 3x + 4 − 3x⁶ − 4x⁵ − 2x² + 5x
Combine the "like terms" ;
+ 4x² − 2x² = + 2x² ;
+ 3x + 5x = 8x ;
And we have:
" -3x⁶ − 4x⁵ + 2x² + 8x + 4 " ;
→ which is: Answer choice: [D]: " -3x⁶ − 4x⁵ + 2x² + 8x + 4 " .
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