Which polynomial function has a leading coefficient of 2 , root negative 4 with multiplicity 3 , and root 10 with multiplicity 1 ?
Answer
A
f of x is equal to 2 open paren x plus 4 close paren open paren x plus 4 close paren open paren x plus 4 close paren open paren x minus 10 close paren
B
f of x is equal to 3 open paren x minus 4 close paren open paren x minus 4 close paren open paren x plus 10 close paren
C
f of x is equal to 2 open paren x minus 4 close paren open paren x minus 4 close paren open paren x minus 4 close paren open paren x plus 10 close paren
D
f of x is equal to 3 open paren x plus 4 close paren open paren x plus 4 close paren open paren x minus 10 close paren
Explanation
A root of −4 gives a factor of (x + 4), and multiplicity 3 means that factor appears three times. A root of 10 gives a factor of (x − 10), appearing once. Multiplying these factors by the leading coefficient 2 gives 2(x + 4)³(x − 10), which is choice D.
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