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Division of a Polynomial by a Monomial

State whether...

Question

State whether True or False.
Multiply: $6 x^{3} - 5 x + 10$ by $4 - 3 x^{2}$ .
The answer is $- 18 x^{5} + 39 x^{3} - 30 x^{2} - 20 x + 40$ .

A

True

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B

False

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Solution

The correct option is A True
$(6 x^{3} - 5 x + 10) \times (4 - 3 x^{2})$
$= (6 x^{3} - 5 x + 10) 4 - (6 x^{3} - 5 x + 10) 3 x^{2}$
$= 24 x^{3} - 20 x + 40 - 18 x^{5} + 15 x^{3} - 30 x^{2}$
$= - 18 x^{5} + 39 x^{3} - 30 x^{2} - 20 x + 40$

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