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The quotient of (x4 + 5x3 – 3x – 15) and a polynomial is (x3 – 3). What is the polynomial?



x7 + 5x6 – 6x4 – 30x3 + 9x + 45


x – 5


x + 5


x7 + 5x6 + 6x4 + 30x3 + 9x + 45

Sagot :

Answer:

g(x) = x+5

Step-by-step explanation:

Given that,

[tex]f(x)=x^4+5x^3-3x-15[/tex]

[tex]q(x) = (x^3-3)[/tex]

We need to find the polynomial. We know that, Euclid division lemma states that

[tex]f(x)=q(x)\times g(x)+r(x)[/tex]

Where

f(x) is dividend

g(x) is the poynomial

q(x) is quotient

r(x) is remainder

So,

[tex]x^4+5x^3-3x-15=(x^3-3)\times g(x) +0\\\\g(x)=\dfrac{x^4+5x^3-3x-15}{(x^3-3)}\\\\g(x)=x+5[/tex]

So, the polynomial is (x+5).

 

Eatmaggottzidn

Answer: its C

Step-by-step explanation: i just took the test

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