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Lorico [155]
3 years ago
13

What is the remainder when (3x4 + 2x3 − x2 + 2x − 19) ÷ (x + 2)?

Mathematics
2 answers:
mel-nik [20]3 years ago
8 0

Answer: The remainder will be 5 only.

Explanation:

Since we have given that

f(x)=3x^4+2x^3-x^2+2x-19

and

g(x)=x+2

Now, using the division algorithm, we'll get,

f(x)=g(x)\times (3x^3-4x^2+7x-12)+5

When we compare it with  division lemma, which says that

f(x)=g(x)\times q(x)+r(x)

We get,

r(x)=5

Hence, the remainder will be 5 only.

Nadusha1986 [10]3 years ago
6 0

Answer: Remainder=5


Step-by-step explanation:

We know that the Remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial (x-a) is equal to f(a).

Here f(x)=3x^4+2x^3-x^2+2x-19

The linear polynomial = (x+2)

\Rightarrow\ a=-2

f(-2)=3(-2)^4+2(-2)^3-(-2)^2+2(-2)-19\\\Rightarrow\ f(-2)=3(16)-16+4-4-19\\\Rightarrow\ f(-2)=48-45\\\Rightarrow\ f(-2)=5

Hence, the remainder of the given division problem is 5.

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