Question

Quadratic polynomial when divided by X+1 and x + 2 leaves no remainder, then f(x) is​

Answer 1

Answer:

Let the quadratic polynomial be denoted as P(x).

The polynomial when divided by x+2 gives a remainder of 1. So, from remainder theorom, P(−2)=1.

Similarly, the polynomial when divided by x−1 gives a remainder of 4. So, from remainder theorom, P(1)=4.

Now, if P(x) is divided by the product (x+2)(x−1), the remainder can be at most be a linear function.

We can write P(x)=C(x+2)(x−1)+(Ax+B), where A, B, and C are constants.

Use P(1)=4 and P(−2)=1.

We get two equations: A+B=1 and −2A+B=1.

Solving, we get A=1 and B=3. Hence, the remainder is

Ax+B=x+3

Step-by-step explanation:

hope this explanation is understandable

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Answer 2

Answer:

The function $f(x)=x^2+3x+2$

Step-by-step explanation:

Given:

Quadratic polynomial when divided by x+1 and x + 2 leaves no remainder

We need to find the function

As the function when divided by x+1 and x + 2 leaves no remainder so x+1,x+2 are the factors of the equation so we can write as

$f(x)=(x+1)(x+2)\\\\f(x)=x^2+x+2x+2\\\\f(x)=x^2+3x+2$