Question

Please answer the question please ....help​

Answer 1

Answer:

No. g(x) is not a factor of the f(x)

Explanation:

Here,

We need check if g(x) = 2x² + 7x + 1 is a factor of f(x) = 10x⁴ + 17x³ - 62x² + 30x - 3

Let's divided the f(x) by g(x), because is g(x) is the factor of f(x) then the remainder after divison must be zero.

So,

5x² - 9x - 2

2x² + 7x + 1 ) 10x⁴ + 17x³ - 62x² + 30x - 3 (

10x⁴ + 35x³ + 5x²

- 18x³ - 67x² + 30x

- 18x³ - 63x² - 9x

- 4x² + 39x - 3

- 4x² - 14x - 2

53x - 1

Since, the remainder is not zero.

We can say that g(x) is not a factor of f(x)

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Note:

Any polynomial g(x) can be called a factor of p(x) only if the remainder after dividing p(x) by g(x) leaves a remainder as zero.

For example :

We will say x as factor of x² because it will leave a remainder after division of x² by x.