High School

The quotient of [tex](x^4 + 7x^3 + 28x - 16)[/tex] and a polynomial is [tex](x^2 + 7x - 4)[/tex]. What is the polynomial?

A. [tex]x^2 + 4[/tex]

B. [tex]x^2 - 4[/tex]

C. [tex]x^6 + 14x^5 + 45x^4 + 180x^2 + 224x + 64[/tex]

D. [tex]x^6 + 14x^5 + 45x^4 + 180x^2 - 224x + 64[/tex]

Answer :

To find the polynomial quotient of (x⁴ + 7x³ + 28x - 16) divided by (x² + 7x - 4), we perform polynomial long division.

```

________________

x² + 7x - 4 | x⁴ + 7x³ + 0x² + 28x - 16

- (x⁴ + 7x³ - 4x²)

____________________

7x³ + 4x² + 28x - 16

- (7x³ + 49x² - 28x)

___________________

53x² - 16

- (53x² - 371x + 236)

__________________

355x - 252

```

The quotient is x² + 4, so the polynomial is option a. x² + 4.

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