Question

Divide the polynomial f(x) by g(x) in the following: (ii) by synthetic division method (a) f(x) = x² - 5x + 8 and g(x) = x-4 (b) f(x) = x³ - 3x² + 3x - 5 and g(x) = x - 2 (c) f(x) = x² + 7x + 9 and g(x) = x + 3 (d) f(x) = 4x³ + 9x² + 3x-7 and g(x) = x + 1 ​

Answer 1

Let's perform synthetic division to divide the given polynomials using the provided divisors:

(a) f(x) = x² - 5x + 8 and g(x) = x - 4

Using synthetic division with the divisor x - 4:

4 | 1 -5 8
|4 -4 16
1 -1 24

The result is 1x - 1 with a remainder of 24.

So, (x² - 5x + 8) / (x - 4) = x - 1 + 24 / (x - 4).

(b) f(x) = x³ - 3x² + 3x - 5 and g(x) = x - 2

Using synthetic division with the divisor x - 2:

2 | 1 -3 3 -5
|2 -2 2
1 -1 5 -3

The result is 1x² - x + 5 with a remainder of -3.

So, (x³ - 3x² + 3x - 5) / (x - 2) = x² - x + 5 - 3 / (x - 2).

(c) f(x) = x² + 7x + 9 and g(x) = x + 3

Using synthetic division with the divisor x + 3:

-3 | 1 7 9
|-3 -12 -9
1 4 0

The result is 1x + 4 with no remainder.

So, (x² + 7x + 9) / (x + 3) = x + 4.

(d) f(x) = 4x³ + 9x² + 3x - 7 and g(x) = x + 1

Using synthetic division with the divisor x + 1:

-1 | 4 9 3 -7
|-4 -5 -2
4 5 -2 -9

The result is 4x² + 5x - 2 with a remainder of -9.

So, (4x³ + 9x² + 3x - 7) / (x + 1) = 4x² + 5x - 2 - 9 / (x + 1).