Two unknowns, direct system

3 The polynomial \(2 x ^ { 3 } + a x ^ { 2 } + b x + 6\), where \(a\) and \(b\) are constants, is denoted by \(\mathrm { p } ( x )\). When \(\mathrm { p } ( x )\) is divided by \(( x + 2 )\) the remainder is - 38 and when \(\mathrm { p } ( x )\) is divided by \(( 2 x - 1 )\) the remainder is \(\frac { 19 } { 2 }\). Find the values of \(a\) and \(b\).

2. $$f ( x ) = x ^ { 4 } - x ^ { 3 } + 3 x ^ { 2 } + a x + b$$ where \(a\) and \(b\) are constants.
When \(\mathrm { f } ( x )\) is divided by \(( x - 1 )\) the remainder is 4
When \(\mathrm { f } ( x )\) is divided by \(( x + 2 )\) the remainder is 22
Find the value of \(a\) and the value of \(b\).

\(f(x) = x^3 - 2x^2 + ax + b\), where \(a\) and \(b\) are constants. When \(f(x)\) is divided by \((x - 2)\), the remainder is 1. When \(f(x)\) is divided by \((x + 1)\), the remainder is 28.

1. Find the value of \(a\) and the value of \(b\). [6]
2. Show that \((x - 3)\) is a factor of \(f(x)\). [2]

$$f(x) = x^3 + ax^2 + bx - 10, \text{ where } a \text{ and } b \text{ are constants.}$$ When \(f(x)\) is divided by \((x - 3)\), the remainder is 14. When \(f(x)\) is divided by \((x + 1)\), the remainder is \(-18\).

1. Find the value of \(a\) and the value of \(b\). [5]
2. Show that \((x - 2)\) is a factor of \(f(x)\). [2]

f(x) = x³ + ax² + bx - 10, where a and b are constants. When f(x) is divided by (x - 3), the remainder is 14. When f(x) is divided by (x + 1), the remainder is -18.

1. Find the value of a and the value of b. [5]
2. Show that (x - 2) is a factor of f(x). [2]