Express fx in the form fx x kqx r for the given value of

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k.

f(x) = 3x⁴ - 2x³ - 10x² + 15; k = 2

Solution

We have f (x) = 3x⁴ - 2x³ - 10x² + 15 so that f ( x - k) =  3( x - k )⁴ - 2 ( x - k)³ - 10(x - k)² + 15. NOw, when k = 2, we have f ( x - 2) = 3( x - 2 )⁴ - 2 ( x - 2)³ - 10(x - 2)² + 15.= 3( x⁴ - 8x³ + 24x² -32x + 16) - 2(x³ - 6x² + 12x - 8) - 10(x² - 4x + 4) + 15 = 3x⁴ - 24x³ + 72x² - 96x + 48 - 2x³ + 12x² -24x + 16 - 10x² + 40x - 40 + 15 = 3x⁴ - 26x³ + 74x² - 80x + 39