Question

f of X is equals to x power4-12x cube+17x square-9x-7thenf of x+ 3=​

Answer 1

f(x + 3) = x⁴ - 37x² - 123x - 124

Step-by-step explanation:

Given that, f(x) = x⁴ - 12x³ + 17x² - 9x - 7

Now, f(x + 3)

= (x + 3)⁴ - 12 (x + 3)³ + 17 (x + 3)² - 9 (x + 3) - 7

= (x⁴ + 12x³ + 54x² + 108x + 81) - 12 (x³ + 9x² + 27x + 27) + 17 (x² + 6x + 9) - 9 (x + 3) - 7

= x⁴ + 12x³ + 54x² + 108x + 81 - 12x³ - 108x² - 324x - 324 + 17x² + 102x + 153 - 9x - 27 - 7

= x⁴ + (12 - 12) x³ + (54 - 108 + 17) x² + (108 - 324 + 102 - 9) x + (81 - 324 + 153 - 27 - 7)

= x⁴ - 37x² - 123x - 124

Note: To solve this type of problems, simply replace x with what asked. Then use algebraic identities and simplify by rearranging like powers.