Question

What should be added to p(x)= x -5x + 3 , show that 3 is the zero of the 2 polynomial ?

Answer 1

Answer:

$Let \: f(x) = {x}^{2} - 5x + 3$

$Then \: f(3) = {3}^{2} - 5 \times 3 + 3$

$\: \: \: \: \: \: \: \: \: \: \: \: = \: 9 - 15 + 3$

$\: \: \: \: \: \: \: \: \: \: \: \: = 9 - 12$

$\: \: \: \: \: \: \: \: \: \: \: \: = - 3$

$for \: f(3) = 0 , 3 must \: be \: added \: to \: \\ f(x)$

Answer 2

Answer:

$Let \: f(x) = {x}^{2} - 5x + 3$

$Then \: f(3) = {3}^{2} - 5 \times 3 + 3$

$\: \: \: \: \: \: \: \: \: \: \: \: = \: 9 - 15 + 3$

$\: \: \: \: \: \: \: \: \: \: \: \: = 9 - 12$

$\: \: \: \: \: \: \: \: \: \: \: \: = - 3$

$for \: f(3) = 0 , 3 must \: be \: added \: to \: \\ f(x)$