Question

find the value of b and c if the polynomial p(x)=(x-5)whole square represents the polynomial x square +bx+c

Answer 1

Given,
$(x - 5)^{2} = {x}^{2} + bx + c$

We have to find the value of b and c in the above equation.

Initially, let's expand the formula
$(a - b) ^{2} = {a}^{2} + {b}^{2} - 2ab$
Here, it is
$(x - 5) ^{2}$
Hence, we get,
${x}^{2} + {5 }^{2} - (2 \times x \times 5)$
On further expansion, we get,
${x}^{2} - 10x + 25$
Comparing with the initial equation, we get,
$b = - 10$
and
$c = 25$
Thus the solution