Question

If x2 +ax+ b , when divided by x-4 , leaves a remainder of 32

Answer 1

Answer:

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Answer 2

${ \large{ \boxed{ \boxed{p(x) = {x}^{2} + ax + b}}}}\\ \\ { \large{ \boxed{f(x) = x - 4}}} \\ { \large{ \boxed {\boxed{ \: \: \: \: \: \: \: \: \: = > x = 4}}}}$

Now,

$p(4) = 32$

Then,

$p(4) = > {(4)}^{2} + a(4) + b = 32\\ \: \: \: \: \: \: \: \: \: = > 16 + 4a + b = 32\\ \: \: \: \: \: \: \: \: \: = > \: \: \: \: \: \: \: \: \: \: 4a + b = 16$

Therefore,

${ \boxed{ \boxed{ \boxed{ \huge{ \red{a = \frac{16 - b}{4} }}}}}} \\ \\ { \boxed{ \boxed{ \boxed{ \huge{ \red{b = 16 - 4a}}}}}}$