Question

P(x) = ( x+3 ) ( x- 5 ) , x= -3, 5

Answer 1

Hello mate :)

here's your answer ☞

1)

$\rm \blue{g(x) = x = (-3) }\\ \\ \rm \implies p(x) = (x + 3) (x - 5) \\ \rm \implies p(-3) = ( \cancel{-3+3)} (-3+5) \\ \rm \implies \red{2} \\ \\ \sf \green{So, \: remainder = 2} \\ \sf \green{ \therefore \: g(x) \: is \: not \: a \: factor \: of \: p(x)}$

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2)

$\rm \blue{g(x) = 5} \\ \\ \implies \rm \: p(x) = (x + 3)(x - 5) \\ \implies \rm \: p(5) = (5 + 3)( \cancel{5 - 5)} \\ \implies \red{ 8} \\ \\ \sf\green {So, \: remainder = 8 } \\ \sf \green{ \therefore \: g(x) \: is \: not \: a \: factor \: of \: p(x)}$

$\underline \mathcal \pink{Additional \: Information}$

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$\maltese \: \: \: \: \: { \tt \green{( - ) \times ( - ) = ( + ) \:}} \\ { \tt \green{negative \times negative = \red{ positive}}} \\ \\ \maltese \: \: \: \: \: { \tt \red{( + ) \times ( - ) = ( - )}} \\ { \tt \red{positive \times negative = \green{negative}}} \\ \\ \maltese \: \: \: \: \: \purple{( + ) \times ( + ) = ( + )} \\ { \tt \purple{positive \times positive = \orange{positive}}}$

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Hope this helps you friend ❤️☺️

Answer 2

Answer:

84

Step-by-step explanation: