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# Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case: (iii) p(x) = x ^3 - 4x ^2 + x + 6, g(x) = x - 3

2.(iii) Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:

(iii)    $p(x) = x^3 - 4x^2 + x + 6, \ g(x) = x - 3$

Views

Zero of polynomial  $g(x)=x-3$  is  $3$

If  $g(x)=x-3$  is factor of polynomial  $p(x) = x^3 - 4x^2 + x + 6$

Then,  $p(3)$  must be equal to zero

Now,

$\Rightarrow p(3) = (3)^3 - 4(3)^2 + 3 + 6$

$\Rightarrow p(3) = 27-36+3+6=0$

Therefore,  $g(x)=x-3$   is a factor of polynomial  $p(x) = x^3 - 4x^2 + x + 6$

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