Factor and Remainder Theorem












-1












$begingroup$


Please help me with this exam style question from the IGCSE 2020 Specimen Paper.
The polynomial
$$p(x)=2x^3 -3x^2 +qx+56$$
has $x-2$ as a factor.
Show that $q=-30$.






polynomials







share|cite|improve this question











$endgroup$












  • $begingroup$
    Divide it straightaway.When you get the remainder in terms of q,say aqx+b,equate each coefficient to zero as it is a factor
    $endgroup$
    – GK A
    Nov 16 '18 at 13:46






  • 1




    $begingroup$
    I think $q = color{blue}{-}30$. Just set $p(2) = 0$.
    $endgroup$
    – trancelocation
    Nov 16 '18 at 13:49
















-1












$begingroup$


Please help me with this exam style question from the IGCSE 2020 Specimen Paper.
The polynomial
$$p(x)=2x^3 -3x^2 +qx+56$$
has $x-2$ as a factor.
Show that $q=-30$.






polynomials







share|cite|improve this question











$endgroup$












  • $begingroup$
    Divide it straightaway.When you get the remainder in terms of q,say aqx+b,equate each coefficient to zero as it is a factor
    $endgroup$
    – GK A
    Nov 16 '18 at 13:46






  • 1




    $begingroup$
    I think $q = color{blue}{-}30$. Just set $p(2) = 0$.
    $endgroup$
    – trancelocation
    Nov 16 '18 at 13:49














-1












-1








-1





$begingroup$


Please help me with this exam style question from the IGCSE 2020 Specimen Paper.
The polynomial
$$p(x)=2x^3 -3x^2 +qx+56$$
has $x-2$ as a factor.
Show that $q=-30$.






polynomials







share|cite|improve this question











$endgroup$




Please help me with this exam style question from the IGCSE 2020 Specimen Paper.
The polynomial
$$p(x)=2x^3 -3x^2 +qx+56$$
has $x-2$ as a factor.
Show that $q=-30$.






polynomials




polynomials






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 18 '18 at 6:41









aleph_two

24912




24912










asked Nov 16 '18 at 13:43









Lombe LombeLombe Lombe

61




61












  • $begingroup$
    Divide it straightaway.When you get the remainder in terms of q,say aqx+b,equate each coefficient to zero as it is a factor
    $endgroup$
    – GK A
    Nov 16 '18 at 13:46






  • 1




    $begingroup$
    I think $q = color{blue}{-}30$. Just set $p(2) = 0$.
    $endgroup$
    – trancelocation
    Nov 16 '18 at 13:49


















  • $begingroup$
    Divide it straightaway.When you get the remainder in terms of q,say aqx+b,equate each coefficient to zero as it is a factor
    $endgroup$
    – GK A
    Nov 16 '18 at 13:46






  • 1




    $begingroup$
    I think $q = color{blue}{-}30$. Just set $p(2) = 0$.
    $endgroup$
    – trancelocation
    Nov 16 '18 at 13:49
















$begingroup$
Divide it straightaway.When you get the remainder in terms of q,say aqx+b,equate each coefficient to zero as it is a factor
$endgroup$
– GK A
Nov 16 '18 at 13:46




$begingroup$
Divide it straightaway.When you get the remainder in terms of q,say aqx+b,equate each coefficient to zero as it is a factor
$endgroup$
– GK A
Nov 16 '18 at 13:46




1




1




$begingroup$
I think $q = color{blue}{-}30$. Just set $p(2) = 0$.
$endgroup$
– trancelocation
Nov 16 '18 at 13:49




$begingroup$
I think $q = color{blue}{-}30$. Just set $p(2) = 0$.
$endgroup$
– trancelocation
Nov 16 '18 at 13:49










2 Answers
2






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2












$begingroup$

If $x-2$ is a factor, then $p(2)= 2cdot 2^3 -3 cdot 2^2 + qcdot 2 + 56 = 0$.
$$Rightarrow 2q = -60$$






share|cite|improve this answer









$endgroup$





















    1












    $begingroup$

    You want $P(2)=0$



    What is $ P(2)$ when $ p(x)=2x^3 -3x^2 +qx+56$?



    Let $x=2$ and solve for $q$






    share|cite|improve this answer









    $endgroup$













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      2 Answers
      2






      active

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      2 Answers
      2






      active

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      active

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      active

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      2












      $begingroup$

      If $x-2$ is a factor, then $p(2)= 2cdot 2^3 -3 cdot 2^2 + qcdot 2 + 56 = 0$.
      $$Rightarrow 2q = -60$$






      share|cite|improve this answer









      $endgroup$


















        2












        $begingroup$

        If $x-2$ is a factor, then $p(2)= 2cdot 2^3 -3 cdot 2^2 + qcdot 2 + 56 = 0$.
        $$Rightarrow 2q = -60$$






        share|cite|improve this answer









        $endgroup$
















          2












          2








          2





          $begingroup$

          If $x-2$ is a factor, then $p(2)= 2cdot 2^3 -3 cdot 2^2 + qcdot 2 + 56 = 0$.
          $$Rightarrow 2q = -60$$






          share|cite|improve this answer









          $endgroup$



          If $x-2$ is a factor, then $p(2)= 2cdot 2^3 -3 cdot 2^2 + qcdot 2 + 56 = 0$.
          $$Rightarrow 2q = -60$$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Nov 16 '18 at 13:52









          trancelocationtrancelocation

          12.6k1826




          12.6k1826























              1












              $begingroup$

              You want $P(2)=0$



              What is $ P(2)$ when $ p(x)=2x^3 -3x^2 +qx+56$?



              Let $x=2$ and solve for $q$






              share|cite|improve this answer









              $endgroup$


















                1












                $begingroup$

                You want $P(2)=0$



                What is $ P(2)$ when $ p(x)=2x^3 -3x^2 +qx+56$?



                Let $x=2$ and solve for $q$






                share|cite|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  You want $P(2)=0$



                  What is $ P(2)$ when $ p(x)=2x^3 -3x^2 +qx+56$?



                  Let $x=2$ and solve for $q$






                  share|cite|improve this answer









                  $endgroup$



                  You want $P(2)=0$



                  What is $ P(2)$ when $ p(x)=2x^3 -3x^2 +qx+56$?



                  Let $x=2$ and solve for $q$







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Nov 16 '18 at 13:52









                  Mohammad Riazi-KermaniMohammad Riazi-Kermani

                  41.6k42061




                  41.6k42061






























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