Find whether 3x+2 is a factor of 3x^4+ 5x^3+ 13x-x^2 + 10

Asked by diyayadav1441 | 27th Jul, 2020, 03:59: PM

Expert Answer:

If 3x + 2 is a factor of p(x) = 3x4+ 5x3+ 13x - x2 + 10 then p(-2/3)= 0

begin mathsize 16px style straight p open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses equals space 3 open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses to the power of 4 space plus space 5 open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses cubed plus space 13 open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses minus open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses squared space plus space 10
space space space space space space space space space space space space space space equals open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses open square brackets 3 open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses cubed plus space 5 open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses squared plus space 13 minus space open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses close square brackets plus space 10
space space space space space space space space space space space space space space equals open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses open parentheses fraction numerator negative 8 over denominator 9 end fraction plus space 20 over 9 plus space 13 space plus space 2 over 3 close parentheses plus space 10
space space space space space space space space space space space space space space equals open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses open parentheses 12 over 9 space plus space 2 over 3 plus space 13 close parentheses plus space 10
space space space space space space space space space space space space space space space equals open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses open parentheses 12 over 9 space plus space 6 over 9 plus space 117 over 9 close parentheses plus space 10
space space space space space space space space space space space space space space space space equals open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses open parentheses 135 over 9 close parentheses plus space 10
space space space space space space space space space space space space space space space space space equals fraction numerator negative 2 over denominator 3 end fraction cross times 15 space plus space 10
space space space space space space space space space space space space space space space space space space equals space minus 10 space plus space 10
space space space space space space space space space space space space space space space space space space equals space 0 space
end style

→ 3x + 2 is a factor of 3x4+ 5x3+ 13x - x2 + 10.

  



Answered by Yasmeen Khan | 27th Jul, 2020, 06:49: PM