Using Remainder Theorem, prove that p(x) = 6x3 + 19x2 + 21x + 9 is completely divisible by 2x + 3.

CBSE Class 9 Answered

Using Remainder Theorem, prove that p(x) = 6x³ + 19x² + 21x + 9 is completely divisible by 2x + 3.

Asked by Topperlearning User | 18 Sep, 2017, 09:42: AM

Expert Answer

$For space straight p left parenthesis straight x right parenthesis space equals space 6 straight x cubed space plus space 19 straight x squared space plus space 21 straight x space plus space 9 space be space completely space divisible space by space 2 straight x space plus space 3 comma space the space remainder space should space be space 0. Thus comma space we space have straight p open parentheses negative 3 over 2 close parentheses space equals space 6 open parentheses negative 3 over 2 close parentheses cubed space plus space 19 open parentheses negative 3 over 2 close parentheses squared space plus space 21 open parentheses negative 3 over 2 close parentheses space plus space 9 space space space space space space space space space space space space space space equals space 6 open parentheses negative 27 over 8 close parentheses space plus space 19 space cross times space 9 over 4 space minus space 63 over 2 space plus space 9 space space space space space space space space space space space space space space equals space minus 81 over 4 space plus space 171 over 4 space minus space 63 over 2 space plus space 9 space space space space space space space space space space space space space space equals fraction numerator negative 81 space plus space 171 space minus space 126 space plus space 36 over denominator 4 end fraction space space space space space space space space space space space space space space equals 0$

Answered by | 18 Sep, 2017, 11:42: AM