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Coordinate Geometry

Question
CBSEENMA9001747
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Check whether 7 + 3x is a factor of 3x3 + 7x.

Solution
7 + 3x will be a factor of 3x3 + 7x only if 7 + 3x divides 3x3 + 7x leaving no remainder.
Let       p(x) = 3x3 + 7x
            7 + 3x = 0   rightwards double arrow   3x = - 7
rightwards double arrow         x = negative 7 over 3
therefore         Remainder =  3 open parentheses negative 7 over 3 close parentheses cubed plus 7 open parentheses negative 7 over 3 close parentheses
           
               equals negative 343 over 9 minus 49 over 3 equals negative 490 over 9 not equal to 0
therefore      7 + 3x is not a factor of 3x3 + 7x

Some More Questions From Coordinate Geometry Chapter

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

4x2 - 3x + 7

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

x10+ y3 + t50

Write the coefficients of x2 in each of the following:

2 + x2 + x

Write the coefficients of x2 in each of the following:
2 - x2 + x3

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