Check whether 7+3x is a factor of 3x^3+7x. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $p(x) = 3x^3 + 7x$.To check if $(7+3x)$ is a factor of $p(x)$,we find the zero of $(7+3x)$ by setting it to $0$:$7 + 3x = 0 \implies 3x = -7 \

Vedclass · Accepted Answer

No

Vedclass · Answer

(B) Let $p(x) = 3x^3 + 7x$.To check if $(7+3x)$ is a factor of $p(x)$,we find the zero of $(7+3x)$ by setting it to $0$:$7 + 3x = 0 \implies 3x = -7 \implies x = -\frac{7}{3}$.According to the Factor Theorem,$(7+3x)$ is a factor of $p(x)$ if and only if $p(-\frac{7}{3}) = 0$.Now,calculate $p(-\frac{7}{3})$:$p(-\frac{7}{3}) = 3(-\frac{7}{3})^3 + 7(-\frac{7}{3})$$= 3(-\frac{343}{27}) + (-\frac{49}{3})$$= -\frac{343}{9} - \frac{49}{3}$$= \frac{-343 - 147}{9} = -\frac{490}{9}$.Since $p(-\frac{7}{3}) = -\frac{490}{9} 
eq 0$,the remainder is not $0$.Therefore,$(7+3x)$ is not a factor of $3x^3+7x$.

Check whether $7+3x$ is a factor of $3x^3+7x$.

Similar Questions

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer: $y + \frac{2}{y}$

Find the value of the polynomial $p(x) = 5x - 4x^2 + 3$ at $x = 2$.

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer: $3 \sqrt{t} + t \sqrt{2}$

Verify: $x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2})$

Find the zero of the polynomial: $p(x) = ax, a \neq 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module