Question

check whether 7+3x is a factor of 3x³+7x

Answer 1

Answer:

No , 7+3x is not factor of 3x³+7x

Step-by-step explanation:

To find whether

$f(x) = 7+ 3x$

is a factor of

$g(x) = 3 {x}^{3} + 7x$

find the value of x from f(x) and put to g(x) ,if expression becomes zero than f(x) is a factor of g(x),otherwise not

$f(x)=>7+3x\\\\3x+7=0\\\\x=\frac{-7}{3} \\\\g(x)=3 {x}^{3} + 7x\\\\g(\frac{-7}{3})=3\Big({\frac{-7}{3}}\Big)^3 + 7 \Big(\frac{-7}{3}\Big)\\</p><p>$

$g\Big(\frac{-7}{3}\Big)=3\Big(\frac{-343}{27}\Big)-\frac{49}{3}\\\\=-\frac{343}{9}-\frac{49}{3}\\\\= -\frac{490}{9}$

g(-7/3) is not zero,hence f(x) is not a factor of g(x)

Hope it helps you.

Answer 2

Answer:

(7 + 3x) is not a factor of (3x³ + 7x).

Step-by-step explanation:

Let f(x) = 3x³ + 7x……….(1)

Zero of 7 + 3 x is  x = - 7/3

Now to check whether (7 + 3x) the polynomial is a factor of 3x³ + 7x, we prove that, f(–7/3) = 0, by using remainder theorem ,  

On putting x = - 7/3 in eq 1,  

f(–7/3) = 3(–7/3)³ + 7 (–7/3)

f(–7/3) = 3(-343/27) – (49/3)

f(–7/3) = (-343/9) – (49/3)

f(–7/3) = (-343 × 3  – 49 × 9)/27

f(–7/3) = (- 1029 - 441)/27

f(–7/3) = - 1470 /27

f(–7/3) = - 490/9

Hence, (7 + 3x) is not a factor of (3x³ + 7x).

HOPE THIS ANSWER WILL HELP YOU…