Question

Find the coefficient of \[x\] in $ -9x{{y}^{2}}z $ is

Answer 1

Hint: Coefficient is the multiplicative value for a variable, i.e., it adds the additional value to a variable for example let an equation be $ a{{b}^{2}}c+d $ . For $ a $ the coefficient is $ {{b}^{2}}c $ . Coefficient of $ b $ is $ ac $ , coefficient of $ c $ is $ a{{b}^{2}} $ and coefficient of $ d $ is $ 1 $ as $ d $ does not have any other multiplicative value which is why it has $ 1 $ as it’s coefficient.

Complete step-by-step answer:
For a structure $ a{{b}^{2}}c $ , coefficient of $ a $ is $ {{b}^{2}}c $ as the value of $ a $ is being multiplied by $ {{b}^{2}}c $ .
This value which adds the multiplicative value is called coefficient.
In the given question $ -9x{{y}^{2}}z $ we are given to find the coefficient of x.
The values adding multiplicative value to $ x $ in the equation $ -9x{{y}^{2}}z $ are $ -9 $ , $ {{y}^{2}} $ and $ z $ .
So, the coefficient of $ x $ in the given equation is $ -9\times {{y}^{2}}\times z $ .
The answer is $ -9{{y}^{2}}z $ .
The coefficient of $ x $ in $ $ $ -9x{{y}^{2}}z $ is $ -9{{y}^{2}}z $ .
So, the correct answer is “ $ -9{{y}^{2}}z $ ”.

Note: In the coefficient the signs should not be altered or ignored as they change the entire value and will lead to unwanted results. Change in sign corresponds to totally different coefficients though the value might be still the same in terms of constants or variables.