Is the leading coefficient 0 or 1? x^3 - 5x - 12
1 answer:
Answer:
Step-by-step explanation:
The coefficient of a polynomial expression is the coefficient of the term with the highest exponent. We can see that the term with the highest exponent is . So, the leading coefficient is its coefficient which is
.
Note that any number can be written as the product of that number and as multiplying by
does not fundamentally change that number. In our given example,
is equivalent to
.
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Given:
The system of equations:
To find:
The number that can be multiplied by the second equation to eliminate the x-variable when the equations are added together.
Solution:
We have,
...(i)
...(ii)
The coefficient of x in (i) and (ii) are 1 and respectively.
To eliminate the variable x by adding the equations, we need the coefficients of x as the additive inverse of each other, i.e, a and -a So, a+(-a)=0.
It means, we have to convert into -1. It is possible if we multiply the equation (ii) by -5.
On multiplying equation (ii) by -5, we get
...(iii)
On adding (i) and (iii), we get
Here, x is eliminated.
Therefore, the number -5 can be multiplied by the second equation to eliminate the x-variable.