UPSKILL MATH PLUS

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A polynomial of the form ax + b, a \neq 0 is a linear polynomial.
 
The graph of a linear polynomial is a straight line.
 
Consider the graph of y = 2x + 1.
 
x
-2
-1
0
1
2
2x + 1
2(-2) + 1
 
= - 4 + 1
 
= -3
2(-1) + 1
 
= - 2 + 1
 
= -1
2(0) + 1
 
= 0 + 1
 
= 1
2(1) + 1
 
= 2 + 1
 
= 3
2(2) + 1
 
= 4 + 1
 
= 5
y = 2x + 1
-3
-1
1
3
5
 
Join the coordinates (-2, -3), (-1, -1), (0, 1), (1, 3) and (2, 5) by a straight line so as to obtain the graph of y = 2x + 1.
 
linear.png
 
 
It is observed that, the graph of the polynomial y = 2x + 1 intersects the x - axis at the point (- 0.5, 1).
 
Also by the definition, the zero of y = 2x + 1 is given by x = \frac{-1}{2} = -0.5.
 
Thus, we can say that the zero of a linear polynomial is the x - coordinate of the point where the graph of the polynomial intersects the x - axis.
 
In general, for a linear polynomial ax + b, a \neq 0, the graph of y = ax + b represents a straight line which intersects the x - axis exactly at the point \left(\frac{-b}{a}, 0\right).
The linear polynomial ax + b, a \neq 0, has exactly one zero namely \frac{-b}{a} which is the x - coordinate of the point where the graph of the polynomial intersects the x - axis.