Understand linear polynomials in one variable, find their zeroes, and connect them to straight-line graphs.
A linear polynomial has the form ax+b, where a≠0. Its zero (the value of x making it equal to 0) is found by solving ax+b=0.
Find the zero of the polynomial 2x−6.
2x−6=0 → x=3
Find the zero of the polynomial −3x+9.
−3x+9=0 → x=3
The graph of a linear polynomial y=ax+b is a straight line. The zero of the polynomial is where this line crosses the x-axis.
For y=x−4, find two points on the graph.
x=0: y=−4; x=4: y=0
Where does the graph of y=2x+6 cross the x-axis?
Set y=0: 2x+6=0, x=−3; crosses at (−3,0)
1. Find the zero of the polynomial 5x−15.
2. Find the zero of the polynomial 4x+8.
3. For y=3x−9, find the point where it crosses the x-axis.
4. For y=−2x+10, find y when x=0 and x=5.
5. Does every linear polynomial have exactly one zero? Explain.