Respuesta :
The product of the binomials f(x) and g(x) is [tex]-2x^2+10x-8[/tex].
Solution:
Let us find the equation of line f.
Points on the line f are (2, 2) and (1, 0).
Slope of the line f:
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]$m=\frac{0-2}{1-2}[/tex]
[tex]$m=\frac{-2}{-1}[/tex]
m = 2
y-intercept of line f = c = -2
Equation of a line f:
y = mx + c
f(x) = 2x - 2
Now, find the equation of line g.
Points on the line f are (0, 4) and (2, 2).
Slope of the line g:
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]$m=\frac{2-4}{2-0}[/tex]
[tex]$m=\frac{-2}{2}[/tex]
m = -1
y-intercept of line g = c = 4
Equation of a line g:
y = mx + c
g(x) = -x + 4
Product of f(x) and g(x):
[tex]=f(x)\cdot g(x)[/tex]
[tex]=(2x-2)\cdot (-x+4)[/tex]
[tex]=-2x^2+8x+2x-8[/tex]
[tex]=-2x^2+10x-8[/tex]
The product of the binomials f(x) and g(x) is [tex]-2x^2+10x-8[/tex].
Binomial equation is the sum of the two terms usually joined by the plus or minus sign.The product of the binomials [tex]f(x)[/tex] and [tex]f(g)[/tex] is,
[tex]f(x)\times g(x)=-2x^2+10x-8[/tex]
Given-
The points of the line [tex]\overline f[/tex] is (2,2) and (1,0).
The points of the line [tex]\overline g[/tex] is (0,4) and (2,,2).
What is binomial function?
Binomial equation is the sum of the two terms usually joined by the plus or minus sign.
Find the equation of the line to solve the problem,
The slope of a line can be given as,
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Thus the slope of the line [tex]\overline f[/tex] is,
[tex]m_f=\dfrac{0-2}{1-2}[/tex]
[tex]m_f=2[/tex]
In the graph Y intercept of line [tex]\overline f[/tex] is -2. Therefore the equation of the line [tex]\overline f[/tex] is,
[tex]f(x)=m_fx+c_f[/tex]
the slope of the line [tex]\overline g[/tex] is,
[tex]m_g=\dfrac{2-4}{2-0}[/tex]
[tex]m_g=-1[/tex]
In the graph Y intercept of line [tex]\overline g[/tex] is 4. Therefore the equation of the line [tex]\overline g[/tex] is,
[tex]g(x)=m_fg+c_g[/tex]
[tex]g(x)=-x+4[/tex]
Now the product of the binomials [tex]f(x)[/tex] and [tex]f(g)[/tex] is,
[tex]f(x)\times g(x)=(2x-2)\times(-x+4)[/tex]
[tex]f(x)\times g(x)=-2x^2+8x+2x-8[/tex]
[tex]f(x)\times g(x)=-2x^2+10x-8[/tex]
Hence the product of the binomials [tex]f(x)[/tex] and [tex]f(g)[/tex] is,
[tex]f(x)\times g(x)=-2x^2+10x-8[/tex]
For more about the binomials, follow the link below-
https://brainly.com/question/3560614
