Create a trinomial where the GCF of the trinomial is 5m^3

5m^5 + 15m⁴ + 35m³

Step-by-step explanation:

GCF means greatest common factor.

The Greatest common factor of two monomials for example, is the product of the common prime factors of both monomials.

We are to develop a trinomial which would have 5m³ as its greatest common factor.

To Create a trinomial where the GCF of the trinomial is 5m³, we would find a trinomial that can't be factored and multiply it by 5m³.

A trinomial is a polynomial which has three terms (monomials) connected by addition or subtraction.

Let's consider the trinomial m² + 3m + 7

This trinomial cannot be factored because there are no common factors between them. The constants to be considered are 3 and 7.

3 is a prime number and therefore can only be factored to 1 and 3.

7 is a prime number and therefore can only be factored to 1 and 7.

Since there are no common factors other than 1, the constants cannot be factored.

By multiplying 5m³ with the trinomial m² + 3m + 7

We would have:

5m³ (m² + 3m + 7) = 5m^5 + 15m⁴ + 35m³

From the above, the trinomial where the GCF of the trinomial is 5m³ = 5m^5 + 15m⁴ + 35m³

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

80 the answer is 80

step-by-step explanation: