When multiplying polynomials for a math assignment, pat found the product to be -4x+8x^2-2x^3+5. he then had to state the leading coefficient of this polynomial. pat wrote down -4. do you agree with pat’s answer? explain your reasoning.

I am not agree with him. Because -2 is the leading coefficient of this  polynomial.

Step-by-step explanation:

Pat multiplied the polynomials for a math assignment.

Then he found the product is

Now Pat wants to find the leading coefficient to this polynomial.

Pat's answer was -4.

But I am not agree with him.

Because for a given polynomial we can calculate the leading coefficient when comparing with degrees of the polynomial.

Leading coefficient means that the coefficient whose degree is the highest.

When compared with the given polynomial we have is the highest degree, so that -2 is the leading coefficient to this polynomial.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions