The product of two binomials, u(x) and v(x), is a binomial of degree 8 with a positive leading coefficient. What must be true about the sum of u(x) and v(x)?

Step-by-step explanation:

If the product of two binomials, u(x) and v(x)has a binomial of degree 8, then the individual binomial will have a binomial of degree 4. For example, lets assume u(x) = ax⁴ + bx and v(x) ax⁴+cx. Note that they are both functions of x and contain only two terms since they are binomial.

Taking their product we have;

u(x)*v(x) =  (ax⁴ + bx)*(ax⁴+cx)

u(x)*v(x) = a²x⁸+acx⁵+abx⁵+bcx²

it can be seen that the higest power of x is 8 which gives the degree of the product.

Taking their sum;

u(x)+v(x) =   (ax⁴ + bx)+(ax⁴+cx)

u(x)+v(x) = ax⁴ + ax⁴+ bx +cx

u(x)+v(x)  = 2ax⁴ + bx +cx

It can be seen that the digest power of x is 4 which gives the degree of the sum of the binomial.

From the above conclusion, it can be inferred that  sum of u(x) and v(x) is a binomial of degree 4 with a positive or negative leading coefficient depending on the value of the constant 'a'

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step-by-step explanation:

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