Answer:
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'
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'
