Answer:
see below
Step-by-step explanation:
You know the leading term will be the product of leading terms, so is ...
(x^2)(3x^2) = 3x^4 . . . . . matches choices A, B, C
The x^3 term of the product will be the sum of the products of x and x^2 terms, so is ...
(x^2)(2x) +(3x^2)(-5x) = 2x^3 -15x^3 = -13x^3 . . . . . matches choice A only
With very little work, we have identified the only viable answer choice:
3x^4 -13x^3 -x^2 -11x +6
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You can work out the product using the distributive property 4 times: multiply each term of one polynomial by all terms of the other. Then collect terms.
A reasonable alternative is to identify the partial products that will make up any given term of the answer. Above we have shown how to find the x^4 and x^3 terms. The x^2 term will be the sum of products (x^2)(constant) +(x)(x), for a total of 3 contributors to that. Similar to the x^3 term, the x term of the product will be the sum of products (x)(constant). Of course, the final constant term in the result is only the product of the constants in each factor.
If you go about this systematically, then errors will not creep in, regardless of which method you use.
