The area of a rectangle is represented by 10x^3+15x^2+4x+6 its dimensions are binomials in x with prime coefficients. What are the dimensions of the rectangle?

Question

The area of a rectangle is represented by
`10x^3+15x^2+4x+6` its dimensions are binomials in x with prime coefficients. What are the dimensions of the rectangle?

Answer 1

(5x^2 + 2) by (2x +3

Answer 2

(5x² +2) by (2x +3)

Explanation:

We want to factor the given polynomial to prime factors. These are factors that cannot be factored further using integers.

Observation

We observe that each pair of coefficients has the same ratio, so we can factor this cubic by pairs:

= (10x³ +15x²) +(4x +6)

= 5x²(2x +3) +2(2x +3)

= (5x² +2)(2x +3)

Conclusion

The factors we found cannot be factored further using integers, so each is a prime binomial factor. These are the factors the problem statement is asking for. We conclude ...

The dimensions of the rectangle are (5x² +2) by (2x +3).