Question

1. the force created by the main engines of a jet can be expressed by the polynomial (5x^{3}-8x^{2}+7x - 12). the force of the secondary engines can be expressed by the polynomial (2x^{2}+7x + 8). what is the combined force of the main and secondary engines?

Explanation:

Step1: Add the two polynomials

$$(5x^{3}-8x^{2}+7x - 12)+(2x^{2}+7x + 8)$$

Step2: Combine like terms

• For \(x^{3}\) term: \(5x^{3}\)
• For \(x^{2}\) term: \(-8x^{2}+2x^{2}=-6x^{2}\)
• For \(x\) term: \(7x + 7x=14x\)
• For constant term: \(-12 + 8=-4\)

Answer:

\(5x^{3}-6x^{2}+14x - 4\)