Answer:
Polynomials are classified according to their number of terms. 4x3 +3y + 3x2 has three terms, -12zy has 1 term, and 15 - x2 has two terms. As already mentioned, a polynomial with 1 term is a monomial. A polynomial with two terms is a binomial, and a polynomial with three terms is a trinomial.
Step-by-step explanation:
Multiplying polynomials combines the laws of exponents for multiplication and adding polynomials. To multiply two polynomials, we use the distributive property, [a(b +c + d) = ab + ac + ad], to make sure that each term of one polynomial is multiplied with every term of the other. Then, we add the results by combining like terms. There are different situations to consider:
(1) Multiplication of a Monomial by another Monomial e.g. (5xy)(-2y) = -10xy²
(2) Multiplication of a Monomial by a Polynomial e.g. (-3x)(2x² - 5x + 1) = (-3x)(2x²) + (-3x)(-5x) + (-3x)(1) = -6x³ + 15x² - 3x
(3) Multiplication of a Polynomial by another Polynomial e.g. (x + 5)(-x² + 8x - 3) = (x)(-x²) + (x)(8x) + (x)(-3) + 5(-x²) + 5(8x) + 5(-3) = -x³ + 8x² - 3x - 5x² + 40x - 15 = -x³ + 3x² + 37x - 15
For example, let's say that the length of a rectangular window is 5 feet more than its width, w². With this information we can write an algebraic expression for the area of the window: we have that its width = w² and its length = w² + 5. So the area of the rectangular window = w²(w² + 5) = w⁴ + 5w².
