Question

Find the product of \[{\text{(5 - 2x)}}\] and \[{\text{(4 + x)}}\]

Answer 1

Hint: Apply the method of product of polynomial as when we find the product of any two polynomials, we just multiply each term of the first polynomial by each term of the second polynomial and then simplify.

Complete step-by-step answer:
Given \[{\text{(5 - 2x)}}\]and \[{\text{(4 + x)}}\]
In order to calculate the product of the polynomial proceed as in the way by multiplication of each and every term
Of one bracket to another bracket.
\[
  {\text{ = (4 + x)}}{\text{.(5 - 2x)}} \\
  {{ = (4 \times 5 + 4 \times ( - 2x) + x(5) + x( - 2x))}} \\
  {\text{On simplifying we get,}} \\
  {\text{ = (20 - 8x + 5x - 2}}{{\text{x}}^{\text{2}}}{\text{)}} \\
  {\text{ = 20 - 3x - 2}}{{\text{x}}^{\text{2}}} \\
  \]
Hence, our required answer is \[{\text{ = 20 - 3x - 2}}{{\text{x}}^{\text{2}}}\].

Note: A polynomial function is a function which involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc. For example, \[{\text{(2x + 5)}}\] is a polynomial which has an exponent equal to \[1\].The product of two numbers is the result you get when you multiply them together.
When we find the product of any two polynomials, we just multiply each term of the first polynomial by each term of the second polynomial then simplify. When we find the product of two binomials, we can use a technique known as the FOIL method. FOIL is an acronym which stands for First, Outside, Inside and Last.