Question

How do you find the product of \[(x + 7)(x + 4)\] ?

Answer 1

Hint: We have multiplication of two polynomials that is \[(x + 7)\] and \[(x + 4)\] . Both the polynomials have degree one. Hence both polynomials are called monomials. To multiply polynomials, first multiply each term in one polynomial by each term in the other polynomial using distributive law. Then, simplify the resulting polynomial by adding or subtracting the like terms.

Complete step-by-step answer:
Given, \[(x + 7) \times (x + 4)\]
In the first polynomial we have two terms and in the second polynomial also we have two terms. Multiply the first term of a polynomial with second polynomial and second term with second polynomial we have,
 \[ = \left( {x \times (x + 4)} \right) + \left( {7 \times (x + 4)} \right)\]
Multiplying we have,
 \[ = {x^2} + 4x + 7x + 28\]
Adding the like terms we have,
 \[ = {x^2} + 11x + 28\]
Thus we have \[(x + 7) \times (x + 4) = {x^2} + 11x + 28\]
So, the correct answer is “ \[(x + 7) \times (x + 4) = {x^2} + 11x + 28\] ”.

Note: Degree of a polynomial is the highest of the degrees of the individual term with non-zero coefficients. We have different polynomials. Those are constant polynomial, linear polynomial, quadratic polynomial, cubic polynomial and quartic polynomial etc. have degree 1, 2, 3 and 4 respectively.
For avoiding mistakes write the terms in the decreasing order of their exponent. Thus we obtained a polynomial of degree two. Hence, the obtained polynomial is quadratic polynomial. When we multiply two polynomials of any degree the obtained polynomial must have degree higher than multiplied individual polynomials. We can check this in the given above problem and it satisfies the condition. Be careful with the sign when you open the brackets. Follow the same procedure for any two polynomials.