Multiply the given polynomials and write the degree of the product .
(x2 - 4x+8) (x2-1)
Answers
Step-by-step explanation:
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Answer:
The product of given polynomials is x⁴-4x³+7x²+4x-8.
The degree of the product is 4.
Step-by-step explanation:
Polynomial:
- Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables.
- For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents, but not division by variable.
- x²+x-12 is an illustration of a polynomial with a single variable. There are three terms in this example: x², x, and -12.
Degree of a polynomial:
- The highest degree of a monomial within a polynomial is referred to as the polynomial's degree.
- As a result, a polynomial equation with one variable having the biggest exponent is referred to as a polynomial degree.
Given, polynomials are (x²-4x+8) and (x²-1)
Product of polynomials is
(x²-4x+8) (x²-1) = x²(x²-1)-4x(x²-1)+8(x²-1)
= x⁴-x²-4x³+4x+8x²-8
= x⁴-4x³+7x²+4x-8
The product of given polynomials is x⁴-4x³+7x²+4x-8.
The highest power is the degree of the product obtained.
The degree of the product is 4.
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