Steve it is a polynomials product it is asking me for the sum the difference and the product for this problem X -1 : X-2 I do not know how to do this as we just started this today thank you sir
No problem, I can help you with that! To find the sum, difference, and product of two polynomials, we need to multiply them together using the distributive property and combine like terms.
In your case, the given polynomials are (X - 1) and (X - 2). To find their product, we'll multiply each term of the first polynomial by each term of the second polynomial.
Step 1: Write down the two polynomials:
(X - 1) and (X - 2)
Step 2: Multiply the terms:
(X * X) + (X * -2) + (-1 * X) + (-1 * -2)
Step 3: Simplify by combining like terms:
X^2 - 2X - X + 2
Step 4: Rearrange the terms in ascending order of the exponent:
X^2 - 3X + 2
So, the product of (X - 1) and (X - 2) is X^2 - 3X + 2.
Now, let's find the sum and difference of the two polynomials.
To find the sum, we'll add the two polynomials:
(X - 1) + (X - 2)
Step 1: Remove the parentheses:
X - 1 + X - 2
Step 2: Combine like terms:
2X - 3
So, the sum of (X - 1) and (X - 2) is 2X - 3.
To find the difference, we'll subtract the second polynomial from the first polynomial:
(X - 1) - (X - 2)
Step 1: Remove the parentheses:
X - 1 - X + 2
Step 2: Combine like terms:
1
So, the difference of (X - 1) and (X - 2) is 1.
Therefore, the sum is 2X - 3, the difference is 1, and the product is X^2 - 3X + 2.