Suppose that x represents the larger of two consecutive odd integers. a. Write a polynomial that represents the smaller integer. b. Write a polynomial that represents the sum of the two integers. Then simplify. c. Write a polynomial that represents the product of the two integers. Then simplify. d. Write a polynomial that represents the difference of the squares of the two integers. Then simplify

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Suppose that x represents the larger of two consecutive odd integers.  a. Write a polynomial that represents the smaller integer.  b. Write a polynomial that represents the sum of the two integers. Then simplify.  c. Write a polynomial that represents the product of the two integers. Then simplify.  d. Write a polynomial that represents the difference of the squares of the two integers. Then simplify

Laaibah Pitt · Accepted Answer

Step 1 Given: x represents the larger of two consecutive odd integers a. a polynomial which represent the smaller integer is x−2 b. a polynomial which represent the sum of two integers are x and x−2 is x+x−2=2x−2 Step 2 c. a polynomial which represent the product of two integers are x(x−2)=x2−2x d. a polynomial which represent the difference of square of two integers are x2−(x−2)2=x2−x2+4x−4=4x−4

star233 · Accepted Answer

Step 1:a. Let&#039;s represent the smaller integer as x−2. Since the integers are consecutive odd numbers, we can deduce that the smaller integer will be two units less than the larger integer.Step 2:b. To represent the sum of the two integers, we simply add them together. Therefore, the polynomial representing the sum of the two integers is x+(x−2).To simplify the expression, we combine like terms:x+(x−2)=x+x−2=2x−2Hence, the simplified polynomial representing the sum of the two integers is 2x−2.Step 3:c. To represent the product of the two integers, we multiply them. Thus, the polynomial representing the product is (x)(x−2).To simplify the expression, we use the distributive property:(x)(x−2)=x2−2xTherefore, the simplified polynomial representing the product of the two integers is x2−2x.Step 4:d. To represent the difference of the squares of the two integers, we square each integer and then find their difference. The larger integer is x, so its square is x2. The smaller integer is x−2, so its square is (x−2)2.Expanding (x−2)2 using the binomial expansion formula, we have:(x−2)2=x2−4x+4Now, we can subtract x2−4x+4 from x2 to find their difference:x2−(x2−4x+4)Using the distributive property, we change the subtraction inside the parentheses to addition with the negation of the terms:x2−x2+4x−4The x2 terms cancel out, and we are left with:4x−4Hence, the simplified polynomial representing the difference of the squares of the two integers is 4x−4.

karton · Accepted Answer

a. The smaller integer can be represented by x−2 since it is the consecutive odd integer that comes before x.b. The sum of the two integers can be represented by (x−2)+x. Simplifying this expression gives 2x−2.c. The product of the two integers can be represented by (x−2)·x. Simplifying this expression gives x2−2x.d. The difference of the squares of the two integers can be represented by x2−(x−2)2. Expanding (x−2)2 gives x2−4x+4. Simplifying the expression gives x2−x2+4x−4, which further simplifies to 4x−4.

Suppose that x represents the larger of two consecutive odd integers. a. Write a polynomial that represents the smaller integer. b. Write a polynomial

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