Question

PLEASE HELP ITS DUE TODAY!!! What is the product of 1/2x-1/4 & 5x^2-2x+6? Write your answer in standard form. (A) show your work. (B) is the product of 1/2x-1/4 & 5x^2-2x+6 equal to the product of 1/4x-1/2 & 5x^2-2x+6? Explain your answer

Answer 1

Answer:

  (A)  (5/2)x^3 -(9/4)x^2 +(7/2)x -3/2

  (B)  No. The factor 1/4x -1/2 is not the same as 1/2x -1/4.

Step-by-step explanation:

(A) With a little practice, you can do these in your head, so there is no "work" to show.

The product of highest-degree terms is (1/2x)(5x^2) = (5/2)x^3.

The x^2 term in the product will be the sum of terms that are one of ...

• x-term × x-term
• constant × x^2

so the x^2 term is ...

  (1/2x)(-2x) + (-1/4)(5x^2) = -x^2 -(5/4)x^2 = -(9/4)x^2

The x-term in the product will be the sum of terms of the form

• constant × x-term

so the x term is ...

  (1/2x)(6) + (-1/4)(-2x) = 3x +(1/2)x = (7/2)x

Finally, the constant term in the product is the product of the constants:

  (-1/4)(6) = -6/4 = -3/2

This makes the product of the two polynomials be ...

  (5/2)x^3 -(9/4)x^2 +(7/2)x -3/2

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(B) One of the factors is the same, but the other is different. The product will be different.

• 1/2x -1/4 = (2x-1)/4
• 1/4x -1/2 = (x -2)/4 . . . . not the same as above