Mathematics
Grade10
Easy

Question

Write the difference in factored form. (24x4 – 15x2 + 6x) – (10x4+ 5x2 – 4x)

  1. 3x(4x2 + 8x – 6)
  2. 3x(4x2 – 8x + 6)
  3. 2x(7x3 – 10x + 5)
  4. 2x(6x3 + 10x – 4)

hintHint:

In this question, we have to find the difference in factored form. left parenthesis 24 x to the power of 4 minus 15 x squared plus 6 x right parenthesis minus left parenthesis 10 x to the power of 4 plus 5 x squared minus 4 x right parenthesis. firstly, we will find the difference of the given expression. Then we will find the factors of the expressions and find the common factors, the product of the common factors will be the GCF. Later we will take common the GCF from the expression to find the required expression.

The correct answer is: 2x(7x3 – 10x + 5)


    left parenthesis 24 x to the power of 4 minus 15 x squared plus 6 x right parenthesis minus left parenthesis 10 x to the power of 4 plus 5 x squared minus 4 x right parenthesis
equals 24 x to the power of 4 minus 15 x squared plus 6 x minus 10 x to the power of 4 minus 5 x squared plus 4 x
equals 14 x to the power of 4 minus 20 x squared plus 10 x
    Factors of 14x4 = 2cross times7cross timesxcross timesxcross timesxcross timesx
    Factors of -20x2 = (-1)cross times2cross times2cross times5cross timesxcross timesx
    Factors of 10x = 2cross times5cross timesx
    Common factors = 2, x
    GCF = 2cross timesx = 2x.
    14 x to the power of 4 minus 20 x squared plus 10 x
equals 2 x left parenthesis 7 x to the power of 4 minus 10 x squared plus 5 right parenthesis

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