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  1. 2

    Step-by-step explanation:

    You have to find a number that added with -6 equals -4, and multiplied equals -12.

    Just have to do the opperations and that is all!

    [tex](x-6)(x+2)=x^2+2x-6x-12=x^2-4x-12[/tex]

    Hope you like it!

  2. Hence, the value that Simon should write on the line i.e. in the blank space is: 2

    ( Since,  [tex]x^2-4x-12=(x+2)(x-6)[/tex] )

    Step-by-step explanation:

    We are asked to fill in the blank with the value obtained on factoring the polynomial:

    [tex]x^2-4x-12[/tex]

    on sing the method of splitting the middle term we will factor our polynomial as follows:

    [tex]x^2-4x-12=x^2-6x+2x-12\\\\x^2-4x-12=x(x-6)+2(x-6)\\\\x^2-4x-12=(x+2)(x-6)[/tex]

    Hence, the value that Simon should write on the line i.e. in the blank space is: 2

    ( Since,  [tex]x^2-4x-12=(x+2)(x-6)[/tex] )

  3. Option C is the answer.

    Step-by-step explanation:

    Simon is factorizing the polynomial x² - 4x - 12 = (x - 6)( x + )

    We will factorize the left hand side of the given expression

    x² - 4x - 12

    = x² - 6x + 2x - 12  

    Now we will break 12 into the factors so that sum of the factors should equal to 4

    { 6 × 2 = 12 and 6 - 2 = 4]

    = x(x - 6) + 2(x - 6)

    = (x + 2)(x - 6)

    Therefore, the blank space should be replaced by 2.

    Option C is the answer.

  4. Simon is factoring the polynomial. x2 – 4x – 12 (x – 6)(x + 2). The value should Simon write on the line is 2

  5. If you would like to know what value should Simon write on the line, you can calculate this using the following step:

    x^2 - 4 * x - 12 = (x - 6) * (x + 2)

    The correct result would be 2.

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