Math

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Can some one explain these to me i need the factors. i am totally lost.
thanks
x^2+x-6
x^2+7x+10
x^2+5x+6
x^2+2xy+15y^2

  • Math -

    (x+a)(x+b)
    FOIL
    x^2 + ax + bx + ab which can be simplified into
    x^2 + (a+b)x + ab
    Use this as a base for all of the your equations.

    Lets do the first one.

    ab will be the same as the last term which is -6. Then look at the second term which is x. In this case there is nothing in front of x. However x is the same as 1 times x since 1 times anything is the same. Look back to the equation I gave you.
    (a+b)x will be equal to 1x which is equal to x. Therefore, a+b has to equal to 1 and we know ab is equal to -6. List all the two pairs of whole numbers whose product is 6.

    1 6
    2 3

    Since 6 is negative it means one of them has to be negative
    -1 6
    1 -6
    -2 3
    2 -3

    (a+b) = 1
    The only pair of numbers above that add up to 1 is 3 and -2. So just let a = 3 and b = -2.
    (x+a)(x+b)
    (x+3)(x-2)
    And there you go. Sorry, if you still don't understand, I know I'm far from being an expert on explaining stuff.

  • Math -

    x^2+7x+10
    x^2+(a+b)x+ab
    ab = 10
    a+b = 7

    Pairs whose product is 10.
    1 10
    2 5

    Then only pair that add up to 7 is 2 and 5. So let a = 2 and b = 5.
    (x+a)(x+b)
    (x+2)(x+5)

    -----------------------------
    x^2+5x+6
    x^2+(a+b)x+ab
    ab = 6
    a+b = 5

    Pairs whose product is 6

    1 6
    2 3

    Then the only pair that adds up to 5 is 2 and 3. So let a = 2 and b = 3.
    (x+a)(x+b)
    (x+2)(x+3)

    -----------------------------
    The last one is complicated... and it involves material that you may not have learned yet if you just started factors. Are you sure it is correct?

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