How do you factor 11x^2-10x-1?

Comments

  • (11x + 1)(x - 1)

    This one's a bit straight forward, we look at the factors of our first term's coefficient and those of our last term

    so lets make two lists

    11 & 1 and that's it

    1 & -1 and that's it

    Now we need to combine them in a way to make -10

    11*1 + 1*(-1) = 10

    11*(-1) + 1*1 = -10

    so now we know that 11 has to multiply the -1

    (11x + 1)(x - 1)

  • HI,

    11x^2-10x-1=>11x^2+1-11x-1 =>x(11x+1)-(11x+1) =>(11x+1)(x-1)

  • 11x² - 10x - 1

    Polynomial like : ax² + bx + c, where :

    a = 11

    b = - 10

    c = - 1

    Δ = b² - 4ac (discriminant)

    Δ = (- 10)² - 4(11 * - 1) = 100 + 44 = 144 = 12²

    x1 = (- b - √Δ) / 2a = (10 - 12) / (2 * 11) = - 2/22 = - 1/11

    x2 = (- b + √Δ) / 2a = (10 + 12) / (2 * 11) = 22/22 = 1

    Therefore, the polynomial can be written :

    = 11[x + (1/11)](x - 1)

    = (11x + 1)(x - 1)

  • (11x+1)(x-1) would yield 11x^2 + 1x - 11x -1, which equals 11x^2 - 10x - 1

  • 11x^2-10x-1=

    =11x^2+1-11x-1=

    =x(11x+1)-(11x+1)=

    =(11x+1)(x-1)

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