Markkkkyyy poo @MarkFL . Factor over the integers the polynomial that is quadratic in form. (Factor your answer completely.) x^4 − 13x^2 + 36 Last question T.T

Okay, first we observe that this is a quadratic in x^2. So, we want to look for two factors of 36 whose sum is -13, and they are -4 and -9...so we have: x^4 - 13x^2 + 36 = (x^2 - 4)(x^2 - 9) Now, we see both factors are differences of squares, so we have: x^4 - 13x^2 + 36 = (x^2 - 4)(x^2 - 9) = (x^2 - 2^2)(x^2 - 3^2) = (x + 2)(x - 2)(x + 3)(x - 3) And we're done.

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That's the largest value it can approach as x gets farther and farther from zero. The smallest value x^2 can be is zero, and that's when x is zero. So, given the smallest value for x^2 is zero, then the smallest value for y will be -7 because y is defined to be x^2 - 7. And so given that y(x) = x^2 - 7, we have: y(0) = 0^2 - 7 = -7 Next we observe that if we move one unit away from zero, to ±1, we find: y(±1) = (±1)^2 - 7 = 1 - 7 = -6 Likewise: y(±2) = (±2)^2 - 7 = 4 - 7 = -3 y(±3) = (±3)^2 - 7 = 9 - 7 = 2 And so the 4 smallest elements of the given set are {-7, -6, -3, 2}.