.
-i*(i - 1)**3*(i + 1)/2
Let l be (-91)/(-42) + 4/(-24). Factor o**3 - 5*o**2 + 4*o**l + 5*o**2 - 2*o**3.
-o**2*(o - 4)
Let x(m) be the first derivative of -m**5/5 + m**4/4 - m**2/2 - 2*m + 119. Let n(w) = 0*w**2 - w**2 + 0*w**2. Let q(g) = -3*n(g) + x(g). Factor q(z).
-(z - 2)*(z - 1)*(z + 1)**2
Suppose 0 = -7*g + 15*g. Let c(h) be the second derivative of -4/3*h**3 + g + 2*h**2 + 5/12*h**4 + 2*h - 1/20*h**5. Factor c(j).
-(j - 2)**2*(j - 1)
Solve 252*y - 296*y - 484*y - 34*y**2 + 23232 + 69*y**2 - 32*y**2 = 0 for y.
88
Let f(p) be the second derivative of -p**8/3360 - p**7/1260 + p**6/180 - 5*p**4/3 + 19*p. Let g(s) be the third derivative of f(s). Suppose g(k) = 0. What is k?
-2, 0, 1
Find f, given that -36*f**2 + 0 - 1 + 0 - 7 + 14*f - 58*f = 0.
-1, -2/9
Let s(z) = -z**3 - 10*z**2 - 17*z - 8. Let i be s(-8). Factor 12*f - f**3 - 5*f**2 + i*f**2 + 3*f**3 - 9*f**2.
2*f*(f - 6)*(f - 1)
Let d(x) be the second derivative of x**7/630 - 7*x**6/90 + 49*x**5/30 + 5*x**4/3 + 14*x. Let l(k) be the third derivative of d(k). Factor l(z).
4*(z - 7)**2
Suppose 0 = 5*m - 5*c - 30, -3*c - 2 = -4*m + 9*m. Suppose 10*f - m*f = 24. Suppose z**2 + 1/2*z + 0 + 1/2*z**f = 0. Calculate z.
-1, 0
Let h(f) = f**3 + 10*f**2 - 10*f + 13. Let k be h(-11). Solve 56*l**5 - 110*l**4 + 48*l**3 - 3*l**k - 7*l + 13*l**2 + 3*l = 0.
-2/7, 0, 1/4, 1
Suppose 0 = -11*p - 1 + 45. Factor -5*c + p*c**4 + 5*c**2 - 3*c**2 + 4*c**3 - 6*c**2 + c.
4*c*(c - 1)*(c + 1)**2
Let v(h) be the first derivative of h**2/2 + 9*h + 6. Let m be v(-5). Find c, given that -3 + m - 6 - 3*c + 3 - c**2 = 0.
-2, -1
Let h be (-8)/(-1) + -4 - 119. Let s = h + 115. Solve 3/2*v - 3/2*v**3 + s*v**2 + 0 = 0.
-1, 0, 1
Let u(q) be the first derivative of 50 + 0*q - 15/4*q**4 + 5/6*q**6 - 5*q**2 + 25/3*q**3 - q**5. Factor u(s).
5*s*(s - 1)**3*(s + 2)
Let r(h) = h**3 - 10*h**2 + 9*h + 12. Let t be r(9). Suppose -33 - t = -5*g. Factor 21*n**2 + 4 + g*n - 3*n - 27*n**3 - 4.
-3*n*(n - 1)*(9*n + 2)
Let r(j) be the first derivative of -2*j**3/9 + 3*j**2 - 12*j + 27. What is m in r(m) = 0?
3, 6
Let c(i) = 36*i**3 - 99*i**2 + 70*i - 11. Let v(j) = 505*j**3 - 1385*j**2 + 980*j - 155. Let o(z) = -55*c(z) + 4*v(z). Factor o(m).
5*(m - 1)**2*(8*m - 3)
Let z(t) be the second derivative of t**6/285 - 6*t**5/95 + 9*t**4/38 + 4*t**3/57 - 36*t**2/19 + 142*t. Suppose z(a) = 0. Calculate a.
-1, 2, 9
Factor 0*d - 4/3*d**3 - 4/3*d**2 + 0.
-4*d**2*(d + 1)/3
Factor 2*z - 44 - 4*z**2 - 4*z**3 + 2*z**5 - 43 - 39 + 172 + 2*z**4 - 44.
2*(z - 1)**2*(z + 1)**3
Let s(k) be the second derivative of k**7/1050 + k**6/225 - k**5/50 - 2*k**3 + 32*k. Let f(w) be the second derivative of s(w). Find n, given that f(n) = 0.
-3, 0, 1
Suppose -5*c + 17 = r, 5*r = -2*c - 7 - 0. Let z be 192/280 - (c/10 + 0). Factor 6/7*x**2 + 0 - z*x**3 - 4/7*x.
-2*x*(x - 2)*(x - 1)/7
Suppose -18 = 7*x + 3. Let i be 8/36*(6 + x). Let 2/3*j**2 - 5/3*j - i + 5/3*j**3 = 0. Calculate j.
-1, -2/5, 1
Let z = -440 - -10115/23. Let k = z + 109/184. Let -k*q**2 + 0*q - 1/8*q**3 + 1/2 = 0. Calculate q.
-2, 1
Let u be 26/7 + (-10)/(-35) + -2. Find c, given that 0*c - 4*c - c**2 + c**2 + c**u = 0.
0, 4
Let w(l) be the first derivative of l**4/2 + 4*l**3/3 + 677. Find q such that w(q) = 0.
-2, 0
Let r(c) = -c**2 + 27. Suppose -3*z + 34 = -5*j, z - 2 - 1 = 0. Let y be r(j). Factor 1/3*u**4 + 1/3 + 2*u**y - 4/3*u - 4/3*u**3.
(u - 1)**4/3
Let q(g) = 6*g**2 - 2*g + 3. Let s be q(0). Let z(t) be the third derivative of 0*t - 1/3*t**3 + s*t**2 - 1/90*t**5 + 0 - 1/9*t**4. Let z(d) = 0. What is d?
-3, -1
Factor -5*w**4 + 3*w**2 + 38*w**2 - 76*w**2 + 15*w + 25*w**3.
-5*w*(w - 3)*(w - 1)**2
Let p(j) be the first derivative of 3*j**4/4 + 5*j**3/3 + j**2 + 217. Factor p(h).
h*(h + 1)*(3*h + 2)
Let q(z) be the third derivative of z**5/420 - z**4/14 - 2*z**3/3 - 5*z**2 + 2*z. Factor q(l).
(l - 14)*(l + 2)/7
Suppose -3*y = -7*y - 10*y + 3*y. Suppose -3/8*o**3 + 3/4 + y*o**2 + 9/8*o = 0. Calculate o.
-1, 2
Let z(w) be the first derivative of w**4/8 + w**3/3 - 5*w**2/4 - 3*w - 123. Suppose z(m) = 0. What is m?
-3, -1, 2
Suppose 2*q - 5*q - 5*p + 11 = 0, 3*q + 2*p - 8 = 0. Solve 0*w - 1/8*w**q - w**4 + 0 - 7/8*w**3 + 2*w**5 = 0.
-1/4, 0, 1
Let u(j) be the third derivative of -j**5/30 + 41*j**4/6 + 83*j**3/3 - 2*j**2 + 4. Determine v so that u(v) = 0.
-1, 83
Let j(a) be the second derivative of a**4/16 + a**3/4 - 2*a - 14. Factor j(b).
3*b*(b + 2)/4
Suppose 96 - 153 = -19*s. Factor 8/5 + 2/5*z**s + 4/5*z**2 - 14/5*z.
2*(z - 1)**2*(z + 4)/5
Suppose -1500 + 516 = 8*w. Let x = 123 + w. Factor 4/5*c - 26/5*c**4 + 2/5*c**2 - 2*c**5 - 18/5*c**3 + x.
-2*c*(c + 1)**3*(5*c - 2)/5
Suppose -8*i + 57 = 825. Let a be (i/(-80))/((-39)/(-30) + -1). Factor -2/17*x**5 + 0 + 4/17*x**2 + 6/17*x**3 + 0*x**a + 0*x.
-2*x**2*(x - 2)*(x + 1)**2/17
Let z(t) be the first derivative of t**6/360 - 4*t**5/75 + t**4/10 - 11*t**3/3 + 11. Let w(o) be the third derivative of z(o). Factor w(b).
(b - 6)*(5*b - 2)/5
Let v = -209 - -209. Let w(q) be the third derivative of 0*q**3 + 0 + 1/45*q**5 + v*q - 1/180*q**6 + 2*q**2 + 0*q**4. Factor w(n).
-2*n**2*(n - 2)/3
Factor -4 + 5*u + 5/4*u**4 - 19/4*u**3 + 3*u**2.
(u - 2)**2*(u + 1)*(5*u - 4)/4
Let y(h) be the first derivative of 3*h**4/4 - 45*h**3 + 2025*h**2/2 - 10125*h + 66. Factor y(v).
3*(v - 15)**3
Let q be ((-12)/(-200)*-35)/((-21)/35). Factor q*l + 17/4*l**2 + 9/8*l**3 - 1.
(l + 2)**2*(9*l - 2)/8
Let a(s) = -6*s**2. Suppose 5*w + 3 = -4*r, -w - 5 = 4*r + 2. Let l(z) = z**3. Let i(x) = w*a(x) + 3*l(x). Let i(c) = 0. What is c?
0, 2
Let i(u) be the second derivative of -u**5/80 + u**4/8 + u**3/24 - 3*u**2/4 - 3*u. Factor i(g).
-(g - 6)*(g - 1)*(g + 1)/4
Let g be (0 + (-42)/15)/(3/(-30)). Suppose -12*m = -19*m + g. What is o in -8/15*o**3 - 4/5*o**2 - 2/15*o**m - 2/15 - 8/15*o = 0?
-1
Let a(r) be the third derivative of -r**8/420 - 2*r**7/315 - 2*r**6/405 + 7*r**3/6 - 23*r**2. Let k(j) be the first derivative of a(j). Factor k(z).
-4*z**2*(3*z + 2)**2/9
Let t be (-1551)/561 - (-3)/1. Factor -t + 2/17*k + 2/17*k**2.
2*(k - 1)*(k + 2)/17
Let l = 12 - 5. Suppose -3*x - 4*k + 30 = 0, -6 = 5*k - l*k. Factor -3*z**3 - 2*z - z + x*z.
-3*z*(z - 1)*(z + 1)
Let n(l) be the second derivative of 5/2*l**2 - 8*l - 1/210*l**5 + 1/21*l**3 + 0*l**4 + 0. Let b(v) be the first derivative of n(v). Let b(i) = 0. Calculate i.
-1, 1
Solve 4/5*c + 0 - 2/5*c**4 + 2/5*c**2 - 4/5*c**3 = 0 for c.
-2, -1, 0, 1
Let s(n) = 233 - 120 + n**2 + 4*n - 113. Let p be 4/(-2) + 8/2. Let f(t) = -3*t**2 - 15*t. Let l(k) = p*f(k) + 9*s(k). Factor l(u).
3*u*(u + 2)
Let f be (-29)/(-9) + (-20)/90. Determine j so that 23*j**2 - 13*j**2 + j**3 - 6*j**f = 0.
0, 2
Suppose 0 = -2*k - 5*x + 2013, -2*k - 3*k = -3*x - 5110. Solve 999 + 5*f**4 - 20*f - k + 15*f**3 + 5*f**3 + 15*f**2 = 0.
-2, -1, 1
Find d such that 134/3*d**3 + 130/3*d**4 - 98/3*d**2 - 148/3*d + 14/3*d**5 - 32/3 = 0.
-8, -1, -2/7, 1
Let g = 11111 + -11111. Suppose g - 4/9*b**3 - 1/9*b**4 + 1/9*b**2 + 4/9*b = 0. What is b?
-4, -1, 0, 1
Factor 516*r**3 - 21*r**2 - 250*r**3 + 18*r - 263*r**3 - 6*r + 36.
3*(r - 6)*(r - 2)*(r + 1)
Let j be -4 + (0 + (-265)/(-120))*-129. Let x = j - -289. Factor -1/8*w**3 + 0 - x*w**2 + 0*w.
-w**2*(w + 1)/8
Let i(c) = -c**3 + 7*c**2 + 16*c - 13. Let w be i(8). Let p = w + -51. Factor 9/7*d**2 + 3/7*d**3 - 12/7 + p*d.
3*(d - 1)*(d + 2)**2/7
Let r(k) be the second derivative of 28*k - 9/7*k**2 + 0 - 1/42*k**4 - 2/7*k**3. Factor r(c).
-2*(c + 3)**2/7
Let s(h) = 26*h**2 - 478*h + 185. Let w be s(18). Determine a, given that 7*a**2 + 2*a**4 - 3*a - 23/4*a**3 + 0 - 1/4*a**w = 0.
0, 1, 2, 3
Suppose -2*t = 0, -2*a - 2*t - 2*t - 62 = 0. Let v = a - -158/5. Determine o, given that -v*o + 3/5*o**2 + 1/5 - 1/5*o**3 = 0.
1
Let l(t) be the first derivative of -35 + 0*t**4 + 1/3*t**6 + 0*t - 2/5*t**5 + 0*t**2 + 0*t**3. Solve l(h) = 0 for h.
0, 1
Let t(v) be the first derivative of -v**5/20 + 3*v**4/4 - 9*v**3/2 + 27*v**2/2 - 10*v - 35. Let g(r) be the first derivative of t(r). Factor g(i).
-(i - 3)**3
Let b be (-17)/14 + 33/(-66) - -2. Factor 22/21*s - 8/21*s**2 + b.
-2*(s - 3)*(4*s + 1)/21
Suppose 11*i = 10*i + 6. Solve 7*l + 7*l - 4*l**2 - 6 + 0*l**3 - i*l**2 + 2*l**3 = 0.
1, 3
Let y be 3*6/(-24)*(-4)/1. Find l such that -16 + 18*l**2 + 20 + y*l**2 - 16 