- k**2 - 3*k + 1. Suppose -4 = 8*s + 12. Let f(m) = s*g(m) + 11*h(m). Solve f(d) = 0 for d.
-1
Let u(w) = w**2 + 27*w - 6*w**2 + 0*w**2 + 4*w**2 - 69. Let s be u(24). Factor 0 + 3/5*n**2 + 0*n - 4/5*n**4 + 11/5*n**s.
-n**2*(n - 3)*(4*n + 1)/5
Let c(t) be the third derivative of t**8/1176 + 2*t**7/147 + 19*t**6/210 + 34*t**5/105 + 19*t**4/28 + 6*t**3/7 + 2*t**2 + 7*t. Suppose c(b) = 0. Calculate b.
-3, -2, -1
Suppose 0 = -4*o - 3*y + 33, 21*o + 132 = 16*o + 21*y. Factor 0 - 2/5*q**4 + 0*q - 2/5*q**2 - 4/5*q**o.
-2*q**2*(q + 1)**2/5
Let m(x) be the second derivative of -x**4/54 + 25*x**3/27 - 28*x**2/3 - 5*x + 2. Let m(j) = 0. What is j?
4, 21
Let n(u) be the first derivative of 5*u**9/1008 - u**8/168 - u**7/168 - 26*u**3/3 + 17. Let d(w) be the third derivative of n(w). Suppose d(c) = 0. What is c?
-1/3, 0, 1
Let y(t) = -t**3 - 7*t**2 - 13*t - 12. Let f be y(-5). Suppose -5*l**2 + 6*l**2 + 2*l**4 + 0*l**f + 6*l**3 + 3*l**2 = 0. What is l?
-2, -1, 0
Determine f so that 22*f**4 + 7*f**5 - 5*f**3 - 2*f**5 - f**2 - 4*f**4 - 9*f**2 - 8*f**4 = 0.
-2, -1, 0, 1
Let x(r) be the first derivative of -3*r**6/2 + 12*r**5/5 + 39*r**4/4 + 6*r**3 + 308. Solve x(a) = 0.
-1, -2/3, 0, 3
Factor 2*p**2 + 3*p**2 - 7*p**2 + 2*p + 10*p**3 - 7*p**2 - 4*p**4 + p**4.
-p*(p - 2)*(p - 1)*(3*p - 1)
Solve -2/7*u**3 + 12/7*u**2 + 0*u + 0 = 0.
0, 6
Factor 121/2*s**4 + 128 + 768*s + 528*s**3 + 1328*s**2.
(s + 4)**2*(11*s + 4)**2/2
Let r be ((-8)/6)/((-8)/12). Factor -5*p**3 - 15*p + 5*p + 10*p**r + 5*p.
-5*p*(p - 1)**2
Factor 27/5*f - 9/10*f**3 + 7/10*f**4 - 27/10*f**2 + 0 - 1/10*f**5.
-f*(f - 3)**3*(f + 2)/10
Let i(h) be the second derivative of 0*h**3 + 0 + 1/4*h**4 - 5*h + 0*h**2 - 3/20*h**5. Factor i(l).
-3*l**2*(l - 1)
Let f(q) be the second derivative of q**7/210 - q**6/45 - q**5/30 + q**4/3 + 8*q**3/3 - 38*q. Let h(z) be the second derivative of f(z). Factor h(i).
4*(i - 2)*(i - 1)*(i + 1)
Let l be (-18492)/135 + 6 - 1/(-5). Let p = l + 131. Factor -4/9 - p*v**2 - 2/3*v.
-2*(v + 1)*(v + 2)/9
Let m(b) = b**3 - 9*b**2 + 4. Let s be m(9). Factor -55*k + 20*k**s - 9*k - 13*k**3 - 84*k**2 - 24*k**3 + 12*k**5 - 16 + 9*k**3.
4*(k - 2)*(k + 1)**3*(3*k + 2)
Let w(b) be the second derivative of b**8/2800 - b**7/700 + b**6/600 + 31*b**3/6 - 2*b. Let d(z) be the second derivative of w(z). Let d(u) = 0. What is u?
0, 1
Let f = 32 - 30. Suppose 3*j - 11*j - 15*j**2 - 6 + 13*j**f = 0. What is j?
-3, -1
Let i(g) be the first derivative of -20*g**3/9 + 8*g**2 + 12*g + 1064. Factor i(n).
-4*(n - 3)*(5*n + 3)/3
Suppose g**5 - 26*g**4 - 4*g**2 + 0*g**2 + 21*g**4 + 8*g**3 = 0. What is g?
0, 1, 2
Let c(r) = -36*r**2 + 14*r + 11. Let y(w) = 7*w**2 - 2 - 83*w + 0 + 80*w. Let q(k) = -2*c(k) - 11*y(k). Factor q(a).
-5*a*(a - 1)
Factor -3/2*p**4 + 0*p**3 + 0 + 3*p + 9/2*p**2.
-3*p*(p - 2)*(p + 1)**2/2
Let v(n) be the second derivative of -n**7/42 + n**6/24 - 5*n**2 + 7*n. Let i(o) be the first derivative of v(o). Find x such that i(x) = 0.
0, 1
Let s(y) = 5*y**2 - 2*y + 3. Let n(m) = -65*m**2 + 25*m - 40. Let g(l) = 3*n(l) + 40*s(l). Find t, given that g(t) = 0.
0, 1
Suppose -2*u - u - 2 = v, -v = -4*u + 2. Let j = -4/43 - -98/129. Solve 2/3*n + u - j*n**3 + n**2 = 0 for n.
-1/2, 0, 2
Suppose 36*u - 38*u = -4. Let 2*k**3 + 5*k + k - 3*k**2 + 7*k**u - 12*k**2 = 0. Calculate k.
0, 1, 3
Let s = 72 - 60. Let f be (-5 - -3 - -3) + 4/s. Factor -2/3*v**2 + 0 - f*v**3 - 2/3*v**4 + 0*v.
-2*v**2*(v + 1)**2/3
Let l(b) be the third derivative of -b**6/240 + 9*b**5/40 - 13*b**4/24 - 2*b**2 - 4. Factor l(u).
-u*(u - 26)*(u - 1)/2
Let y(f) be the second derivative of 7*f**6/45 + f**5/30 - 43*f**4/18 - 61*f**3/9 - 8*f**2 - 324*f. Solve y(k) = 0 for k.
-8/7, -1, 3
Let b(k) be the second derivative of k**7/280 + k**6/120 - k**5/40 - k**4/8 + 13*k**3/6 - 15*k. Let c(n) be the second derivative of b(n). Factor c(l).
3*(l - 1)*(l + 1)**2
Let w(o) be the third derivative of -o**5/110 + 5*o**4/22 - 25*o**3/11 + 308*o**2. Let w(k) = 0. Calculate k.
5
Let h be (-4)/8 - (4 + 38/(-4)). Let i(w) be the third derivative of 0 + 0*w - 1/1050*w**7 + 3*w**2 + 0*w**6 + 0*w**h + 0*w**3 + 0*w**4. Factor i(c).
-c**4/5
Let s(r) be the first derivative of r**3/27 - 7*r**2/9 + 8*r/3 + 52. Suppose s(k) = 0. What is k?
2, 12
Let n(w) = -w**3 - 5*w**2 + 11*w - 17. Let x be n(-7). Let f be -3 + 19/20*x. Factor 18/5*i**2 - f*i - 14/5*i**3 + 0.
-2*i*(i - 1)*(7*i - 2)/5
Suppose t = 3 + 8. Suppose -4*g + 5 + t = 0. Determine v so that 0 - v**2 + 1 - g*v + 4*v = 0.
-1, 1
Let n = 831 - 2492/3. Solve n*u**3 + 2/3*u**2 + 1/3*u + 0 = 0.
-1, 0
Suppose -2*x + 2*o = -6, -2*x + 0*o = 3*o - 16. Factor -33*f**5 + 20*f**4 + 20*f**2 - 30*f**3 + 7*f + 28*f**x - 12*f.
-5*f*(f - 1)**4
Let a be 1016 + 6/(-2) - 0. Let c be 3/(-2) - a/(-2). Suppose -75*l**3 + 5*l + 10 + 3*l + c*l**4 - 155*l**2 - 300*l**5 + 7*l = 0. What is l?
-2/5, -1/4, 1/3, 1
Let n(r) be the first derivative of -3*r**4/8 + 113*r**3/2 - 593. Factor n(t).
-3*t**2*(t - 113)/2
Let i(j) be the third derivative of 15*j**2 - 1/6*j**3 - 1/70*j**7 + 1/15*j**5 + 0*j + 0 - 1/12*j**4 + 1/60*j**6. Factor i(n).
-(n - 1)**2*(n + 1)*(3*n + 1)
Let g be 77/2772*36/3. Factor -1/3 + 1/3*r**2 - 1/3*r**3 + g*r.
-(r - 1)**2*(r + 1)/3
Suppose 43*u - 51*u + 24 = 0. Let a(h) be the second derivative of 0*h**4 + 0*h**2 + 0*h**5 + 0*h**u + 0 + 1/60*h**6 + h. Factor a(r).
r**4/2
Suppose 2*g = 3*g - 3. Suppose -g*i - 10 = 4*q - 74, -3*q + 63 = 3*i. Factor i*t - 16*t + 3 - 3 + 14*t**2.
2*t*(7*t + 2)
Let j = -58 - -61. Solve -j*b**5 + b**4 - 2*b**2 - 4*b**2 + 4*b**3 + 5*b**2 - b**3 = 0 for b.
-1, 0, 1/3, 1
Let c = 10 + -7. Let n(k) be the second derivative of 0 + 0*k**2 + 0*k**4 - 5/24*k**c + 1/16*k**5 + 10*k. Find r, given that n(r) = 0.
-1, 0, 1
Let p(x) be the second derivative of -x**5/180 + x**3/54 + 5*x + 1. Factor p(q).
-q*(q - 1)*(q + 1)/9
Let d be (9 + -2 + 3)/1. Suppose -6*f = -f - d. Determine b so that -f*b + 3*b - b - b**2 = 0.
0
Let w(d) be the first derivative of -d**3 - 12*d**2 - 21*d + 75. Factor w(m).
-3*(m + 1)*(m + 7)
Let u = 40 + -38. Let o(p) be the first derivative of -5 - 1/18*p**4 + 0*p**3 + 0*p + 1/9*p**u. Determine s, given that o(s) = 0.
-1, 0, 1
Let r(s) be the second derivative of -1/2*s**3 + 0*s**2 + 279/40*s**5 - 63/10*s**6 - 9 - 11/8*s**4 + s. Suppose r(f) = 0. Calculate f.
-2/21, 0, 1/3, 1/2
Let s(g) be the second derivative of -9*g - 7/30*g**4 + 0 + 2/25*g**5 + 2/15*g**3 + 1/5*g**2. Factor s(v).
2*(v - 1)**2*(4*v + 1)/5
Let n be ((224/21)/(-2))/(15/(-9)). Factor 2*r**2 - n*r - 8/5.
2*(r - 2)*(5*r + 2)/5
Let u(y) be the first derivative of y**3/9 - 23*y**2/6 - 761. Find z, given that u(z) = 0.
0, 23
Factor -2*l**4 - 9720*l + 11664 + 115*l**3 - 388*l**3 + 167*l**3 - 1836*l**2.
-2*(l - 1)*(l + 18)**3
Suppose -50 = -5*r - 5*b, -4*r + b - 2*b + 46 = 0. Let 15*d**2 - 9*d + 3*d**2 - 3*d + 3 + 3*d**4 - r*d**3 = 0. Calculate d.
1
Factor 0*k + 2/5*k**5 - 2/5*k**3 - 2/5*k**2 + 2/5*k**4 + 0.
2*k**2*(k - 1)*(k + 1)**2/5
Let t = -105 + 105. Let i(y) be the second derivative of 1/36*y**4 - 4*y + 0 - 1/18*y**3 + t*y**2. Factor i(b).
b*(b - 1)/3
Let z(u) = 3*u + 759 - 752 - 2*u. Let c be z(-3). Determine n, given that 0 + 1/2*n**3 + 1/3*n**c - 1/3*n**2 + 0*n = 0.
-2, 0, 1/2
Let w = 5563 + -5561. Let 4/7*c**4 - 12/7*c**3 + 0 + 0*c + 8/7*c**w = 0. What is c?
0, 1, 2
Let j(d) be the third derivative of d**8/5880 - d**7/1470 + d**6/1260 - 17*d**3/6 - 6*d**2. Let o(y) be the first derivative of j(y). Let o(r) = 0. What is r?
0, 1
Let c(x) be the second derivative of 0 - 1/90*x**5 + 1/27*x**3 - 1/54*x**4 + 1/9*x**2 - x. Suppose c(i) = 0. What is i?
-1, 1
Let y = -126521/9 + 14059. Determine l, given that y*l**3 + 2/9*l**4 + 0 + 14/9*l**2 + 2/3*l = 0.
-3, -1, 0
Let w(p) be the third derivative of 2/3*p**3 + 1/60*p**4 + 1/900*p**6 - 1/150*p**5 + 0*p - 7*p**2 + 0. Let n(y) be the first derivative of w(y). Factor n(i).
2*(i - 1)**2/5
Let p(l) = l**4 + 7*l**3 + 18*l**2 + 2. Let w(n) = 6*n**4 + 27*n**3 + 75*n**2 + 9. Let v(b) = 9*p(b) - 2*w(b). Suppose v(d) = 0. Calculate d.
-1, 0, 4
Let q = 89 + -84. Suppose 0 = -q*u - 3*j + 1, -5*j - 21 + 2 = -2*u. Suppose -4/7 - 6/7*z - 2/7*z**u = 0. Calculate z.
-2, -1
Let a be (-2*(-4)/8 - 6)*1. Let v be a + 2 - 39/(-12). What is b in 0*b - 1/4*b**2 + 0 - 1/4*b**3 + 1/4*b**5 +