*r.
-2*(r - 2)**2
Let n be (-2)/(9/(-81)*6). What is t in 0*t + 2/3*t**n - 2/3*t**5 - 2/3*t**4 + 2/3*t**2 + 0 = 0?
-1, 0, 1
Let y(i) = -6*i - 42. Let g be y(-7). Solve 2/3*d**2 - 1/3*d**3 + 0 + g*d = 0.
0, 2
Let c = 93 + -91. Let k(h) be the third derivative of -1/660*h**6 + 0*h + 1/165*h**5 + 0*h**3 - 1/132*h**4 + 3*h**c + 0. Factor k(m).
-2*m*(m - 1)**2/11
Let w(k) be the second derivative of 5*k**4/12 - 13*k**3/6 - 3*k**2 - 7*k. Factor w(l).
(l - 3)*(5*l + 2)
Let j(c) be the third derivative of 0*c + 0*c**3 + 3/70*c**7 - 3/20*c**5 + 1/112*c**8 - 1/4*c**4 + 2*c**2 + 1/40*c**6 + 0. Determine u so that j(u) = 0.
-2, -1, 0, 1
Let h(u) be the third derivative of -u**7/14 + u**6/40 + u**5/4 - u**4/8 + 8*u**2 - u. Suppose h(v) = 0. Calculate v.
-1, 0, 1/5, 1
Let h = 9 - 5. Let w(x) = -7*x**3 - 6*x**2 + x. Let b(y) = 15*y**3 + 12*y**2 - 3*y. Let a(u) = h*b(u) + 9*w(u). Let a(c) = 0. What is c?
-1, 0
Let k(v) = v**2 - 3*v - 5. Let a be k(5). Let g be (-12)/(-180) - (-3)/a. Solve -1/3*d**3 - 1/3*d**4 + d**2 + g + 5/3*d = 0.
-1, 2
Let x(m) = 4*m**3 - 7*m**2 + 3. Let l(z) = -4*z**3 + 8*z**2 - 4. Let p(n) = -3*l(n) - 4*x(n). Let p(o) = 0. What is o?
0, 1
Suppose 4*c - b = b - 10, 5*b = c + 25. Let n(i) be the third derivative of 0 + 3/4*i**3 - 1/8*i**4 + 4*i**2 + 1/120*i**5 + c*i. Solve n(g) = 0 for g.
3
Let h(m) be the first derivative of -6 - 2/55*m**5 - 4/33*m**3 + 0*m**2 - 3/22*m**4 + 0*m. Find s, given that h(s) = 0.
-2, -1, 0
Let u(s) = s**3 + 6*s**2 - 2. Let y be u(-6). Let f be (y/5)/((-1)/5). Factor 6/7*x - 2/7*x**f - 4/7.
-2*(x - 2)*(x - 1)/7
Let o be 8/(1 + 1) + (-21)/21. Factor -2/3 + 2/3*k**2 + 2/3*k - 2/3*k**o.
-2*(k - 1)**2*(k + 1)/3
Let v(q) be the second derivative of -q**9/7560 - q**8/4200 + q**7/2100 + q**6/900 - 2*q**3/3 - 4*q. Let r(a) be the second derivative of v(a). Factor r(y).
-2*y**2*(y - 1)*(y + 1)**2/5
Let c(z) be the second derivative of -3/100*z**5 - 6/5*z**2 + 0 + 5*z + 2/5*z**3 + 1/20*z**4. Determine t so that c(t) = 0.
-2, 1, 2
Suppose -t - 3*t = 3*k - 11, 3*k = -9. Suppose t*m - 24 = 2*m. Suppose 12*o**2 - m + 2 - 7*o**2 + 16*o**2 - 15*o = 0. What is o?
-2/7, 1
Suppose 2 = -i - 2*y, 4*i + 5*y - 3 - 4 = 0. Solve i*w - 7*w - 4*w - 3*w**2 = 0 for w.
-1, 0
Factor 5*s**2 - s**4 - 4*s**2 - 1 + 1.
-s**2*(s - 1)*(s + 1)
Suppose 3 + 7 = 5*d. Suppose 3*m = 4*f + d*m - 18, 2 = -f - 3*m. Suppose z**2 - 2 - z**4 + 3*z**2 - z**f = 0. What is z?
-1, 1
Let r be ((-30)/(-8))/(6/8). What is a in 12*a**r - 18*a**4 + 3*a**3 - 7*a**5 + 9*a**5 + a**3 = 0?
0, 2/7, 1
Let y(i) be the first derivative of i**6/360 + i**5/180 - i**4/72 - i**3/18 - 2*i**2 + 3. Let x(c) be the second derivative of y(c). Factor x(w).
(w - 1)*(w + 1)**2/3
Suppose 4*w = -g + 7, -5*w - 3*g - 12 = -19. Suppose 6/13*z**4 - 10/13*z**5 + 0*z + 0 + 0*z**w + 4/13*z**3 = 0. Calculate z.
-2/5, 0, 1
Let s(d) be the second derivative of 1/9*d**3 + 0*d**2 + 0 - 1/12*d**4 + 0*d**5 + 2*d + 1/90*d**6. What is p in s(p) = 0?
-2, 0, 1
Let i = 16/33 - 10/33. Determine k so that 0 + i*k**2 + 6/11*k = 0.
-3, 0
Suppose 6*z + 0*z = 18. Let g(t) be the second derivative of 0 + 1/21*t**4 + 1/21*t**z - t + 0*t**2 + 1/70*t**5. Let g(v) = 0. What is v?
-1, 0
Let m(v) = -5*v**2 + 12*v + 5. Let r(l) = -9*l**2 + 22*l + 11. Let a(z) = 10*m(z) - 6*r(z). Suppose a(n) = 0. What is n?
-1, 4
Let h be (-3)/(-11)*17/((-102)/(-4)). Factor 2/11 + 2/11*a - h*a**2 - 2/11*a**3.
-2*(a - 1)*(a + 1)**2/11
Let r(g) be the third derivative of g**7/420 - g**6/80 + g**5/120 + g**4/16 - g**3/6 + 7*g**2. Factor r(p).
(p - 2)*(p - 1)**2*(p + 1)/2
Let f(m) = -3*m**2 - 8*m + 1. Let d(n) = -8*n**2 - 24*n + 4. Let g(u) = 5*d(u) - 14*f(u). Factor g(r).
2*(r - 3)*(r - 1)
Let a(y) be the first derivative of -20*y**5 + 60*y**4 - 184*y**3/3 + 24*y**2 - 4*y - 19. Determine x, given that a(x) = 0.
1/5, 1
Let s = 3/776 + 1089/19400. Let a(z) be the second derivative of 0*z**3 - s*z**5 + 0 - 1/30*z**4 + 2*z + 0*z**2. Suppose a(d) = 0. Calculate d.
-1/3, 0
Let i = 86 - 84. Factor 0*h - 2/13*h**5 + 4/13*h**4 - 2/13*h**3 + 0*h**i + 0.
-2*h**3*(h - 1)**2/13
Factor -2/3*t**4 + 8/3*t + 2*t**2 - 4/3*t**3 - 8/3.
-2*(t - 1)**2*(t + 2)**2/3
Let z(u) be the second derivative of 0*u**3 + 3*u + 0 + 3/10*u**5 - 1/6*u**4 + 0*u**2 + 4/15*u**6. Factor z(p).
2*p**2*(p + 1)*(4*p - 1)
Let i(x) be the second derivative of x**7/105 + x**6/60 - x**5/15 - x**2/2 + 6*x. Let t(q) be the first derivative of i(q). Factor t(d).
2*d**2*(d - 1)*(d + 2)
Let j(g) be the second derivative of -g**5/120 + g**4/72 + g**3/9 - g**2/3 - 6*g. Let j(z) = 0. What is z?
-2, 1, 2
Suppose 80 = 3*u + 2*u. Suppose u = j - 5*g + 3, -j - 7 = 5*g. Solve 2/3*a + 0 + 2/3*a**j - 4/3*a**2 = 0.
0, 1
Let c(p) = -p + 16. Let z be c(9). Let b be (z - 8/2)*1. Factor 54/5 + 18/5*r**2 + 2/5*r**b + 54/5*r.
2*(r + 3)**3/5
Let z(l) = l - 1. Let u be z(6). Let g(m) be the third derivative of -1/40*m**u - 1/120*m**6 + 0 + 1/140*m**7 + 1/24*m**4 + m**2 + 0*m**3 + 0*m. Factor g(x).
x*(x - 1)*(x + 1)*(3*x - 2)/2
Let j = 8 - 6. Find t, given that 2*t - 3*t**j - 4*t**2 + 4*t**2 + 2*t**2 = 0.
0, 2
Let m = 13 - 36. Let f = m - -73/3. Factor 0 - f*b**3 + 2/3*b + 0*b**2 + 0*b**4 + 2/3*b**5.
2*b*(b - 1)**2*(b + 1)**2/3
Suppose -91*b + 87*b = -12. Determine s, given that -4/7*s**2 + 0*s + 0 - 2/7*s**4 + 6/7*s**b = 0.
0, 1, 2
Let x(w) be the second derivative of 2*w + 1/12*w**4 + 0 + 0*w**2 - 1/6*w**3. Factor x(m).
m*(m - 1)
Let r(l) be the second derivative of -l**5/90 + l**4/54 + l**3/27 - l**2/9 + 3*l. Find f such that r(f) = 0.
-1, 1
Suppose 450*q = 462*q - 36. Let -4/9 - 14/9*i - 2/9*i**4 - 2*i**2 - 10/9*i**q = 0. What is i?
-2, -1
Let o(k) = -8*k**4 - 6*k**3 + 8*k**2 + 2*k + 4. Let p(u) = -9*u**4 - 7*u**3 + 9*u**2 + 2*u + 5. Let d(a) = -5*o(a) + 4*p(a). Factor d(h).
2*h*(h - 1)*(h + 1)*(2*h + 1)
Suppose -3*g - 2*g = 0. Let h(a) be the third derivative of 1/54*a**4 - a**2 + 1/27*a**3 + 1/270*a**5 + g*a + 0. Suppose h(p) = 0. What is p?
-1
Let o = -35 + 10. Let s be (-5)/o*(-30)/(-9). Find k such that -7*k**2 + 13/3*k - s = 0.
2/7, 1/3
Let h(s) be the first derivative of 1/108*s**4 + 0*s + 2/27*s**3 + 2 - 1/180*s**6 - s**2 - 2/135*s**5. Let a(k) be the second derivative of h(k). Factor a(q).
-2*(q + 1)**2*(3*q - 2)/9
Factor 0 + 3/5*j**4 + 0*j - 12/5*j**2 + 0*j**3.
3*j**2*(j - 2)*(j + 2)/5
Let t(m) be the first derivative of -2 - 1/2*m**3 + 7/20*m**5 - 5/8*m**2 + 1/8*m**4 - 1/4*m + 1/8*m**6. Let t(w) = 0. Calculate w.
-1, -1/3, 1
Let o(h) be the third derivative of -1/120*h**4 + 0*h + 0 - h**2 + 1/300*h**5 + 1/600*h**6 - 1/30*h**3. Factor o(p).
(p - 1)*(p + 1)**2/5
Let d(c) be the second derivative of c**7/1260 + c**6/180 + c**5/60 - c**4/6 + 2*c. Let b(w) be the third derivative of d(w). Determine f, given that b(f) = 0.
-1
Let w(s) be the first derivative of -s**3/5 + 3*s**2/5 - 3*s/5 - 3. Factor w(r).
-3*(r - 1)**2/5
Let s = -30 - -30. Suppose -1/3*v**3 + 1/3*v + 1/6 + s*v**2 - 1/6*v**4 = 0. Calculate v.
-1, 1
Suppose 4*b = 6*b - 12. Factor 3*p**3 - 3*p**2 - 3*p + b - 5*p**2 + 2*p**2.
3*(p - 2)*(p - 1)*(p + 1)
Factor -4/3*k - 1/3*k**2 + 0.
-k*(k + 4)/3
Let d be (-8)/(-12) + 14/(-30). Let n(m) be the first derivative of -d*m**2 - 3 + 0*m + 2/15*m**3. Factor n(z).
2*z*(z - 1)/5
Let x(u) be the first derivative of 5*u**4/4 + 5*u**3 + 15*u**2/2 + 5*u - 14. Let x(i) = 0. Calculate i.
-1
Factor -2/3*b**3 - 2/9*b**2 + 2/9 + 2/3*b.
-2*(b - 1)*(b + 1)*(3*b + 1)/9
Let i(b) = b**3 + 6*b**2 + 8. Let j be i(-6). Let d be (0 - -2)/(j/60). Factor -2 + 6 - d*g + 18*g**2 - 3*g.
2*(3*g - 2)*(3*g - 1)
Let q(l) = 6*l - 12. Let s be q(5). Let x be (-6)/(-8)*12/s. Factor 0*d - 1/2*d**5 + 0*d**2 + 0*d**4 + x*d**3 + 0.
-d**3*(d - 1)*(d + 1)/2
Let b(h) be the second derivative of 0 + 1/12*h**4 - h + 1/3*h**3 + 1/2*h**2. Factor b(n).
(n + 1)**2
Let -4/3*u**2 + 0 + 2/9*u = 0. Calculate u.
0, 1/6
Let z(w) be the third derivative of 0 + 0*w - 1/120*w**6 - 5*w**2 + 1/420*w**7 + 1/120*w**5 + 0*w**3 + 0*w**4. Let z(x) = 0. What is x?
0, 1
Factor 0*n**2 + 2/15*n - 2/5*n**5 + 0 - 4/5*n**3 - 16/15*n**4.
-2*n*(n + 1)**3*(3*n - 1)/15
Let q be (-8)/28 - (-102)/(-35). Let v = 69/20 + q. Suppose -v*y**4 + 0*y + 1/2*y**3 + 0 - 1/4*y**2 = 0. What is y?
0, 1
Let y be -3*(-2)/(-39) - 4/(-26). Factor y + 6/7*g**3 - 6/7*g**4 + 0*g + 2/7*g**5 - 