e the third derivative of p**8/2016 - p**7/1260 - p**6/144 + p**5/360 + p**4/18 + p**3/9 + 6*p**2. What is u in n(u) = 0?
-1, 2
Let c(w) be the third derivative of 0 - 1/12*w**4 + 4*w**2 + 0*w + 1/210*w**7 + 0*w**3 + 0*w**6 - 1/20*w**5. Find s such that c(s) = 0.
-1, 0, 2
Let l be ((-6)/(-8))/((-51)/(-136)). Factor 0 + 3/4*p**l + 3/4*p.
3*p*(p + 1)/4
Let y(v) be the first derivative of -5*v**4/16 + 5*v**3/6 + 35*v**2/8 + 5*v - 8. Suppose y(u) = 0. Calculate u.
-1, 4
Factor -l**2 + 33 + 3*l**2 - 33.
2*l**2
Find t, given that -2*t + 1 + 0*t - 74*t**2 - 5 + 76*t**2 = 0.
-1, 2
Factor 8*q**3 + 42*q - 4*q**2 - 2*q**5 - 23*q - 25*q + 4.
-2*(q - 1)**3*(q + 1)*(q + 2)
Let d be 41/(-287) - 12/(-35). Factor 0*u**3 - d*u - 2/5*u**4 + 1/5*u**5 + 2/5*u**2 + 0.
u*(u - 1)**3*(u + 1)/5
Let x(p) be the first derivative of 1/12*p**3 + 1/16*p**4 + 0*p + 0*p**2 + 3. Find d such that x(d) = 0.
-1, 0
Factor 2*i**3 + 2*i**4 - 4*i**3 - 4*i**2 + 2 + 2*i**3.
2*(i - 1)**2*(i + 1)**2
Factor 4/3 - 4/3*m + 1/3*m**2.
(m - 2)**2/3
Solve 5*r + 4*r + 11*r - 5*r + 5*r**2 = 0.
-3, 0
Suppose -3*j - j + 40 = 0. Let l = j + -7. Factor -2*w**l + 2*w**2 + 0 - 2/3*w + 2/3*w**4.
2*w*(w - 1)**3/3
Let d(j) = -5 + 4 - 2*j + 3*j. Let y be d(1). Factor a**2 + 0*a + 3*a**3 + y*a - 2*a**3.
a**2*(a + 1)
Let s(y) = 2*y - 2. Suppose 3*z - 4*b = -1 + 15, b - 6 = -4*z. Let r be s(z). Find p such that -7*p**3 - 5*p + 2*p**r + 5*p + 3*p**3 + 2*p**4 = 0.
0, 1
Let c be ((-8)/(-6))/((-320)/(-96)). What is g in -8/5*g - c - 12/5*g**2 - 8/5*g**3 - 2/5*g**4 = 0?
-1
Suppose 0 + 3 = -3*w, 2*w + 14 = 3*m. Let f(b) be the second derivative of 0 + 1/18*b**3 + 1/36*b**m + 0*b**2 + 2*b. Factor f(k).
k*(k + 1)/3
Let u(g) be the first derivative of -1/6*g**4 + 10/9*g**3 - 7/3*g**2 + 5 + 2*g. What is p in u(p) = 0?
1, 3
Let n(d) be the third derivative of 0 - 1/20*d**5 - 2*d**2 + 0*d + 1/24*d**4 + 0*d**3 + 1/70*d**7 + 1/84*d**8 - 1/24*d**6. Solve n(q) = 0 for q.
-1, 0, 1/4, 1
Let l(i) be the third derivative of 1/12*i**4 - 4*i**2 - 1/60*i**6 - 1/3*i**3 + 1/30*i**5 + 0*i + 0. Find s such that l(s) = 0.
-1, 1
Let c(d) be the first derivative of d**6/60 - d**5/30 - 2*d**2 - 4. Let t(k) be the second derivative of c(k). Let t(n) = 0. What is n?
0, 1
Suppose 8 = 5*p - 12. Suppose -2*c = 2*g - 7 - 7, -2*g - p = -4*c. Factor -2/5*l**c - 4/5*l**2 + 0 + 0*l.
-2*l**2*(l + 2)/5
Determine q, given that -40/7*q - 2*q**3 + 16/7 + 2/7*q**4 + 36/7*q**2 = 0.
1, 2
Let q(h) be the second derivative of -h**4/54 - 2*h**3/27 - h**2/9 - 12*h. Factor q(d).
-2*(d + 1)**2/9
Let h = 7 + -2. Factor 2*p + p**2 - 1 - 3*p**3 - p**3 - 5*p**2 + 2*p**4 + 2*p**h + 3.
2*(p - 1)**2*(p + 1)**3
Let v(u) be the second derivative of -u**4/3 + 2*u**3 + 8*u**2 + 18*u. Factor v(j).
-4*(j - 4)*(j + 1)
Let m(u) be the first derivative of -10*u**5/9 + 5*u**4/2 - 16*u**3/9 + 4*u**2/9 + 8. Factor m(w).
-2*w*(w - 1)*(5*w - 2)**2/9
Let v(k) be the second derivative of k**6/180 + k**5/60 - k**3/18 - k**2/12 - 12*k. Solve v(l) = 0 for l.
-1, 1
Let i be (-1)/5 + 57/135. Let a(z) be the first derivative of -1/6*z**4 - 2/3*z - 2 + i*z**3 + 1/3*z**2. Solve a(f) = 0.
-1, 1
Let n(f) = -f**2 - f + 1. Let i(l) = 15*l**2 - 30*l - 12. Let g(o) = -o**2 + 3*o - 3. Let d be g(2). Let t(a) = d*i(a) - 3*n(a). What is b in t(b) = 0?
-1/4, 3
Let q(c) be the third derivative of -c**6/40 - c**5/5 - 5*c**4/8 - c**3 - 12*c**2. Solve q(l) = 0.
-2, -1
Let y(o) be the second derivative of -2*o**6/75 + o**5/25 + o**4/15 - 2*o**3/15 - 17*o. Factor y(c).
-4*c*(c - 1)**2*(c + 1)/5
Let u(q) = q**2 + q - 1. Let r(o) = 14*o**2 + 2*o - 20. Let m(l) = -5*l**2 - l + 7. Let t(c) = -7*m(c) - 2*r(c). Let s(h) = -t(h) + 5*u(h). Factor s(g).
-2*(g - 2)*(g + 1)
Factor 37*i**2 + 21*i**4 + 23*i**2 + 825*i**5 - 122*i**3 - 776*i**5 - 8*i.
i*(i - 1)*(i + 2)*(7*i - 2)**2
Let h = -3 + 3. Let q be 1/2*(h + 1). What is u in 1/4*u**5 + 0*u**3 + 0 - 1/2*u**2 - 1/4*u + q*u**4 = 0?
-1, 0, 1
Let s(q) = 2*q**2 - 9*q + 13. Let y be s(2). Factor -25/4*o**4 + 15/2*o**y + 0 + 2*o + 9*o**2.
-o*(o - 2)*(5*o + 2)**2/4
Let p(v) be the first derivative of -v**6/57 - 4*v**5/95 + v**4/38 + 4*v**3/57 + 11. Find k, given that p(k) = 0.
-2, -1, 0, 1
Let b = -4 + 7. Suppose -6 + 3 = -b*s, 0 = z - 5*s + 2. Factor 8*i**2 + 0*i - i + z*i.
2*i*(4*i + 1)
Let t(r) be the third derivative of 0*r + 3*r**2 - 2/9*r**3 + 1/180*r**6 + 5/36*r**4 + 0 - 2/45*r**5. Find d, given that t(d) = 0.
1, 2
Suppose 0 = r + 3*x - 5, -3*r - 3*x = 2 - 17. Let b(m) be the second derivative of 0*m**2 + 3/20*m**r - 1/4*m**4 + 1/6*m**3 - 1/30*m**6 + 0 - 2*m. Factor b(t).
-t*(t - 1)**3
Let q(k) be the third derivative of -k**9/120960 + k**7/3360 - k**6/720 - 2*k**5/15 - 8*k**2. Let m(d) be the third derivative of q(d). Factor m(j).
-(j - 1)**2*(j + 2)/2
Let m(q) be the third derivative of q**6/168 + q**5/60 + q**4/84 - 3*q**2. Determine t so that m(t) = 0.
-1, -2/5, 0
Let o(p) be the first derivative of -10*p**5/3 - 95*p**4/6 - 76*p**3/3 - 52*p**2/3 - 16*p/3 - 6. Solve o(q) = 0 for q.
-2, -1, -2/5
Let -4*f**4 - 1049*f + 4*f**2 + 1049*f + 2*f**5 - 2*f**3 = 0. Calculate f.
-1, 0, 1, 2
Let t(o) be the second derivative of -o**5 - o**4 + 4*o**3/3 - 9*o. What is j in t(j) = 0?
-1, 0, 2/5
Let n(t) = t**3 - 5*t**2 - 6*t + 4. Let p be n(6). Determine z so that -z**2 + 2*z**4 + 4 - 5*z**2 - 2*z**3 + 2*z + 0*z**4 + 0*z**p = 0.
-1, 1, 2
Let h be 0/2*(153/(-27) - -6). Factor h + 0*y + 4/5*y**3 + 4/5*y**2.
4*y**2*(y + 1)/5
Find d such that -2/5*d**3 - 4/5 + 4/5*d**2 + 2/5*d = 0.
-1, 1, 2
Let l = 30 - 30. Suppose -6/5*a**2 + 0*a + l*a**3 + 3/5*a**4 + 3/5 = 0. What is a?
-1, 1
Let t = -11/5 + 137/60. Let p(l) be the second derivative of -1/40*l**5 + 1/12*l**4 + 0*l**2 + 0 - t*l**3 + 2*l. Determine k, given that p(k) = 0.
0, 1
Let j(s) be the second derivative of -1/42*s**7 + 0*s**3 + 0 + 0*s**4 - 1/20*s**5 + 0*s**2 - 4*s + 1/15*s**6. Determine k so that j(k) = 0.
0, 1
Factor -31*q**2 + 17*q**2 + 2*q + 15*q**2 - 3.
(q - 1)*(q + 3)
Suppose 0 = -4*a - 50 - 6. Let x = a - -22. Factor x*v**4 + 12*v**3 - 4*v**5 + 5*v**2 + 3*v**2 + 6*v**5 + 2*v.
2*v*(v + 1)**4
Let o(k) be the first derivative of -4*k**3/27 - k**2/9 + 2. Solve o(v) = 0.
-1/2, 0
Let t = 2257687/14444 - 3589/23. Let o = t - 2/157. Factor -1/4*b**3 - 1/2 + 1/2*b**2 + o*b.
-(b - 2)*(b - 1)*(b + 1)/4
Let c(x) = x**5 + 3*x**4 + x**2 + x + 1. Let n(a) = a**5 - a**4 - a**2 - a - 1. Let r(g) = -c(g) - n(g). Factor r(y).
-2*y**4*(y + 1)
Let m(g) = g**2 - 1. Let h(p) be the second derivative of 2*p**4/3 - p**3/3 - 3*p**2 - 2*p. Let o(u) = h(u) - 6*m(u). Solve o(i) = 0 for i.
0, 1
Factor -75*w**2 + w**4 - 19 - 11*w**3 - 6*w**4 - 65*w - 1 - 24*w**3.
-5*(w + 1)**3*(w + 4)
Let n(y) be the first derivative of y**4 - 20*y**3/3 + 6*y**2 + 36*y + 6. Find h such that n(h) = 0.
-1, 3
Let l be (7 + 119/(-14))*-2. Factor -2/5*a**l + 2/5*a**2 + 0*a + 0.
-2*a**2*(a - 1)/5
Let u(r) be the second derivative of r**9/15120 + r**8/16800 - r**7/2520 - r**6/1800 - r**4/4 - r. Let j(h) be the third derivative of u(h). Factor j(k).
k*(k - 1)*(k + 1)*(5*k + 2)/5
What is g in -g + 1/6*g**3 + 1/6*g**2 + 0 = 0?
-3, 0, 2
Let q = 3/23 - -63/46. Factor -7/2*b**3 - b**2 + 0 - 4*b**4 - q*b**5 + 0*b.
-b**2*(b + 1)**2*(3*b + 2)/2
Let a = -5 - -10. Factor v**5 - 3*v**5 + 0*v**a + 4*v**5.
2*v**5
Suppose -6/11*u - 12/11*u**4 - 24/11*u**3 - 2/11*u**5 - 20/11*u**2 + 0 = 0. What is u?
-3, -1, 0
Let f(b) be the first derivative of -b**6/16 - 3*b**5/20 - 3*b**4/32 - 9. Factor f(s).
-3*s**3*(s + 1)**2/8
Suppose -3*w - 7 + 22 = 0. Suppose -w*l = -10 - 0. What is n in 0 + 0*n + 1/4*n**3 + 1/4*n**l = 0?
-1, 0
Let k = 2 - -1. Factor n + n + 5*n**2 - 5 + 3 - k*n**2 - 2*n**3.
-2*(n - 1)**2*(n + 1)
Let r(y) be the second derivative of -y**8/112 + y**7/70 - y**2 + y. Let p(t) be the first derivative of r(t). Factor p(l).
-3*l**4*(l - 1)
Let c(l) be the third derivative of -l**5/60 - l**4/8 + 11*l**2. Factor c(m).
-m*(m + 3)
Suppose p = -4*p. Let c be (-2 - -4) + 0 - p. Let 2*r**2 + 4*r**3 - 8*r**c - 2 + 1 + 4*r - r**4 = 0. Calculate r.
1
Factor 40/3*g + 400/3 + 1/3*g**2.
(g + 20)**2/3
Let y(o) = -o**3 + 6*o**2 + o - 3. Let i be y(3). Suppose -5*m + 2*m + i = 0. Determine b, given that m*b**2 + 2 - 2 - 2*b = 0.
0, 2/9
Find o, given that -4/7*o**3 - 8/7*o**2 + 6/7*o + 8/7*o**4 - 2/7