 1)*(t + 1)**2*(7*t + 2)/2
Suppose 0 = -7*j + 11*j - 112. Determine k, given that -j*k**2 - 36*k**4 + 32*k**3 + 53*k**4 - 29*k**4 + 8*k = 0.
0, 2/3, 1
Let p(z) = z**4 - 4*z**3 + z**2 - z. Let m(q) = 10*q**4 - 805*q**3 + 41345*q**2 - 743605*q + 703040. Let b(k) = m(k) - 5*p(k). Factor b(t).
5*(t - 52)**3*(t - 1)
Let s(m) be the third derivative of -m**5/20 - 9*m**4/4 - 28*m**3 + 27*m**2 - 10*m. Factor s(r).
-3*(r + 4)*(r + 14)
Let z(i) be the first derivative of i**5/5 - i**4/4 - i**3/3 + i**2/2 + 631. Find u, given that z(u) = 0.
-1, 0, 1
Factor -1/6*k + 1/6*k**3 - 4/3 + 4/3*k**2.
(k - 1)*(k + 1)*(k + 8)/6
Let j(m) = -m**2 - m - 1. Let z = -33 - -39. Let g(t) = t**3 + 18*t**2 + 27*t + 16. Let c(x) = z*j(x) + g(x). Factor c(p).
(p + 1)**2*(p + 10)
Let p = 581 - 576. Let y(r) be the first derivative of -r**2 - 4 + 0*r - 64/5*r**p + 4/3*r**3 + 16/3*r**6 + 15/2*r**4. Let y(g) = 0. What is g?
-1/4, 0, 1/4, 1
Suppose 3*s - 5 = -5*n - 4, 4*n = -2*s. Let h be (s/(-3))/((-24)/9). Factor -d**3 + 1/4*d**2 + d - h.
-(d - 1)*(d + 1)*(4*d - 1)/4
Suppose -24 = g - 28. Factor g*y**4 + 715*y**3 - 725*y**3 + y**4.
5*y**3*(y - 2)
Suppose 25/2*j**3 - 1/2*j**4 + 31/2*j**2 + 39 - 133/2*j = 0. Calculate j.
-3, 1, 26
Suppose q - 20 = -4*q. Suppose 0 = n - q + 2. Factor -5*c**2 - c + n*c**2 - 3 - 5*c.
-3*(c + 1)**2
Suppose -219 - 51 = -54*c. Let h(x) be the second derivative of 1/42*x**4 + 12*x + 1/21*x**3 - 1/7*x**2 - 1/70*x**c + 0. Factor h(s).
-2*(s - 1)**2*(s + 1)/7
Determine c so that -c**3 + 1 + 60*c**2 + c**4 - 1 - 60*c**2 = 0.
0, 1
Let o(q) be the third derivative of q**5/90 - 5*q**4/8 + 11*q**3/9 + 2*q**2 + 171*q. Factor o(n).
(n - 22)*(2*n - 1)/3
Let w(n) be the second derivative of n**6/120 + n**5/40 - n**4/4 - 2*n**3/3 - 4*n. Let g(l) be the second derivative of w(l). Suppose g(i) = 0. Calculate i.
-2, 1
Let y(z) be the first derivative of z**3/12 + 13*z**2/4 + 25*z/4 - 24. Factor y(j).
(j + 1)*(j + 25)/4
Let p(g) = -g**3 + 36*g**2 - 3*g + 111. Let t be p(36). Let l(a) be the first derivative of -1/6*a**t + 1/2*a**2 - 13 + 0*a. Factor l(r).
-r*(r - 2)/2
Let l(x) = -23*x**4 + 19*x**3 - 71*x**2 + 17*x + 34. Let r(h) = -8*h**4 + 6*h**3 - 24*h**2 + 6*h + 12. Let y(w) = -6*l(w) + 17*r(w). Factor y(d).
2*d**2*(d - 3)**2
Find z such that 6/7*z**4 + 36/7*z - 4/7*z**3 - 54/7*z**2 + 0 = 0.
-3, 0, 2/3, 3
Let i(y) be the first derivative of -13 - 1/5*y**3 + 24/5*y**2 - 192/5*y. Let i(b) = 0. What is b?
8
Let x(k) be the first derivative of -2 - 20*k - 25/3*k**3 - 5/4*k**4 - 20*k**2. Factor x(t).
-5*(t + 1)*(t + 2)**2
Let k be 3 + 0/5 + -1. Suppose 0 = b - 7 - 0. Find r, given that -b*r + r**k + 4*r + 4*r = 0.
-1, 0
Suppose -6*n + 5*n**3 - n**2 + 14*n**3 - 18*n**3 = 0. What is n?
-2, 0, 3
Let b(x) = -3*x**2 - 25*x - 4. Let d(w) = 2*w**2 + 26*w + 3. Let a(f) = -3*b(f) - 4*d(f). Let a(t) = 0. What is t?
0, 29
Let m be 3/(1 + (-1)/(-2)). Suppose 3*i - 9 = -t - 5, 0 = 4*i - 2*t - 22. Factor 2*w**5 + w**m + 3*w**i + 4*w**2 - w**2 + 8*w**4 + 7*w**3.
2*w**2*(w + 1)**2*(w + 2)
Let v(g) = -5*g**5 + 132*g**4 - 243*g**3 + 122*g**2. Let y(m) = -110*m**5 + 2905*m**4 - 5345*m**3 + 2685*m**2. Let o(s) = -45*v(s) + 2*y(s). Solve o(a) = 0.
0, 1, 24
Let d(x) = -3*x**4 + x**3 + 8*x**2 + 8*x. Let l(j) = j**4 + j**3 - j. Let g(a) = -d(a) - 4*l(a). What is t in g(t) = 0?
-2, -1, 0
Let l(u) be the first derivative of 0*u**4 + 3/5*u**5 - 3*u**2 + 23 - 3*u**3 + 0*u. Find h such that l(h) = 0.
-1, 0, 2
Let q(j) be the third derivative of -j**7/385 - 13*j**6/132 + 5*j**5/66 + 65*j**4/132 - 2*j**3/3 - 627*j**2. What is d in q(d) = 0?
-22, -1, 1/3, 1
Let u(z) be the third derivative of z**5/12 + 40*z**4/3 + 2560*z**3/3 + 66*z**2. Factor u(r).
5*(r + 32)**2
Let h(b) = 2*b**2 + 3*b. Let i be h(-3). Let d be -2*(-5)/(30/i). Factor -3*y**d - 3/2*y**4 + 0 - 3/2*y**2 + 0*y.
-3*y**2*(y + 1)**2/2
Let v = -2081 - -6247/3. Determine w, given that -w**3 + v - 5/3*w**2 + 4/3*w = 0.
-2, -2/3, 1
Determine s, given that -2/17*s**4 - 72/17*s**3 - 72*s - 716/17*s**2 - 34 = 0.
-17, -1
Suppose a - 20 = -5*m - 0*a, -2*m = -a - 1. Let u(w) = -w**3 + 2*w**2 + 3*w + 2. Let g be u(m). Factor 18*p - 19*p - p**2 + p**3 + g - 1.
(p - 1)**2*(p + 1)
Suppose -4*v**3 + 46*v**3 - 67*v**2 - 2*v**4 + 27*v**2 = 0. Calculate v.
0, 1, 20
Let q(g) = -6*g + 36. Let y be q(12). Let o be 5/(-6) - 57/y. Factor -3/4 + 0*a + o*a**2.
3*(a - 1)*(a + 1)/4
Suppose -4*w = 4*f, -f + 1 = -2*w + 7. Suppose 0 = -3*n + 17 + 10. Factor -p**3 - 8 + p**2 + w*p**2 + n - 3*p.
-(p - 1)**3
Let j(a) = 18*a - 5*a - 15*a + 41. Let x be j(19). Factor 1/2*o - o**2 + 1/2*o**4 - o**x + 1/2 + 1/2*o**5.
(o - 1)**2*(o + 1)**3/2
Let m(f) be the second derivative of 1/60*f**6 + 1/84*f**7 - 1/20*f**5 - 1/12*f**4 + 0 + 1/12*f**3 + 1/4*f**2 + 2*f. Determine r so that m(r) = 0.
-1, 1
Let o(x) be the third derivative of 0*x**3 + 0 - 13*x**2 - 1/300*x**6 - 1/15*x**4 + 2/75*x**5 + 0*x. Factor o(y).
-2*y*(y - 2)**2/5
Let n(z) = z**2 - 32*z - 1. Let w be n(18). Let b = w + 257. Factor -1/2 + 3/4*l**b - 5/4*l**3 + 5/4*l - 1/4*l**2.
(l - 1)**2*(l + 1)*(3*l - 2)/4
Factor 0 - 28/3*b - 10*b**3 + 1/3*b**4 + 19*b**2.
b*(b - 28)*(b - 1)**2/3
Determine h, given that -6*h**2 - 16 + 18*h + 1/2*h**3 = 0.
2, 8
Let z(d) be the third derivative of d**7/6300 + d**6/1350 - 10*d**3/3 + 4*d**2. Let o(u) be the first derivative of z(u). Factor o(i).
2*i**2*(i + 2)/15
Let z(l) be the second derivative of l**4/66 + 3*l**3/11 - 10*l**2/11 - 180*l. Find y, given that z(y) = 0.
-10, 1
Let h(y) = -1154*y + 18466. Let x be h(16). Factor 3/2*g**5 + 0*g - 3/2*g**4 - 3/2*g**3 + 0 + 3/2*g**x.
3*g**2*(g - 1)**2*(g + 1)/2
Let d be (-4 - (1 - 6)) + 2. Factor -1 - 13*i - 24*i + 34*i - d*i**2 + 7.
-3*(i - 1)*(i + 2)
Let a(q) be the second derivative of 0 - 1/12*q**3 + 1/40*q**5 - 1/24*q**4 + 1/4*q**2 + 3*q. Factor a(s).
(s - 1)**2*(s + 1)/2
Let o(n) = -4*n - 5. Let b be o(-2). Suppose -6*w = -b*w. Let w*p - 4 + 3*p**2 + 2*p**3 - p + p**2 - p = 0. What is p?
-2, -1, 1
Suppose 26*v - 815 + 644 - 2195 + 38*v**2 - 2*v**3 = 0. Calculate v.
-7, 13
Let s(f) = f**3 + f**2 - f. Let k(b) = 8*b**3 + 23*b**2 + 13*b. Let n = 82 + -81. Let q(o) = n*s(o) + k(o). Find m, given that q(m) = 0.
-2, -2/3, 0
Find d, given that -8*d - 47*d + 36*d**2 + 106*d + 103*d + 196 + 14*d = 0.
-7/3
Let k(y) be the first derivative of -2*y**5/5 - 13*y**4/2 - 82*y**3/3 - 47*y**2 - 36*y - 16. What is i in k(i) = 0?
-9, -2, -1
Let h(o) be the third derivative of -o**5/6 - o**4/4 + 2*o**3/3 - 11*o**2 - 2. Let h(c) = 0. What is c?
-1, 2/5
Let o(i) be the first derivative of 0*i + 1/2*i**3 - 26 - 3/10*i**5 - 1/12*i**6 - i**2 + 5/8*i**4. Let o(n) = 0. What is n?
-4, -1, 0, 1
Let w(p) be the second derivative of p**8/784 - 2*p**7/245 + 3*p**6/140 - p**5/35 + p**4/56 - 3*p**2 - p. Let f(x) be the first derivative of w(x). Factor f(s).
3*s*(s - 1)**4/7
Suppose 14*r = -0*r. Let y(t) be the second derivative of 0*t**4 + r*t**2 + 4*t + 0 + 1/24*t**3 - 1/80*t**5. Factor y(k).
-k*(k - 1)*(k + 1)/4
Let s(n) = -n**2 - n - 2. Let k(x) = -3*x**2 - 3*x - 7. Suppose 5*j + 90 = 3*p, -p = -j + p - 11. Let v(i) = j*s(i) + 6*k(i). Factor v(c).
3*c*(c + 1)
Let q(y) be the second derivative of -y**6/360 - y**5/60 + y**3/3 + 5*y**2 + 32*y. Let f(b) be the second derivative of q(b). Factor f(l).
-l*(l + 2)
Let z = 1 - -2. Suppose -5*n + a + 13 = -2*a, 7 = 5*n + 3*a. Solve -4 + 5 + z*p**2 - 6*p + n = 0.
1
Let x(p) be the first derivative of 3*p**5/5 + 9*p**4/2 - p**3 - 9*p**2 + 134. Factor x(m).
3*m*(m - 1)*(m + 1)*(m + 6)
Let g be (114/(-27) - -4) + 115/450. Let f(k) be the second derivative of g*k**5 + 1/18*k**4 + 0*k**2 + 4*k + 0 + 0*k**3. Factor f(t).
2*t**2*(t + 1)/3
Suppose 7 + 9 = 4*w. Suppose -2*p + 0 = -w. Factor -r + 6*r**2 + 5*r - 4*r**2 + 4*r**p.
2*r*(3*r + 2)
Let z = -52922/7 - -7562. Solve -16/7 + 0*o - 4/7*o**3 + z*o**2 = 0 for o.
-1, 2
Let n(i) be the first derivative of 2*i**3/39 + 25*i**2/13 + 48*i/13 - 89. Let n(f) = 0. What is f?
-24, -1
Suppose 17 - 197 = 4*k. Let l = k - -91/2. Determine r, given that 1 + 1/2*r**3 - r**2 - l*r = 0.
-1, 1, 2
Factor 0*f + 1/4*f**2 + 0 - 5/8*f**3 - 7/8*f**4.
-f**2*(f + 1)*(7*f - 2)/8
Factor -40/7*n**2 + 100/7*n + 0 + 4/7*n**3.
4*n*(n - 5)**2/7
Let z be (-1)/6 + (-98)/(-84) + 1. Let f(x) be the first derivative of 0*x -