g(u).
3*(u - 1)*(u + 1)**3*(4*u - 1)
Suppose 6*i**4 - 24*i**5 - 2*i**3 - i**3 + 16*i**4 - 3*i**2 + 8*i**4 = 0. Calculate i.
-1/4, 0, 1/2, 1
Let r(b) be the second derivative of b**4/24 + b**3/6 + b**2/4 + 6*b. Find w such that r(w) = 0.
-1
Let t(h) be the second derivative of -h**5/80 - 7*h**4/16 - 49*h**3/8 - 343*h**2/8 + 23*h. What is d in t(d) = 0?
-7
Let g = 37/108 + -5/54. Solve -g*s + 0 + 1/4*s**2 = 0.
0, 1
Suppose 4*x - g - g - 8 = 0, -2*g = 4*x + 8. Suppose 3*y = 2*y + 5*o + 24, -3*y + 3*o + 24 = 0. Let -2 + 2*h**4 + x*h**3 + 0*h**3 + y*h**3 - 4*h = 0. What is h?
-1, 1
Let z(t) be the third derivative of 0*t**3 + 0 - 3*t**2 - 1/840*t**7 + 1/96*t**4 + 0*t - 1/480*t**6 + 1/240*t**5. Let z(n) = 0. What is n?
-1, 0, 1
Let g(a) be the first derivative of 0*a - 2 + 0*a**2 + 0*a**5 - 1/12*a**4 + 0*a**3 + 1/18*a**6. Let g(p) = 0. What is p?
-1, 0, 1
Let h(b) be the second derivative of b**9/4536 + b**8/840 - b**6/135 - b**3/2 - 6*b. Let g(d) be the second derivative of h(d). Factor g(u).
2*u**2*(u - 1)*(u + 2)**2/3
Suppose 18 = 2*l + 4*l. Let t(k) be the second derivative of -2*k + 0 + 0*k**2 + 0*k**l + 0*k**4 + 1/30*k**6 + 1/20*k**5. Factor t(g).
g**3*(g + 1)
Let w(a) be the second derivative of -1/6*a**2 + 5*a - 1/72*a**4 - 1/12*a**3 + 0. Factor w(r).
-(r + 1)*(r + 2)/6
Suppose 10/3*o - 5/3*o**2 + 0 = 0. Calculate o.
0, 2
Let f(v) be the first derivative of -v**6/480 - v**5/160 + v**3/3 - 7. Let x(n) be the third derivative of f(n). Factor x(o).
-3*o*(o + 1)/4
Let r = -4 + 0. Let s = r - -6. Factor -1/4*x**s - 1/2*x - 1/4.
-(x + 1)**2/4
Let w be ((-522)/4)/((-1)/(-2)). Let k = w + 791/3. Solve -2/3*o**2 - 8/3 - k*o = 0.
-2
Let p(z) be the third derivative of 1/540*z**6 + 0*z - 2*z**2 - 1/108*z**4 + 2/27*z**3 + 0 - 1/135*z**5. Factor p(r).
2*(r - 2)*(r - 1)*(r + 1)/9
Let a(h) be the first derivative of h**6/1080 - h**5/120 + h**4/36 - h**3/3 + 1. Let v(b) be the third derivative of a(b). Solve v(c) = 0 for c.
1, 2
Let c(g) be the first derivative of -g**6/12 - g**5/2 + 5*g**4/8 + 25*g**3/6 - 10*g**2 + 8*g - 9. Determine l so that c(l) = 0.
-4, 1
Let k(t) = -3*t - 7. Let r be k(-4). Factor 0*d**2 + 0*d**3 + 0*d - 2/3*d**r + 2/3*d**4 + 0.
-2*d**4*(d - 1)/3
Suppose k = -k. Suppose d = -k*d. Factor 0*u + d - 2/3*u**2.
-2*u**2/3
Let h(s) be the first derivative of 4*s**5/5 - 44*s**3/3 - 36*s**2 - 32*s + 20. Suppose h(q) = 0. Calculate q.
-2, -1, 4
Factor 0*f**2 + 0*f**4 + 3/4*f**3 - 3/4*f**5 + 0*f + 0.
-3*f**3*(f - 1)*(f + 1)/4
Let i(s) be the third derivative of s**5/240 - s**4/48 + s**3/24 - 4*s**2. Factor i(h).
(h - 1)**2/4
Let n be ((-6)/(-3) - 4) + 4. Factor g**2 + 2*g - 1 + 0 + 0*g + n.
(g + 1)**2
Let p(d) be the first derivative of -d**5/50 - d**4/30 + d**3/15 + d**2/5 - 3*d - 2. Let b(h) be the first derivative of p(h). Let b(l) = 0. Calculate l.
-1, 1
Let d be ((-8)/(13 - -11))/((-1)/6). Let 1/3*w + 2/3 - w**d = 0. Calculate w.
-2/3, 1
Let v = -134 + 537/4. What is k in 1/2*k + 0 - 1/4*k**3 + v*k**2 = 0?
-1, 0, 2
Let h(j) = j - 5. Let v be h(9). Factor 2*s**2 - 4 + 6*s**3 + s + 3*s**v - 7*s - s**4.
2*(s - 1)*(s + 1)**2*(s + 2)
Let i(c) be the first derivative of -3*c**5/5 + 9*c**4/4 - 2*c**3 + 21. Factor i(q).
-3*q**2*(q - 2)*(q - 1)
Let j(x) be the first derivative of x**6/18 - 2*x**5/15 - 2*x**4/3 - 8. Suppose j(z) = 0. What is z?
-2, 0, 4
Let j(m) be the first derivative of -3/2*m - 1 - 1/4*m**3 - 9/8*m**2. Determine t so that j(t) = 0.
-2, -1
Let h(g) be the first derivative of -3/5*g**5 - 2 + 0*g**2 + 0*g + g**3 + 0*g**4. Factor h(z).
-3*z**2*(z - 1)*(z + 1)
Suppose 2 = -4*r + 2*g, 2*r + 0*g + 3*g - 19 = 0. Solve 2/9*v**3 + 2/9 - 2/9*v - 2/9*v**r = 0.
-1, 1
Let p(u) = -6*u + 1 + u**3 - 2*u**3 - 2*u - 2*u**2. Let x(l) = l**3 + 3*l**2 + 9*l - 1. Let q(t) = -6*p(t) - 5*x(t). Factor q(s).
(s - 1)**3
Determine l, given that -10*l**3 + 18*l + 12*l**2 - 5*l**3 + 17*l**3 = 0.
-3, 0
Let j(g) be the second derivative of -g**5/10 - g**4/2 - 2*g**3/3 + 11*g. Factor j(t).
-2*t*(t + 1)*(t + 2)
Let o(b) = 8 - b + 7 - 5 + 0. Let l be o(7). Let -9/4*q**l + 0 + 1/2*q**2 + 0*q = 0. Calculate q.
0, 2/9
Let c(y) be the first derivative of -4*y**3/3 + 10*y**2 - 16*y - 3. What is p in c(p) = 0?
1, 4
Suppose -4*l + r - 92 = -30, 2*l - 2*r = -28. Let j be (l/(-6))/(-4)*-9. Factor 0 - 3*o**3 + 0 - 10*o**5 + 7*o**5 + j*o**4.
-3*o**3*(o - 1)**2
Factor -4*b**3 + 2*b**3 + 10*b**4 - 12*b**4.
-2*b**3*(b + 1)
Let n = 368/9 - 40. Suppose 0 - n*o**3 + 2/9*o + 2/3*o**2 = 0. Calculate o.
-1/4, 0, 1
Let p(a) be the second derivative of -a**4/6 - 2*a**3/3 - a**2 - 6*a. Suppose p(w) = 0. What is w?
-1
Let b(d) be the second derivative of -9*d**5/80 + d**4/24 + 3*d**3/8 - d**2/4 + 10*d. Factor b(l).
-(l - 1)*(l + 1)*(9*l - 2)/4
Let n(v) be the first derivative of -1/6*v**2 - 2/3*v + 1/12*v**4 + 2/9*v**3 + 2. Determine s, given that n(s) = 0.
-2, -1, 1
Let j(m) = -m**3 + 5*m**2 + 10*m. Let n(o) = 6*o**3 - 24*o**2 - 51*o. Let f(c) = -21*j(c) - 4*n(c). Suppose f(d) = 0. Calculate d.
-2, -1, 0
Determine g so that g**3 - 3*g**3 + 824*g - 878*g - 54 - 18*g**2 = 0.
-3
Factor 19 - 193*w**2 + 21 + 2 - 9*w + 178*w**2.
-3*(w + 2)*(5*w - 7)
Let q be 12/(-8) - (-4869)/3240. Let h(k) be the third derivative of -q*k**6 - 5/72*k**4 + 0*k + 4*k**2 + 1/9*k**3 + 1/45*k**5 + 0. Factor h(w).
-(w - 2)*(w - 1)**2/3
Let s(a) be the third derivative of -a**7/1120 + 3*a**5/160 - a**4/16 + 5*a**3/6 + a**2. Let r(v) be the first derivative of s(v). Factor r(q).
-3*(q - 1)**2*(q + 2)/4
Let h(z) be the second derivative of -z**10/45360 + z**9/11340 - z**7/1890 + z**6/1080 - z**4/12 + 4*z. Let s(i) be the third derivative of h(i). Factor s(g).
-2*g*(g - 1)**3*(g + 1)/3
Let d be (-12)/(-18) - 4/(-12). Let g be 33/6 - (d - 1). What is m in -5/2*m**5 - 21/2*m**3 + g*m**2 - m + 0 + 17/2*m**4 = 0?
0, 2/5, 1
Solve 3*b**2 - b**2 - 12*b - 8*b**2 - 3*b**2 - 3 = 0.
-1, -1/3
Let 8/13*a**4 + 2/13*a**5 + 6/13*a**3 - 8/13*a**2 - 8/13*a + 0 = 0. Calculate a.
-2, -1, 0, 1
Let d = 30 - 30. Let v(b) be the third derivative of 1/108*b**4 - 2/27*b**3 + d + 0*b - 1/540*b**6 - 2*b**2 + 1/135*b**5. Determine a, given that v(a) = 0.
-1, 1, 2
Let n be -4*(-44)/192 - (-2)/(-8). Factor 4/3*x**2 - n*x**5 + 2/3*x + 0*x**3 - 4/3*x**4 + 0.
-2*x*(x - 1)*(x + 1)**3/3
Let n(o) be the first derivative of -1/5*o**5 - 3/8*o**4 - 1/8*o**2 + 0*o - 1/3*o**3 - 1/24*o**6 - 1. Determine t, given that n(t) = 0.
-1, 0
Let t(s) be the first derivative of s**6/3 + 2*s**5 + 3*s**4/2 - 6*s**3 + 21. Find n, given that t(n) = 0.
-3, 0, 1
Suppose -5*r = -4*u - 11, -u - 12 = 4*r + u. Let g = 1 - r. Factor -n - n - n**2 + g*n**3 - n**3.
n*(n - 2)*(n + 1)
Factor -2*v**5 + 2*v + 0*v**5 + 32*v**4 - 36*v**4 + 4*v**2.
-2*v*(v - 1)*(v + 1)**3
Find m, given that 2/9*m**2 + 8/9*m + 2/3 = 0.
-3, -1
Suppose 21 = 5*k - 14. Let s(h) be the third derivative of -h**2 + 0*h**3 + 1/12*h**6 + 0*h + 0*h**4 + 1/35*h**k + 0 + 1/15*h**5. Suppose s(c) = 0. What is c?
-1, -2/3, 0
Let l(r) = 7*r**4 - 5*r**3 - 14*r**2. Let d(c) = -6*c**4 + 6*c**3 + 13*c**2 + c. Let j(o) = -3*d(o) - 2*l(o). Factor j(v).
v*(v - 3)*(2*v + 1)**2
Let d(g) = 4*g**3 + 3*g**2 - 3*g. Let b(n) = n**3 + n**2 - n. Let t(l) = -3*b(l) + d(l). Factor t(u).
u**3
Find j such that -16/9 - 550/9*j**3 - 136/9*j - 140/3*j**2 - 250/9*j**4 = 0.
-1, -2/5
Let j(v) be the third derivative of 1/84*v**4 + 0*v**3 + 2/105*v**5 + 0 + 1/1176*v**8 + 0*v + 4/735*v**7 + 1/70*v**6 - 6*v**2. Factor j(x).
2*x*(x + 1)**4/7
Let -2/3*x - 4/9 + 2/3*x**3 + 2/9*x**4 + 2/9*x**2 = 0. Calculate x.
-2, -1, 1
Suppose 0 = l + 5*v - 8 - 7, 0 = -2*l - 2*v + 22. Let j be l/(-4)*8/(-40). Solve j - 1/2*c + 1/2*c**3 - 1/2*c**2 = 0 for c.
-1, 1
Let t(b) be the third derivative of 0*b - 1/120*b**6 + 1/630*b**7 + 0*b**3 - 1/180*b**5 + 1/1008*b**8 + 0 + 1/36*b**4 - b**2. Factor t(h).
h*(h - 1)**2*(h + 1)*(h + 2)/3
Let m(n) = 3*n**2 - 9*n + 12. Let x(s) = 5*s - 2. Let i be x(-2). Let q(w) = w - 1. Let v(z) = i*q(z) - m(z). Solve v(y) = 0.
-1, 0
Let c(b) be the second derivative of -b**7/42 - 3*b**6/20 - 3*b**5/10 - b**4/6 + 9*b. Determine w so that c(w) = 0.
-2, -1/2, 0
Let u(a) be the third derivative of a**7/3360 - a**6/480 + a**5/160 - a**4/96 + a**3/2 + 3*a**2. Let n(x) be the first derivative of u(x). Factor n(c).
(c - 1)**3/4
Let g(z) be the first