 t(b) = 0. Calculate b.
2
Let z be (0 - 3/21)*-7. Let r be z/4 - (-3)/36. Factor r*t**2 + 1/3 - 2/3*t.
(t - 1)**2/3
Let f(s) = s**2. Let k(g) = 2*g**3 - 2*g**2. Let w = 2 + 4. Let p(x) = w*f(x) + k(x). Determine a, given that p(a) = 0.
-2, 0
Let j(m) be the second derivative of 0*m**6 - 3/140*m**5 + 1/294*m**7 + 0*m**2 + 0 + 1/42*m**4 - 6*m + 0*m**3. Find n such that j(n) = 0.
-2, 0, 1
Suppose -84*t - 9 = -87*t. Solve -1/2 - 3/4*s**t + 1/4*s + s**2 = 0 for s.
-2/3, 1
Solve -6/5 - 21/5*x + 12/5*x**2 - 21/5*x**5 - 6/5*x**4 + 42/5*x**3 = 0 for x.
-1, -2/7, 1
Let x = -2 - 24. Let t be 4/x - 434/(-455). Factor -t*d - 2/5*d**2 - 2/5.
-2*(d + 1)**2/5
Suppose 3*w = 5*t, w + 0*t = t. Factor 1/5*v - 3/5*v**2 + w - 1/5*v**3 + 3/5*v**4.
v*(v - 1)*(v + 1)*(3*v - 1)/5
Let n(y) be the second derivative of -y**7/630 + y**6/60 - y**5/15 - 7*y**4/12 + 3*y. Let h(t) be the third derivative of n(t). Factor h(l).
-4*(l - 2)*(l - 1)
Let f(v) be the third derivative of v**5/60 + 5*v**4/24 - v**3 + 3*v**2. Let b be f(-6). Factor 0*c + b - 1/3*c**2.
-c**2/3
Let q(x) be the third derivative of x**7/280 - 3*x**6/160 + 3*x**5/80 - x**4/32 + 4*x**2. Factor q(a).
3*a*(a - 1)**3/4
Let y(s) be the second derivative of 3*s**8/2240 - s**7/560 + s**6/1440 + 2*s**3/3 + 3*s. Let q(h) be the second derivative of y(h). Factor q(p).
p**2*(3*p - 1)**2/4
Factor -4*l**2 + 5*l + l**2 - l**3 + 3 + l**2 + 3*l**2.
-(l - 3)*(l + 1)**2
Let h(b) be the first derivative of 2/7*b + 2/7*b**2 - 1 + 2/21*b**3. What is y in h(y) = 0?
-1
Let w(r) be the second derivative of r**5/30 - r**3/3 + 2*r**2/3 + 4*r. Let w(y) = 0. What is y?
-2, 1
Let c(b) = -9*b**2 - b - 11. Let i(q) = -4*q**2 - 5. Let a be (-1 - 3/(-2))*-14. Let l(u) = a*i(u) + 3*c(u). Let l(n) = 0. Calculate n.
1, 2
Let g(r) = 2*r. Let f = 1 + 0. Let c be g(f). Find w such that w**3 + 2*w**2 + c*w**4 + 3*w**3 + 0*w**2 = 0.
-1, 0
Let t(r) be the first derivative of r**6/45 - r**4/18 + 3*r + 2. Let u(s) be the first derivative of t(s). Factor u(a).
2*a**2*(a - 1)*(a + 1)/3
Let h(q) = q**3 + 2*q**2 - q. Let d be h(-2). Determine f so that -5*f**3 + d*f**4 + f**4 + 40*f**2 - 38*f**2 = 0.
0, 2/3, 1
Let t = 5 + -8. Let n be t/(6/(-10)) - 2. Solve -3*d**4 + 2*d - 3*d**4 + 4*d**2 - 2*d**n + 2*d**4 = 0 for d.
-1, -1/2, 0, 1
Factor 4/7*d**2 + 12/7*d**3 + 0*d + 8/7*d**4 + 0.
4*d**2*(d + 1)*(2*d + 1)/7
Let h(n) be the second derivative of 0*n**3 + 1/30*n**4 + 9*n + 0*n**2 + 0. Factor h(t).
2*t**2/5
Let f(d) be the first derivative of -d**5/25 + 3*d**4/20 - d**3/5 + d**2/10 - 16. Factor f(i).
-i*(i - 1)**3/5
Suppose 781 = -5*g - 2*v, -2*g = v + 137 + 176. Let b = -1083/7 - g. Factor 0 - 6/7*t**3 - 6/7*t**4 + 0*t - 2/7*t**5 - b*t**2.
-2*t**2*(t + 1)**3/7
Find s, given that 0*s**2 + 6/5*s**4 + 0 + 0*s**3 + 0*s + 2/5*s**5 = 0.
-3, 0
Solve 112/3*t**5 - 8/3*t**2 + 0*t + 0 - 4*t**3 + 36*t**4 = 0 for t.
-1, -1/4, 0, 2/7
Let j(p) be the second derivative of 0 + 1/30*p**4 - 1/5*p**2 + 0*p**3 - 2*p. What is x in j(x) = 0?
-1, 1
Let w(t) be the third derivative of t**5/300 - t**3/30 - t**2. Solve w(n) = 0.
-1, 1
Let n(x) be the second derivative of x**6/420 + x**5/105 + x**4/84 + x**2/2 - 3*x. Let g(h) be the first derivative of n(h). Solve g(v) = 0.
-1, 0
Let b(k) = -k**3 + k - 1. Let m(j) = 5*j**5 + 5*j**4 + 25*j**3 - 5*j**2 - 30*j + 30. Let w(v) = -30*b(v) - m(v). Factor w(q).
-5*q**2*(q - 1)*(q + 1)**2
Let t(y) = 4*y**5 - 12*y**4 + 16*y**3 - 8*y**2 + 2*y. Let j(m) = m**5 - m**4 + m. Let g(x) = 2*j(x) - t(x). Let g(c) = 0. What is c?
0, 1, 2
Suppose m + 19 - 22 = 0. Suppose b - 4*t - 4 = 0, 4*t = -2*b + 3*t + 8. Factor 0*o**m - 1/2*o**5 + 0 + 1/2*o + o**b - o**2.
-o*(o - 1)**3*(o + 1)/2
Let h(o) be the first derivative of -o**7/420 - o**6/90 - o**5/60 + o**3/3 - 3. Let s(x) be the third derivative of h(x). Find q such that s(q) = 0.
-1, 0
Let s(h) = -5*h + 2. Let o be s(0). Factor 3/4*k**3 + 0 - 1/4*k**o - 3/4*k**4 + 1/4*k**5 + 0*k.
k**2*(k - 1)**3/4
Let y(t) = -t**4 + t**3 + t. Let d be 1*15 + (-2 - -5). Let n(z) = 8*z**4 - 7*z**3 - 11*z + 1. Let l(f) = d*y(f) + 2*n(f). Solve l(m) = 0 for m.
-1, 1
Let n(x) be the first derivative of x**8/3360 - x**6/720 + 4*x**3/3 + 3. Let y(p) be the third derivative of n(p). Suppose y(j) = 0. Calculate j.
-1, 0, 1
Let d(q) be the second derivative of 10*q**7/21 - 7*q**6/6 + q**5/2 + 5*q**4/12 + 44*q. Determine b so that d(b) = 0.
-1/4, 0, 1
Let o be 5 + -2 - (-1 + 0). Find d, given that -144*d + o*d**3 - 3*d**3 + 18*d**2 + 192 + 18*d**2 - 4*d**3 = 0.
4
Suppose -10 = -4*w - 2. Suppose -3*t + 9 = -u, 3*u - u = -6. Factor b**4 + b**t + 2*b**3 - w*b + 2*b.
b**2*(b + 1)**2
Factor 15*g - 15*g - 3*g**3 + 3*g**2 + 9*g**2 + 15*g.
-3*g*(g - 5)*(g + 1)
Suppose -10 = -5*f - 2*p + 8, -3*p = f - 1. Suppose -2*n = -8, -f*q + 4*n = 10 - 2. Determine v, given that -6/7*v**q + 4/7 + 2/7*v = 0.
-2/3, 1
Let v(b) be the first derivative of -b**3/3 + b**2/2 - 18. What is c in v(c) = 0?
0, 1
Let g(i) be the third derivative of 0*i + 2/15*i**6 + 0 + 0*i**3 + 1/3*i**4 + 2/105*i**7 + 2*i**2 + 1/3*i**5. Factor g(j).
4*j*(j + 1)**2*(j + 2)
Let i be (-11)/(-3) - (-22)/(-33). Let d(g) be the first derivative of -2/45*g**5 + 0*g**i + 2/9*g**2 + 2/9*g - 1/9*g**4 + 1. Factor d(a).
-2*(a - 1)*(a + 1)**3/9
Let f = -3 - -7. Solve 2*v**3 + 4*v + v - 3*v + f*v**2 = 0.
-1, 0
Let t = -127 + 891/7. Suppose -2/7*g**5 + 2/7*g**3 + 0*g + t*g**4 + 0 - 2/7*g**2 = 0. What is g?
-1, 0, 1
Let q = 1/47 + 44/141. Let w = -94/3 - -32. Let q*s + 0 - w*s**2 + 1/3*s**3 = 0. What is s?
0, 1
Let t(w) = -w**3 + 25*w**2 - 25*w**2 + 3*w**5 - 2*w**5. Let l(h) = -12*h**5 + 15*h**3 + 2*h**2 - 3*h - 2. Let p(u) = 2*l(u) + 22*t(u). Factor p(g).
-2*(g - 2)*(g - 1)*(g + 1)**3
Factor 0 + 1/2*s**4 + 1/4*s - 1/2*s**2 + 0*s**3 - 1/4*s**5.
-s*(s - 1)**3*(s + 1)/4
Let g(b) be the first derivative of 4*b**5/5 + b**4 - 4*b**3 - 10*b**2 - 8*b + 5. Determine t, given that g(t) = 0.
-1, 2
Let u(l) be the first derivative of l**8/168 - 2*l**7/105 + l**6/60 - 3*l**2 - 5. Let j(o) be the second derivative of u(o). Determine g, given that j(g) = 0.
0, 1
Let b(j) = -j**3 - 3*j**2 - 3*j - 2. Let p be b(-3). Determine s so that -19*s + p*s + 85*s**3 - 88*s**3 - 12*s**2 = 0.
-2, 0
Let s(m) be the first derivative of 0*m**2 + 1/6*m**3 - 1/12*m**6 + 4 + 0*m + 1/8*m**4 - 1/10*m**5. Suppose s(h) = 0. Calculate h.
-1, 0, 1
Let k(u) be the second derivative of u**4/54 + 16*u**3/27 + 5*u**2/3 - 29*u. Factor k(b).
2*(b + 1)*(b + 15)/9
Let h be 8/3*240/64. Factor -4/3 + h*d**2 - 38/3*d**3 + 14/3*d**4 - 2/3*d.
2*(d - 1)**3*(7*d + 2)/3
Suppose -3*m + 12*f - 14*f + 10 = 0, -3*f = -4*m + 2. Factor -6/7*k + 0 + 3/7*k**m.
3*k*(k - 2)/7
Let c(q) be the third derivative of q**6/900 - q**4/60 - 2*q**3/3 + 2*q**2. Let g(j) be the first derivative of c(j). Suppose g(s) = 0. Calculate s.
-1, 1
Let x(m) be the first derivative of -1 + 0*m**5 + 0*m**4 + 1/3*m**3 + 0*m**2 - 1/420*m**7 + 0*m + 0*m**6. Let s(u) be the third derivative of x(u). Factor s(v).
-2*v**3
Let k = -6 + 9. Let s(o) be the third derivative of 0 + 2*o**2 - 1/24*o**4 + 0*o**k + 0*o - 1/60*o**5. Factor s(q).
-q*(q + 1)
Factor 0 + 2/9*n**2 + 2/9*n.
2*n*(n + 1)/9
Let -24/5 + 3*d**3 - 12*d + 6/5*d**2 = 0. What is d?
-2, -2/5, 2
Suppose -1 - 11 = -3*b. Let s = -8 - -11. Let 2*h + 4 - h**b + h**3 - 3*h**s - 3 = 0. Calculate h.
-1, 1
Let k = 8 + -5. Suppose 5*p = 4*m + 6 - 3, m - k*p = -6. Factor 0 - 15*r + 9*r**2 - r**3 + 5 + 4*r**3 + 1 - m*r**4.
-3*(r - 1)**3*(r + 2)
Solve 24/7 - 27/7*q + 3/7*q**2 = 0.
1, 8
Find g such that 24*g**2 + 4*g**4 - 102*g**5 + 10*g**4 - 32*g**3 + 100*g**5 = 0.
0, 2, 3
Let y(x) be the first derivative of x**6/21 - x**4/14 + 1. Factor y(o).
2*o**3*(o - 1)*(o + 1)/7
Let r = 3 + 1. Suppose -c + r = c. Factor 2 - c*w**2 + 0 - 4*w + 4*w.
-2*(w - 1)*(w + 1)
Let p = 11/14 + -1/2. Let 0*u + 0 - 2/7*u**3 + 4/7*u**2 - p*u**4 = 0. What is u?
-2, 0, 1
Let f(u) be the third derivative of -2*u**2 + 0 + 0*u**5 + 0*u**3 + 0*u + 1/300*u**6 - 1/60*u**4. Determine o, given that f(o) = 0.
-1, 0, 1
Suppose -5*i + d = -95, i - 2*d = -2*i + 50. Let t be (-6)/4*i/(-15). Find q such that t*q**3 - 3*q**5 + 2*q**5 - q**5 = 0.
-1, 0, 1
Suppose 1 - 1/4*u + 1/4*u**3 - u**2 = 0. What is u?
-1, 1, 4
Factor 2*j**3 - 2*j - 4*j**2 - 2*j + 4*j + 2*j.
2*j*(j - 1)**2
Let f 