u**3.
-3*u**2*(u - 2)*(3*u - 2)/4
Suppose -2*x - a = -9, x + a + 33 = 6*x. Let n(m) = m**2 - 5*m - 4. Let b be n(x). Determine u so that 0 - 2*u**3 - 4/3*u**b + 2/3*u = 0.
-1, 0, 1/3
Let y(w) = w**2 + 2*w - 3. Let j be y(-3). Let z(b) be the first derivative of j*b + 2/7*b**3 + 3/14*b**4 + 2/35*b**5 + 1/7*b**2 + 2. Factor z(v).
2*v*(v + 1)**3/7
Let r(m) be the second derivative of m**9/30240 + m**8/13440 - m**4/6 - 3*m. Let q(y) be the third derivative of r(y). Factor q(x).
x**3*(x + 1)/2
Solve -1/4*f**5 - 9/4*f**4 - 7/4*f**2 + 6*f - 23/4*f**3 + 4 = 0.
-4, -1, 1
Let l = 491/3 + -163. Factor l*k**2 + 4/3 + 2*k.
2*(k + 1)*(k + 2)/3
Let c(j) be the first derivative of -8*j - 22*j**2 + 4 + 52/3*j**3. Suppose c(l) = 0. What is l?
-2/13, 1
Let u = 6 + -2. Suppose x + 2*x + 8 = -u*g, 9 = x - g. Solve j**3 - 4*j**2 + 2*j - 3*j**3 - 4*j**3 + x + 4*j**3 = 0 for j.
-2, -1, 1
Suppose -12 = -3*o - h, -5*h = 2*o - 1 - 7. Let 4 - 8*t**3 + 2*t - 4*t**o + 10*t - 4*t = 0. What is t?
-1, 1
Suppose y = 3*t - 6, -4*t + 10 = y + t. Let v = 2 - y. Suppose w**2 - 3*w**2 - 5*w - 1 - 7*w**2 - v*w**4 - 7*w**3 = 0. What is w?
-1, -1/2
Suppose -2*y + 2*i - 2 = 4, -33 = -4*y - 5*i. Find c, given that -2/5*c + 1/5*c**y + 0 = 0.
0, 2
Let u(m) be the third derivative of 0*m - 1/3*m**4 - 1/60*m**7 - 4*m**2 - 1/3*m**3 + 0 - 19/240*m**6 - 1/672*m**8 - 5/24*m**5. Factor u(q).
-(q + 1)**3*(q + 2)**2/2
Let b = 974/45 - 193/9. Let 1/5*l**2 - b*l**4 - 1/5*l**5 + 0 + 0*l + 1/5*l**3 = 0. Calculate l.
-1, 0, 1
Let k(u) = u**3 - 3*u**2 - 3*u + 4. Let j be k(3). Let p = j + 8. Factor -a**3 - 6*a**p - 4 + 2 + 6*a - a**3.
-2*(a + 1)*(2*a - 1)**2
Let d(c) be the third derivative of -c**6/240 - 11*c**5/480 + 19*c**4/192 - c**3/12 - c**2. Suppose d(u) = 0. Calculate u.
-4, 1/4, 1
Let c(n) = n**4 - n**2 - 1. Let f(o) = 4*o**4 - 4*o**4 - 4 - 5*o**2 + 3*o**4 + 2*o**2. Let j be (-12)/10 - 1/(-5). Let h(g) = j*f(g) + 4*c(g). Factor h(p).
p**2*(p - 1)*(p + 1)
Let c(i) be the third derivative of 1/210*i**6 - 1/42*i**4 + 0 + 2*i**2 + 0*i**5 + 0*i - 1/21*i**3 + 1/735*i**7. Factor c(b).
2*(b - 1)*(b + 1)**3/7
Suppose -2*i + 32 = 2*i. What is m in 24*m**4 - 14*m**2 - 6*m + 4 - i*m**3 + 14*m**5 - 6*m**2 - 8*m**2 = 0?
-1, 2/7, 1
Let h(j) be the first derivative of 48*j**5/25 - j**4 - 8*j**3/5 - 2*j**2/5 - 10. Let h(u) = 0. Calculate u.
-1/3, -1/4, 0, 1
Factor -6*l**2 + 0*l + 3*l**3 - l + l + 9*l**4.
3*l**2*(l + 1)*(3*l - 2)
Let a be 2/(-15) + 31/210. Let t(s) be the third derivative of a*s**7 + 0*s**4 + 0*s**6 + 2*s**2 - 1/20*s**5 + 0*s + 0 + 0*s**3. Solve t(g) = 0 for g.
-1, 0, 1
Let a(p) = 5*p**2 - 7*p - 6. Suppose -10 = -4*t + 2. Suppose 44 = -t*g - g. Let d(n) = -9*n**2 + 13*n + 11. Let h(f) = g*a(f) - 6*d(f). Factor h(j).
-j*(j + 1)
Suppose 3*m - 2*s - 5 - 1 = 0, -m + 2 = 3*s. Let b(a) be the first derivative of 2/7*a + 2 + 0*a**m - 2/21*a**3. Factor b(q).
-2*(q - 1)*(q + 1)/7
Let x be 35/(-14)*(3 + 42/(-10)). Let r(l) be the first derivative of -1/7*l**2 - 1/14*l**4 + 0*l + 4/21*l**x + 4. Factor r(q).
-2*q*(q - 1)**2/7
Let r(m) = -2. Let j(g) = 0*g**2 + 0*g**2 + g**2 - 2 - g + 1. Let w(s) = -2*j(s) - r(s). Factor w(p).
-2*(p - 2)*(p + 1)
Let j(h) be the second derivative of h**6/480 - h**5/240 - h**2/2 + 5*h. Let f(k) be the first derivative of j(k). Factor f(g).
g**2*(g - 1)/4
Factor 5 - 9*j**2 - 5 + 3*j.
-3*j*(3*j - 1)
Suppose 19*s - 30 = 46. Let 11/4*y**s - 1/2*y**5 + 2*y - 9/2*y**3 + y**2 + 0 = 0. Calculate y.
-1/2, 0, 2
Let s = -7/16 - -9/16. Let r(c) be the third derivative of -s*c**6 + 0*c**3 - 1/5*c**5 + 0 + 0*c - 1/8*c**4 - c**2 - 1/35*c**7. Factor r(g).
-3*g*(g + 1)**2*(2*g + 1)
Let r(q) be the third derivative of 1/100*q**5 + 4*q**2 + 1/120*q**6 + 0 - 1/350*q**7 - 1/420*q**8 - 1/120*q**4 + 0*q**3 + 0*q. Suppose r(n) = 0. Calculate n.
-1, 0, 1/4, 1
Let j(f) be the second derivative of f**10/45360 - f**9/22680 - f**8/10080 + f**7/3780 + f**4/6 + 2*f. Let y(x) be the third derivative of j(x). Factor y(w).
2*w**2*(w - 1)**2*(w + 1)/3
Let q(i) = -i + 2. Let y be q(0). Suppose 2/3*x**y + 2*x + 4/3 = 0. What is x?
-2, -1
Let k(m) be the third derivative of m**8/80640 - m**7/20160 + m**5/60 + 4*m**2. Let t(h) be the third derivative of k(h). What is p in t(p) = 0?
0, 1
Let s(n) be the second derivative of -3*n**5/70 - n**4/14 + n**3/7 + 3*n**2/7 + 19*n. Suppose s(v) = 0. What is v?
-1, 1
Let y = 139 - 139. Let r(d) be the second derivative of -1/147*d**7 - 1/105*d**6 + 1/42*d**4 + y*d**3 + 0 + 0*d**2 + 1/70*d**5 - 4*d. Solve r(c) = 0.
-1, 0, 1
Let w = -18 - -20. Factor -5*r**w - 21*r - 3 - 3*r - 43*r**2.
-3*(4*r + 1)**2
Let b(o) be the third derivative of 2*o**7/105 + o**6/10 + 2*o**5/15 + 21*o**2. Let b(y) = 0. What is y?
-2, -1, 0
Let a(f) = 2*f**3 + f**2 - 3*f. Let l(n) = -n**3 + n. Suppose 2 + 10 = -4*m. Let j(b) = m*l(b) - a(b). Suppose j(c) = 0. What is c?
0, 1
Let v = 481 + -9623/20. Let z = 1/4 - v. Let 0*f - z*f**2 + 2/5 = 0. What is f?
-1, 1
Let y(k) be the third derivative of -1/90*k**5 - k**2 - 1/180*k**6 + 1/36*k**4 + 1/9*k**3 + 0 + 0*k. Factor y(z).
-2*(z - 1)*(z + 1)**2/3
Let m(a) = -4*a + 12*a**2 - 2 - 10*a**2 + a. Let v(q) = -3*q**2 + 4*q + 3. Let x = 5 + -2. Let f(l) = x*v(l) + 4*m(l). Factor f(n).
-(n - 1)*(n + 1)
Let -2/3*h**3 - 4/3*h**2 - 2/3*h + 0 = 0. Calculate h.
-1, 0
Let i = -2789/15 + 186. Let p(r) be the second derivative of 0*r**3 - r + 0*r**2 - 3/20*r**5 + 0 + i*r**6 + 1/14*r**7 - 1/6*r**4. Find u such that p(u) = 0.
-1, -2/3, 0, 1
Factor 1/5*v**3 + 8/5 + 12/5*v + 6/5*v**2.
(v + 2)**3/5
Let n(t) = -t**3 + 7*t**2 - 17*t - 1. Let w(b) = b**3 - 7*b**2 + 18*b + 2. Let p(j) = 7*n(j) + 6*w(j). Factor p(g).
-(g - 5)*(g - 1)**2
Let k(i) be the third derivative of -i**5/60 + i**3/6 + 16*i**2. Suppose k(b) = 0. Calculate b.
-1, 1
Let i(d) be the second derivative of -d**4/78 + 5*d**3/39 - 4*d**2/13 + 33*d. Suppose i(q) = 0. What is q?
1, 4
Let y = 0 + 10. Let b be 2/(-10) + 22/y. Determine g so that 5 - 2*g + g**2 - 6 + b = 0.
1
Let q(b) = b**2 - 6*b + 3. Let o be q(6). Determine t so that -7*t**5 + t**5 + 24*t**2 + 2*t + 3*t**3 - 4 + 28*t**4 - 47*t**o = 0.
-1/3, 1, 2
Let n be ((-2)/(-7))/(3/7). Find y such that -2/3*y**3 + n*y**2 + 4/3*y + 0 = 0.
-1, 0, 2
Let g(c) be the second derivative of c**8/2520 - c**7/420 + c**6/180 - c**5/180 - c**3/2 - 5*c. Let x(o) be the second derivative of g(o). Factor x(r).
2*r*(r - 1)**3/3
Let -3*j**4 + 52*j + 3*j**3 + 9*j**3 - 3 - 40*j - 18*j**2 = 0. What is j?
1
Find o such that -1/2*o**2 + 1/2 + 1/2*o**3 - 1/2*o = 0.
-1, 1
Let l(u) = 39*u**3 + 60*u**2 + 60*u + 24. Let a(y) = -8*y**3 - 12*y**2 - 12*y - 5. Let d(v) = -24*a(v) - 5*l(v). Let d(h) = 0. What is h?
-2, 0
Suppose -27*m + 8 = -23*m. Find f such that f**m + 0 - 1/2*f**3 - 1/2*f = 0.
0, 1
Suppose -2 = -2*l, 2*m - 5*l + 9*l = 8. Factor 2/3*t**m + 4/3*t + 2/3.
2*(t + 1)**2/3
Let u(m) = 4*m**2 + 2*m + 2. Let h(z) = -z + 1. Let p(a) = 2*h(a) - u(a). Let p(x) = 0. What is x?
-1, 0
Let d(c) = c**2 + 5*c - 3. Let f = 7 + -13. Let i be d(f). What is a in 0*a**2 + 0 + 1/3*a**5 + 0*a + 0*a**i - 1/3*a**4 = 0?
0, 1
Let j(z) = -4*z**4 - 4*z**3 + 24*z**2 - 20*z + 10. Let r(i) = i**4 - i**3 - i**2 + i - 1. Let b(w) = j(w) + 6*r(w). Suppose b(x) = 0. Calculate x.
1, 2
Solve -7*u**3 + 10*u**3 - 4*u - 150*u**4 + 149*u**4 = 0.
-1, 0, 2
Let k(z) be the first derivative of 8*z**5/55 + 5*z**4/22 + 2*z**3/33 - 1. Solve k(i) = 0 for i.
-1, -1/4, 0
Suppose -3*j + 33 + 27 = 0. Let w be 17/j + 6/(-10). Factor 1/4*n**2 - 1/4 + 1/4*n**3 - w*n.
(n - 1)*(n + 1)**2/4
Let j(v) = 4*v**4 - 20*v**3 + 19*v**2 - 3*v + 3. Let x(t) = -12*t**4 + 60*t**3 - 56*t**2 + 8*t - 8. Let q(r) = 8*j(r) + 3*x(r). Let q(o) = 0. Calculate o.
0, 1, 4
Let j(u) be the second derivative of 2*u**5/5 - 7*u**4/6 - 2*u**3/3 - 8*u. Find p such that j(p) = 0.
-1/4, 0, 2
Let x be 1/((-2)/6) + -1. Let n = 6 + x. Solve -t**n + t**2 + t**2 - t = 0 for t.
0, 1
Let x = 44 + -130/3. Let -x*l**4 - 8/9*l**3 + 2/9*l**2 + 0 + 4/9*l = 0. Calculate l.
-1, 0, 2/3
Let g be (3 - (-39)/(-6))*(-16)/28. Factor -125/2*y**3 - 2 - 125/2*y**g - 20*y.
-(5*y + 1)*(5*y + 2)**2/2
Suppose 5*i - 13 - 2 = 0. Let l be 6/1 - 0/1. Factor 3 - i*h**2 + l*h - 4*h - 2*h.
-3*(h - 1)*(h + 1)
Let k(a) = a**2 - a. Let i(m) = m. Let u = -3 + 2. Let p(v) = u*i(v) - k(v). Determine s, giv