-1, 0
Suppose 14 = 4*f - 2. Let m = 10 - 6. Let -2*u**m + 16*u**5 - 4*u**3 + 2*u + 0*u**2 - 2 - 14*u**5 + f*u**2 = 0. What is u?
-1, 1
Suppose l - 2*j + 8 = 0, 6 = 5*j - 19. Factor -2/3*d**l + d + 2/3.
-(d - 2)*(2*d + 1)/3
Factor 0*d + 0 - 2/3*d**2 + 2/3*d**3.
2*d**2*(d - 1)/3
Let z(l) be the second derivative of l**7/21 - l**5/10 + 21*l. What is n in z(n) = 0?
-1, 0, 1
Let b(n) be the third derivative of n**6/30 - 14*n**5/15 + 49*n**4/6 + 4*n**2. Solve b(p) = 0 for p.
0, 7
Factor 2*l**4 - 6*l**2 + 114 + 114 - 224 - 2*l**3 + 0*l**3 + 2*l.
2*(l - 2)*(l - 1)*(l + 1)**2
Let i(l) be the third derivative of -l**5/180 + 11*l**4/36 - 121*l**3/18 + 2*l**2. Solve i(q) = 0 for q.
11
Suppose -c + 3*j + 9 = 0, -5*c + 4*j = -0*j - 12. Find p such that 3/4*p + c + 3/4*p**4 - 3/4*p**3 - 3/4*p**2 = 0.
-1, 0, 1
Let a = 45 - 223/5. Solve -2/5*h**2 + 0 + a*h = 0.
0, 1
Let v(h) be the third derivative of -h**8/16800 - h**7/6300 - h**4/4 + 7*h**2. Let o(s) be the second derivative of v(s). Factor o(i).
-2*i**2*(i + 1)/5
Let w(l) = -2*l**4 - 3*l**3 + 9*l**2 + 4*l - 3. Let d(p) = -4*p**4 - 5*p**3 + 17*p**2 + 8*p - 5. Let v(f) = 6*d(f) - 10*w(f). Solve v(b) = 0 for b.
-1, 0, 2
Let f(c) be the second derivative of c**7/105 + c**6/25 - 2*c**4/15 - 6*c. What is m in f(m) = 0?
-2, 0, 1
Let l(a) = -220*a**2 + 92*a - 4. Let m(v) = 219*v**2 - 92*v + 3. Let p(x) = 5*l(x) + 4*m(x). Factor p(u).
-4*(7*u - 2)*(8*u - 1)
Let h = -200 - -200. Let a(o) be the third derivative of 0*o + h*o**4 + 0*o**3 - 1/35*o**7 + 1/15*o**5 + 4*o**2 - 1/12*o**6 + 0. Factor a(q).
-2*q**2*(q + 2)*(3*q - 1)
Let n = -486 - -12152/25. Let w = 94/75 + n. Factor w*a - 10/3*a**2 + 0.
-2*a*(5*a - 2)/3
Suppose -12*w + w**2 + 0*w**2 - w**2 + 2*w**3 + 2*w**2 = 0. Calculate w.
-3, 0, 2
Let p(j) be the second derivative of 5*j + 0 - 1/12*j**4 - 1/2*j**3 - j**2. Solve p(q) = 0 for q.
-2, -1
Let a(q) be the first derivative of 1/6*q**4 + 1/15*q**5 - 1/3*q**2 + 0*q - 5 - 1/9*q**3. Factor a(w).
w*(w - 1)*(w + 1)*(w + 2)/3
Let b(k) be the third derivative of -k**7/168 + 7*k**6/96 - 3*k**5/8 + 25*k**4/24 - 5*k**3/3 - 12*k**2. Factor b(o).
-5*(o - 2)**3*(o - 1)/4
Let g be 44/56 + 1/4*-2. Factor g*j**2 - 4/7*j + 2/7.
2*(j - 1)**2/7
Suppose 0*s - 2/3*s**5 - 8/3*s**4 + 0 - 8/3*s**3 + 0*s**2 = 0. Calculate s.
-2, 0
Suppose 0 = -5*v + l + 11, v - 2 - 1 = l. Find h, given that -3*h - 2*h + h + v*h**2 + 2*h**2 = 0.
0, 1
Factor 175*y + 4*y**3 - 172*y - 6*y**2 - y**3.
3*y*(y - 1)**2
Factor 19*g**3 - 4*g - 16*g - 40*g**3 + 25*g**2 + 16*g**3.
-5*g*(g - 4)*(g - 1)
Let w(s) = -7*s**5 + 7*s**4 + 22*s**3 + 8*s**2 - 8*s - 8. Let i(b) = 2*b**5 - 2*b**4 - 7*b**3 - 3*b**2 + 3*b + 3. Let m(o) = -8*i(o) - 3*w(o). Factor m(n).
5*n**3*(n - 2)*(n + 1)
Let b(q) = q**3 + 36*q**2 + 77*q + 48. Let z(r) = 3*r**3 + 90*r**2 + 192*r + 120. Let u(m) = 12*b(m) - 5*z(m). Find c, given that u(c) = 0.
-2
Let f(z) be the third derivative of z**6/660 - z**4/132 - 3*z**2. Suppose f(x) = 0. Calculate x.
-1, 0, 1
Factor 0*a + 0 - 1/2*a**2 + 1/2*a**4 + 1/2*a**5 - 1/2*a**3.
a**2*(a - 1)*(a + 1)**2/2
Let r be (-18 + 28)*(-1)/(-30)*4. Let a(v) be the first derivative of -4/5*v**5 + v**2 - 1/3*v**6 + 2 + 0*v + r*v**3 + 0*v**4. Factor a(q).
-2*q*(q - 1)*(q + 1)**3
Let i(g) = 8*g**2 - 38*g + 248. Let o(v) = v**2 + v + 1. Let f(t) = -i(t) + 6*o(t). Factor f(s).
-2*(s - 11)**2
Determine g, given that -3*g**5 + 76*g**2 + 8*g**5 + 24*g + 84*g**3 + 0*g**2 - g**5 + 36*g**4 = 0.
-6, -1, 0
Let 5*f**3 + 8*f**4 - 10*f**2 + 2*f**4 - 5*f**4 = 0. What is f?
-2, 0, 1
Find l such that 27*l**4 + 28*l**2 + 0*l**5 + 4*l**3 - 4*l**5 - 16 - 39*l**4 = 0.
-2, -1, 1
Suppose -s - g - 4 = 0, -4*g - 22 = -5*s + 3*s. Let p be (s - 0)*3/6. Factor 1/2*o**3 + p*o + o**2 + 0.
o*(o + 1)**2/2
Determine a so that -2/9 - 2/9*a + 2/9*a**2 + 2/9*a**3 = 0.
-1, 1
Suppose d + 12 + 11 = 5*a, 5*d - 4*a = -10. Solve -1/4 - 3/4*k**d - 3/4*k - 1/4*k**3 = 0.
-1
Let d(p) be the second derivative of -p**6/120 + p**5/10 - p**4/2 + 7*p**3/6 - 6*p. Let n(c) be the second derivative of d(c). Factor n(z).
-3*(z - 2)**2
Let a = 582/5 + -116. Factor 0 + a*s**2 + 2/5*s.
2*s*(s + 1)/5
Let b(f) be the first derivative of -f**2 + 2 - 3*f - 1/9*f**3. Let b(t) = 0. What is t?
-3
Let b(y) = 2*y**2 - 6*y + 7. Let f(d) = -1. Let v = 0 - 1. Let t(a) = v*b(a) - 3*f(a). Factor t(u).
-2*(u - 2)*(u - 1)
Let p(a) be the first derivative of 2*a**3/3 - a**2 - 4*a + 7. Find o, given that p(o) = 0.
-1, 2
Let v(l) = -3*l**4 - 6*l**3 + 4*l + 5. Let s(b) = 9*b**4 + 18*b**3 - 11*b - 16. Let z(g) = -2*s(g) - 7*v(g). Find f such that z(f) = 0.
-1, 1
Determine t, given that 1 + 1/2*t**3 - t - 3/4*t**2 + 1/4*t**4 = 0.
-2, 1
Let n = 7 + 1. Let l(d) = -34*d**2 - 11*d**3 + 4 - 20*d + 4 - 15*d**3. Let x(f) = 9*f**3 + 11*f**2 + 7*f - 3. Let b(j) = n*x(j) + 3*l(j). Factor b(a).
-2*a*(a + 2)*(3*a + 1)
Factor -5*c**4 - c - 4*c**2 - c**5 - 13*c**3 + 5*c**3 + c.
-c**2*(c + 1)*(c + 2)**2
Let i(t) = t**2 + 14*t - 15. Let v be i(-15). Let x(p) be the third derivative of 0*p**3 + 1/60*p**6 + 0 + v*p + 0*p**4 + 1/30*p**5 - p**2. Factor x(f).
2*f**2*(f + 1)
Let 2/3*m**3 - 4/15*m + 8/15*m**4 + 0 - 14/15*m**2 = 0. Calculate m.
-2, -1/4, 0, 1
Suppose 6*o - 1 - 17 = 0. Let q(d) be the first derivative of 2 + 1/6*d**2 + 2/3*d - 2/9*d**o - 1/12*d**4. Find s, given that q(s) = 0.
-2, -1, 1
Factor 0 - 5/2*z**3 + 5/2*z**2 + 5/2*z - 5/2*z**4.
-5*z*(z - 1)*(z + 1)**2/2
Let r(o) be the third derivative of 0 + 3*o**2 - 1/3*o**3 + 0*o - 1/120*o**6 + 1/8*o**4 + 0*o**5. Factor r(q).
-(q - 1)**2*(q + 2)
Let s(c) = -c**2 - 70*c + 359. Let u(f) = -f**2 - 139*f + 719. Let v(g) = 7*s(g) - 4*u(g). Find h such that v(h) = 0.
11
Let w(i) be the second derivative of -i**7/21 - 2*i**6/15 + 3*i**5/10 + 2*i**4/3 - 4*i**3/3 - i. Suppose w(d) = 0. What is d?
-2, 0, 1
Let t be 2/((22/(-4) + 6)*2). Solve -2*k**4 + 4/3*k**3 - 8/9 - 8/9*k + 22/9*k**t = 0 for k.
-2/3, 1
Let b be 2/(-10)*(-22 - 3). Suppose 0 = -2*x + 3 + 5. Determine v, given that -11*v**x - 4*v - 9*v**3 + b*v + v**2 + 2*v**4 = 0.
-1, -1/3, 0, 1/3
Let v(i) = 5*i - 3. Let l be v(2). Let b be (1 - 1)/(l + -8). Factor -4/9*z**2 + 0 + 4/9*z**4 + b*z**3 - 2/9*z**5 + 2/9*z.
-2*z*(z - 1)**3*(z + 1)/9
Suppose -236*m**2 + 52*m + 114*m**2 - 18 + 2*m**4 + 74*m**2 + 12*m**3 = 0. Calculate m.
-9, 1
Let o be ((-114)/(-12) - 3 - 1) + -5. Factor o*j**3 - 1 + 0*j**2 - 3/2*j.
(j - 2)*(j + 1)**2/2
Let h(n) be the third derivative of -n**8/20160 - n**7/5040 - n**5/30 + 2*n**2. Let g(b) be the third derivative of h(b). Factor g(z).
-z*(z + 1)
Let z(a) be the first derivative of a**6/45 + 2*a**5/75 - a**4/15 - 4*a**3/45 + a**2/15 + 2*a/15 + 11. Solve z(g) = 0.
-1, 1
Let m(f) = -f**3 + f**2 - f. Let w = -6 + 7. Let n(u) = -5*u**3 + u**2 - u + 2. Let q(r) = w*n(r) - 3*m(r). Let q(k) = 0. Calculate k.
-1, 1
Let t(m) = -m**2 + m. Let j(s) = 2*s**3 - 23*s**2 + 59*s - 54. Let x(o) = j(o) - 5*t(o). Solve x(a) = 0 for a.
3
Let m(v) = -v**4 + v**3 - v. Let r(k) = -3*k**4 + 2*k**3 + k**2 - 2*k. Let o = -8 + 7. Let i(p) = o*r(p) + 2*m(p). Factor i(a).
a**2*(a - 1)*(a + 1)
Let y(f) be the second derivative of 49*f**5/80 - 7*f**4/12 + f**3/6 - 66*f - 1. What is n in y(n) = 0?
0, 2/7
Let b(l) be the first derivative of 1/2*l - 1/16*l**4 + 2 + 0*l**3 + 3/8*l**2. Factor b(c).
-(c - 2)*(c + 1)**2/4
Let w be 0/(6/9*-3). Let b(t) be the first derivative of -2 - 1/4*t**2 - 1/6*t**3 + w*t. Suppose b(j) = 0. What is j?
-1, 0
Let r be (104/(-286))/(2/(-11)). Factor 0 + 1/2*k + 1/2*k**3 - k**r.
k*(k - 1)**2/2
Let q(h) be the second derivative of -h**9/25200 + h**8/5600 - h**7/4200 + 5*h**4/12 + 8*h. Let m(a) be the third derivative of q(a). Let m(b) = 0. Calculate b.
0, 1
Let c(s) be the second derivative of s**5/5 - 2*s**4/3 - 2*s**3/3 + 4*s**2 - 2*s. Factor c(v).
4*(v - 2)*(v - 1)*(v + 1)
Factor -70 + 4*b + 70 + 4*b**2 - 4*b**3 - 4*b**4.
-4*b*(b - 1)*(b + 1)**2
Let n(q) be the first derivative of q**6/54 + 7*q**5/45 + 7*q**4/18 + 2*q**3/27 - 5*q**2/6 - q - 20. Suppose n(v) = 0. What is v?
-3, -1, 1
Let q(c) = -11*c**2 - 29*c. Let p = -8 - -14. Let l(z) = 32 + 5*z - 32 + 2*z**2. Let t(m) = p*q(m) + 34*l(m). Determine f so that t(f) = 0.
0, 2
Let z be -6*(-1 + (-1)/(-2)). Solve 8 - 4*f**2 - 4*f**4 - 8*f - 9*f + 12*f**z + 5*f = 0 for f.
-1, 1, 2
Let v(d) be the first deriv