-b*(b - 1)**2*(b + 1)**2/4
Let z = -8 + 13. Suppose 1 = -2*g + z. Determine t so that -10*t**g - 3*t**3 - 2*t**2 + 6*t**2 = 0.
-2, 0
Let x = 2392 + -2390. Let w(j) be the second derivative of 0 + 1/3*j**3 + x*j - 1/18*j**4 - 2/3*j**2. Suppose w(l) = 0. Calculate l.
1, 2
Let z(v) be the third derivative of v**8/42 + 18*v**7/35 + 79*v**6/30 - 121*v**5/15 - 91*v**4/2 - 196*v**3/3 - 2*v**2 + 116*v. Let z(j) = 0. What is j?
-7, -1, -1/2, 2
Let a be (3*-1)/(-53 - -52). Let z(t) be the first derivative of -1/3*t**2 - 1/9*t**a + 0*t + 5. Let z(j) = 0. Calculate j.
-2, 0
Let b(j) be the first derivative of -23 - 5/9*j**2 - 1/18*j**4 + 4/9*j**3 + 0*j. Let b(m) = 0. Calculate m.
0, 1, 5
Let j be (-2)/10 - 8/(-40). Suppose j = m + c - 8, -4*m - 3*c + 33 = -0*c. Factor 14*q**4 - 14*q**2 - 2*q**2 + 31*q**3 - 46*q**4 + 2*q + m*q**3.
-2*q*(2*q - 1)**2*(4*q - 1)
Suppose 0 = 3*w - 4*p - 40, p + 22 = w + 4*p. Let 8*o - w*o**4 - 6*o**3 + 25*o**3 + 33*o**3 - 44*o**2 = 0. Calculate o.
0, 1/4, 1, 2
Let s(v) be the first derivative of -1/240*v**5 - 1/1440*v**6 + 0*v**2 + 2/3*v**3 + 0*v - 3 - 1/96*v**4. Let g(m) be the third derivative of s(m). Factor g(x).
-(x + 1)**2/4
Suppose 0 + 268/3*i**2 - 8978/3*i - 2/3*i**3 = 0. Calculate i.
0, 67
Let q(t) be the first derivative of 7*t**4/12 - 4*t**3/9 - t**2/2 + 71. Determine j, given that q(j) = 0.
-3/7, 0, 1
Let y = 2/23 - -17/69. Let 0 - 1/3*o**2 + y*o = 0. Calculate o.
0, 1
Suppose -6*a = 2*a - 8. Let g(p) = -2*p**2 + 12*p + 3. Let w(s) = -s**2 + s - 1. Let j(h) = a*g(h) + 3*w(h). Factor j(z).
-5*z*(z - 3)
Factor 346*j - 2521*j**3 - 9*j**2 + 51*j**2 + 200 - 106*j + 2523*j**3.
2*(j + 1)*(j + 10)**2
Suppose -7*q = -4*q - 12. Let u(w) be the first derivative of 20*w**2 + 3/2*w**q + 5 - 28/3*w**3 - 16*w. Let u(h) = 0. What is h?
2/3, 2
Determine x so that 0 + 0*x - 16/11*x**2 - 2/11*x**3 = 0.
-8, 0
Let c(r) = 12*r**2 - 84*r - 176. Let a(l) = 26*l**2 - 168*l - 350. Let z(i) = -4*a(i) + 9*c(i). Factor z(g).
4*(g - 23)*(g + 2)
Suppose -3*k + 2*y + 22 = 0, -11*y = -5*k - 14*y + 5. Let b(t) be the first derivative of -3/7*t**2 - 2 - 1/7*t**k - 1/7*t - 3/7*t**3. Factor b(c).
-(c + 1)**2*(4*c + 1)/7
Let x = 6833/4270 + -1/4270. Factor 14/5*l**2 - 2/5*l + 26/5*l**4 - 6*l**3 - x*l**5 + 0.
-2*l*(l - 1)**3*(4*l - 1)/5
Let f = 1277/4494 - -1/642. Find u such that -2/7*u**2 - 4/7*u + 0 + f*u**3 = 0.
-1, 0, 2
Let a(z) = z**2 + 14*z - 12. Let h be a(-15). Factor -3*d**h - 16*d + 3*d + 16*d + 36*d**2 - 111*d.
-3*d*(d - 6)**2
Let k(y) be the second derivative of y**6/45 + 19*y**5/75 + 19*y**4/90 - 14*y**3/45 - 94*y - 2. Find s such that k(s) = 0.
-7, -1, 0, 2/5
Let z = -1625/6 + 271. Let f(k) be the first derivative of -65/24*k**4 - 3 - 5/4*k**6 + 0*k - z*k**2 - 19/18*k**3 - 31/10*k**5. Let f(s) = 0. Calculate s.
-1, -2/5, -1/3, 0
Let p(c) be the first derivative of -15 + 2/27*c**3 + 2/9*c**2 + 2/9*c. Suppose p(q) = 0. What is q?
-1
Let s(k) = k**2 + 39*k - 82. Let q be s(2). Let f(r) be the third derivative of q*r + 2*r**2 + 0 - 1/30*r**6 + 2/15*r**5 - 1/6*r**4 + 0*r**3. Factor f(i).
-4*i*(i - 1)**2
Let u(f) be the first derivative of -4*f**5/25 + 3*f**4 - 88*f**3/5 + 232*f**2/5 - 288*f/5 + 124. Suppose u(j) = 0. What is j?
2, 9
What is a in -116 + 47 - 5*a**2 - 13*a - 56 - 37*a = 0?
-5
Let j be (-4)/(-6) + 33/396. Suppose 0 + 1/4*w**5 + 1/4*w**2 - j*w**3 - 1/4*w**4 + 1/2*w = 0. Calculate w.
-1, 0, 1, 2
Solve 28 - 134/5*n + 2/5*n**3 - 8/5*n**2 = 0.
-7, 1, 10
Suppose z - 4*m + 4 = -z, 0 = z + 2*m - 10. Let v = 4 - z. Find y such that 0*y**2 + 4*y**2 + v*y**2 - 2*y**2 = 0.
0
Let f be 4 - 29*(-2)/2. Let a be (3/(-5) + f/30)*12. Factor a*d**2 + 18 - 18*d - 2/3*d**3.
-2*(d - 3)**3/3
Let c(t) be the third derivative of t**6/480 + 5*t**5/16 + 49*t**4/32 + 73*t**3/24 + 48*t**2. Factor c(s).
(s + 1)**2*(s + 73)/4
Let d = -65 + 65. Let z(g) be the third derivative of 0*g**3 + 0*g**5 + 1/60*g**6 - g**2 + 0 + 0*g**4 + d*g - 1/105*g**7. Let z(j) = 0. What is j?
0, 1
Let j be 9/(-6) + 20/8 + 3. Let u be (48/18 - j)/(4/(-6)). Suppose -1/2*q**u + 0 + 0*q - q**3 - 1/2*q**4 = 0. What is q?
-1, 0
Suppose -63 = -6*v - 39. Suppose 4*i + 0 + 2 = -5*l, l + 2*i + v = 0. Factor 0 - 1/3*h + 0*h**l + 1/3*h**3.
h*(h - 1)*(h + 1)/3
Let l(t) be the second derivative of t**5/210 - t**4/84 - 2*t**2 + 11*t. Let v(q) be the first derivative of l(q). Let v(k) = 0. What is k?
0, 1
Let z(p) be the third derivative of p**6/480 + 3*p**5/20 - 13*p**4/32 - 37*p**3/12 - 2*p**2 + 211*p. Factor z(i).
(i - 2)*(i + 1)*(i + 37)/4
Factor 0 + f - 1/4*f**4 - 9/4*f**2 + 3/2*f**3.
-f*(f - 4)*(f - 1)**2/4
Suppose 5 = 3*x - 33*j + 34*j, -5*j = -5*x + 35. Determine w, given that -4/3*w**2 - 14/9*w + 4/9 + 8/9*w**4 + 14/9*w**x = 0.
-2, -1, 1/4, 1
Let n(t) = 7*t - 3. Let o be n(2). Let b = 12 + -10. Let o + b*k**2 + 8*k + 1 - 4 = 0. Calculate k.
-2
Let w be (56/49)/(2/7). Factor 4 + s**w + 10*s**2 + 10*s**2 + 2*s**3 - 23*s**2 - 4*s.
(s - 1)**2*(s + 2)**2
Let u(z) = -4*z**4 - z**3 + 5*z**2 - 5. Let c(g) = -g**4 + g**2 - 1. Let p = -37 - -42. Let i(b) = p*c(b) - u(b). Suppose i(w) = 0. What is w?
0, 1
Suppose -14*f - 45*f**3 - 23 + 35*f**2 + 12 + 11 + 25*f**4 + 4*f - 5*f**5 = 0. What is f?
0, 1, 2
Suppose 2*x = -2*x - 8*x. Let f(o) be the second derivative of 1/54*o**4 + 0 + x*o**2 + 3*o + 2/27*o**3. What is m in f(m) = 0?
-2, 0
Factor -2620 + 0*d**2 + 156*d + 2068 - 5532 - d**2.
-(d - 78)**2
Let n(l) = l**2 - l. Let b(r) = -2*r**3 + 11*r**2 - 5*r. Let k be (-496)/(-28) + 4/14. Let j(c) = k*n(c) - 2*b(c). Factor j(w).
4*w*(w - 2)*(w + 1)
Let a(x) be the second derivative of x**8/2240 - x**7/840 - x**6/60 + x**5/10 - x**4/3 - 25*x. Let m(l) be the third derivative of a(l). Factor m(f).
3*(f - 2)*(f - 1)*(f + 2)
Find p, given that 2/9*p**2 - 26/9*p + 8/3 = 0.
1, 12
Let s(m) be the third derivative of m**5/90 - m**4/8 - 5*m**3/18 + 2*m**2 + 65. Factor s(j).
(j - 5)*(2*j + 1)/3
Let l(o) be the first derivative of -10 + 0*o + 14/27*o**3 + 5/18*o**4 + 2/45*o**5 + 1/3*o**2. Solve l(i) = 0.
-3, -1, 0
Find k, given that 688 - 48*k - 41*k + 29*k - 238 + 2*k**2 = 0.
15
Let x = -12 - -15. Solve t + 3 + 3*t**2 + x*t - 5*t - 5*t = 0 for t.
1
Let r = 91 + -88. Factor -176 - 13*x - 2*x**r + 172 - 8*x**2 + 3*x.
-2*(x + 1)**2*(x + 2)
Let y(j) = j**2 - 7*j - 8. Let c be y(8). Suppose 2*x + u - 9 = c, 0*x - x + 12 = 2*u. Let -2*s**3 + 0*s**3 + 18*s**x - 14*s**2 = 0. What is s?
0, 2
Let q(y) = y**2 + 21*y + 23. Let r be (-2)/((-11)/(-10) + -1). Let i be q(r). Factor 3/2*s**i - 3/2*s - 1/2*s**2 + 1 - 1/2*s**4.
-(s - 2)*(s - 1)**2*(s + 1)/2
Let f(y) be the third derivative of -y**8/336 + y**6/60 - y**4/24 + 16*y**2 + y. Find l, given that f(l) = 0.
-1, 0, 1
Let n = 277/8 - 1337/40. Find x such that 0 + 0*x + 6/5*x**2 + 0*x**3 - n*x**4 = 0.
-1, 0, 1
Let t be 12 - (-12)/10*(-20)/(-8). Suppose 0 = t*v - 7*v - 10*v. Factor 2/5*n**2 + 2/5*n**3 - 2/5*n**4 - 2/5*n**5 + v + 0*n.
-2*n**2*(n - 1)*(n + 1)**2/5
Factor 11*f - 34/3*f**2 + 1/3.
-(f - 1)*(34*f + 1)/3
What is k in 0 + 1/5*k**3 + 13/5*k**2 + 0*k = 0?
-13, 0
Suppose 239*r = 883 + 1132 + 853. Solve 3/4*p**3 + 6*p - 21/4*p**2 + r = 0.
-1, 4
Let i be -7 - 938/126*-1. Suppose -3*s + 3*l = 14 - 38, -5*l - 28 = -2*s. Determine g so that 0*g**2 + 2/9*g**s + i*g**3 + 0 + 0*g = 0.
-2, 0
Factor -1/9*p**3 - 1/3*p + 1/3*p**2 + 1/9.
-(p - 1)**3/9
Suppose 12 = 4*i + 5*q + 19, -4*i + 5*q = 57. Let u be 4/i*80/(-45). Factor 0 - 2*n**3 - u*n - 8/3*n**2.
-2*n*(3*n + 2)**2/9
Let z(b) = -b**3 - 2*b**2 + 5*b + 6. Let c(m) = m**3 + 12*m**2 - 12*m + 10. Let q be c(-13). Let s be z(q). Factor 0 - 1/5*w**4 - 4/5*w + 3/5*w**3 + s*w**2.
-w*(w - 2)**2*(w + 1)/5
What is b in 90*b**4 - 89*b**4 + 19 + 21*b**2 - 11 - 8*b**3 - 22*b = 0?
1, 2, 4
Suppose 0 = -0*b - 2*b - 6. Let x = b + 6. Let 3*i**x + 8*i - 5*i - 6*i = 0. Calculate i.
-1, 0, 1
Suppose 23/2*p**2 - 1/2*p**4 + 33/2*p + 7 + 3/2*p**3 = 0. What is p?
-2, -1, 7
Let t(v) = v**3 - v**2 + 5. Suppose -r - 2*x = -4*x - 33, -3*x = r - 13. Suppose -2*q - 3*q = r. Let d(z) = -3. Let c(o) = q*d(o) - 3*t(o). Factor c(m).
-3*m**2*(m - 1)
Let q(y) be the third derivative of y**8/100800 - y**7/25200 - y**6/600 - 2*y**5/5 + 24*y**2. Let c(u) be the third derivative of q(u). Solve c(h) = 0.
-2, 3
Let u be (8/(-10))/(900/(-675)). Factor 0*m + 0*m**2 - u*m**3