- 4*t**2 + 0 + 8/3*t = 0.
-2, 0, 1
Factor -13448/15 - 2/15*s**2 - 328/15*s.
-2*(s + 82)**2/15
Let j = -855 + 857. Factor -1/2 + 4*d**4 - 23/4*d**j + 6*d**3 - 15/4*d.
(d - 1)*(d + 2)*(4*d + 1)**2/4
Let i(p) be the third derivative of 20*p**2 + 0*p - 1/18*p**3 - 1/30*p**5 + 1/16*p**4 + 0 + 1/180*p**6. Factor i(f).
(f - 2)*(2*f - 1)**2/6
Let l(w) be the second derivative of 3*w**5/2 + 13*w**4/6 - 2*w**3/3 + 5*w - 5. Factor l(p).
2*p*(p + 1)*(15*p - 2)
Suppose 107*r**2 + 7*r**4 + 20*r**3 + 8*r**2 - 34*r**2 - 5*r**4 - 31*r**2 = 0. Calculate r.
-5, 0
Let y(x) be the second derivative of x**7/525 - x**5/50 + x**4/30 - 5*x**2/2 + 7*x. Let o(h) be the first derivative of y(h). Determine d, given that o(d) = 0.
-2, 0, 1
Solve 7*p**2 + 50*p - 6*p**3 + 76*p**2 - 2*p + 4*p**5 - 15*p**2 + 2*p**3 - 20*p**4 = 0.
-1, 0, 3, 4
Let a(u) be the first derivative of u**3/3 + 5*u**2/2 - 84*u - 59. Factor a(f).
(f - 7)*(f + 12)
Determine w so that 0*w**3 - 2/9*w**4 + 4/9*w + 2/3*w**2 + 0 = 0.
-1, 0, 2
Solve 26*l**2 + 21*l**2 - 12 + 12*l**3 - 2*l + 22*l - 3*l**2 = 0 for l.
-3, -1, 1/3
Let n(u) = -u**4 - 5*u**3 + 3*u**2 + u - 2. Let s(w) = 4*w**3 + 0*w**3 - 3*w**2 + 22 + 2*w**3 - 19. Let a(x) = -3*n(x) - 2*s(x). Factor a(j).
3*j*(j - 1)*(j + 1)**2
Let i(h) be the third derivative of -1/21*h**3 + 11/420*h**5 + 0 - 3/490*h**7 - 8*h**2 + 0*h + 1/24*h**4 - 1/120*h**6. What is z in i(z) = 0?
-1, 2/9, 1
Let -8/9 + 4/3*b**4 + 2*b - 16/9*b**3 - 2/9*b**5 - 4/9*b**2 = 0. Calculate b.
-1, 1, 4
Let u be (-22)/5 + 8/20. Let y be (5 - 1)/u*(-2)/5. Factor -1/5*k**4 + 0 + y*k**2 + 0*k - 1/5*k**3.
-k**2*(k - 1)*(k + 2)/5
Let w be 5*(740/182 - 4) + 2/7. Determine j, given that 2/13*j**2 - w + 0*j = 0.
-2, 2
Let t(q) = -4*q - 11. Let d be t(-2). Let z be 6 - (-1 + 0)*d. Find u, given that -1/4*u**z + 1/4*u + 0 + 0*u**2 = 0.
-1, 0, 1
Suppose 6*m - 3*m - 3*p = 3, -2*m - 2*p + 10 = 0. Let 3/5*w**m + 3*w**2 + 12/5 + 24/5*w = 0. Calculate w.
-2, -1
Suppose i = -2*o + 1, -5*o - 260*i + 19 = -263*i. Find h such that -h + 1/3*h**o + 0 = 0.
0, 3
Let s be 481/111 + (-6)/1 - -2. Suppose -3*f + 3*x = 0, 5*x = -4*f + 6*f + 15. Factor 1/3*h + 0*h**3 - s*h**f - 2/3*h**2 + 0 + 2/3*h**4.
-h*(h - 1)**3*(h + 1)/3
Let n(b) be the second derivative of b**4/12 - 17*b**3 + 2601*b**2/2 - 6*b + 2. Suppose n(c) = 0. Calculate c.
51
Let g(y) be the second derivative of -5*y**9/3024 + y**8/84 - y**7/42 - 13*y**3/3 - 15*y. Let i(s) be the second derivative of g(s). Factor i(v).
-5*v**3*(v - 2)**2
Let y be (0 - -1)*-7 - -11. Let c(p) be the first derivative of 0*p**2 - 1/4*p**y + 0*p + 7 + 1/3*p**3. Let c(r) = 0. Calculate r.
0, 1
Determine s so that 1176 + 28*s + 1/6*s**2 = 0.
-84
Let w = 768 - 6911/9. Let a = -15 + 15. Factor -2/9*i**4 + 0*i + 0*i**2 - w*i**3 - 1/9*i**5 + a.
-i**3*(i + 1)**2/9
Let c(a) be the first derivative of a**5/5 + 11*a**4/2 - 23*a**3/3 - 41. Solve c(m) = 0.
-23, 0, 1
Suppose -5*p - 3*h + 22 = h, -4*h = -p - 10. Let i be (12 + (p - 2))/1. Find n, given that -54*n - 81*n**2 - i - 81/2*n**3 = 0.
-2/3
Suppose -y = -3*q + 152, 0*q = y + 2*q + 162. Let x = -1418/9 - y. Solve -2/9*d**2 - 2/9 + x*d = 0.
1
Let g(k) = -k**2 - 11*k + 10. Let i be g(-10). Factor -i*w**3 - 10 - 10*w**2 - 3*w**5 + 168*w - 3*w**5 + w**5 + 20*w**4 - 143*w.
-5*(w - 2)*(w - 1)**3*(w + 1)
Let w = 87 + -86. Let v be -2*3/9 + w. Determine h so that -1/3*h**2 - v*h**3 + 1/3*h + 0 + 1/3*h**4 = 0.
-1, 0, 1
Factor 16/9 - 10/3*f + 14/9*f**2.
2*(f - 1)*(7*f - 8)/9
Let 1/2*i**4 - 1/2 - i + i**3 + 0*i**2 = 0. Calculate i.
-1, 1
Let m(k) = -k + 2. Let p be m(-4). Factor -1 - p*l + 4 + 0*l + 3*l**2.
3*(l - 1)**2
Find i such that -1/4*i**2 - 6*i + 25/4 = 0.
-25, 1
Let h be ((-27)/18)/((-12)/16). Let x be 3/6 + 14/20. Factor -4/5 - x*n + 2/5*n**3 + 0*n**h.
2*(n - 2)*(n + 1)**2/5
Let b(l) = -9*l**2 + 20*l - 11. Let h(r) = 5*r**2 - 9*r + 6. Let f(i) = 6*b(i) + 11*h(i). Determine v so that f(v) = 0.
-21, 0
Let a(u) be the first derivative of u**5 - 5*u**4/2 + 5*u**3/3 - 18. Factor a(k).
5*k**2*(k - 1)**2
Let r(l) be the second derivative of -1/15*l**3 + 0 + 0*l**2 - 1/75*l**6 + 1/50*l**5 - 6*l + 1/30*l**4. Suppose r(b) = 0. Calculate b.
-1, 0, 1
Let i be 9/15 - (-1)/(15/306). Factor i + 5 - 28*n + 2*n**2 + 72.
2*(n - 7)**2
Factor 16 - 16 + 5*v**2 - v**2 + 825*v - 777*v.
4*v*(v + 12)
Factor -15/4*n**2 + 69/8*n + 3/8*n**5 - 15/4 + 3/2*n**4 - 3*n**3.
3*(n - 1)**3*(n + 2)*(n + 5)/8
Let g(i) be the third derivative of 0*i - 13/84*i**4 + 0 - 2/21*i**3 + 7*i**2 - 11/210*i**5. Factor g(n).
-2*(n + 1)*(11*n + 2)/7
Let d(x) = -3*x**3 - 5*x**2 - 3*x + 2. Let v be d(-2). Factor 0*u - 2*u + v*u + 2*u - 4*u**2 - 9.
-(2*u - 3)**2
Factor -127*u**4 + 11*u - 18*u**2 - 2*u**3 + 129*u**4 + 7*u.
2*u*(u - 3)*(u - 1)*(u + 3)
Let y(c) = 2*c**2 - 4*c - 7. Let x(f) = -f**2 + 2*f + 3. Let g = -60 + 53. Let p be (2 - 1)/((-4)/12). Let w(v) = g*x(v) + p*y(v). Solve w(t) = 0 for t.
0, 2
Let a(p) be the first derivative of -2/5*p**5 + 0*p + p**4 - 2*p**2 - 21 + 2/3*p**3. Factor a(l).
-2*l*(l - 2)*(l - 1)*(l + 1)
Let c(d) be the third derivative of -d**8/504 + d**6/60 - d**5/45 + 2*d**2 + 4*d. Factor c(v).
-2*v**2*(v - 1)**2*(v + 2)/3
Let u(z) be the third derivative of -z**6/780 + z**5/39 - 25*z**4/156 - 2*z**2 + 134. Solve u(d) = 0 for d.
0, 5
Factor 0*j - 1/4*j**3 + 0 + 7/4*j**2.
-j**2*(j - 7)/4
Let g(a) be the first derivative of -a**8/1680 - a**7/840 + a**6/180 + 12*a**3 - 6. Let p(s) be the third derivative of g(s). Determine z, given that p(z) = 0.
-2, 0, 1
Let q = 8065 + -72583/9. Determine s so that q*s - 2/9*s**2 + 2/9 - 2/9*s**3 = 0.
-1, 1
Let z(m) = 6*m**3 + 836*m**2 + 58800*m + 1372000. Let r(l) = -31*l**3 - 4178*l**2 - 294000*l - 6860000. Let x(t) = 2*r(t) + 11*z(t). Factor x(p).
4*(p + 70)**3
Let v(u) = -u**2 + 3*u + 3. Let j be v(0). What is s in 3*s**4 - s**3 + 3*s - 2*s**j - 88*s**2 + 85*s**2 = 0?
-1, 0, 1
Let q(r) = r**3 + 2. Let n be q(0). Let s be (-6 - (1 + -10)) + 0. Factor 3*t - 3 - n*t**2 - 5*t**s + 2*t + 3 + 2.
-(t - 1)*(t + 1)*(5*t + 2)
Suppose 14*i = 12*i + 48. Let r = i - 21. Let 10*f**4 + 4*f + f**3 - 7*f**3 - 10*f**2 + 2*f**r = 0. Calculate f.
-1, 0, 2/5, 1
Factor -9/5*p**2 + 0 + 3/5*p.
-3*p*(3*p - 1)/5
Let i(j) = -7*j**2 + 32*j + 62. Let h be i(6). Factor 0 - 1/3*v**4 + 0*v**h + 1/3*v**3 + 0*v.
-v**3*(v - 1)/3
Let c(w) = -2*w**2 + 18. Let o(u) = u**2 + 3*u. Let a(n) = -c(n) + o(n). Solve a(y) = 0 for y.
-3, 2
Let k = -226 - -228. Suppose -s - 5*u - 14 = -u, 0 = 3*s + 5*u + 14. Suppose -s*j + 3*j**k + j**2 - 3*j**2 - 3 = 0. What is j?
-1, 3
Suppose -1206*j = -1212*j + 192. Let -4/3*u**3 - 48 - j*u + 44/3*u**2 = 0. What is u?
-1, 6
Let s(t) be the second derivative of 5*t**5 - 85*t**4/3 + 64*t**3 - 72*t**2 - 33*t. Determine w, given that s(w) = 0.
1, 6/5
Let s(i) be the first derivative of -8/9*i**3 + i**4 + 1/9*i**6 - 8/15*i**5 + 10 + 1/3*i**2 + 0*i. Let s(j) = 0. Calculate j.
0, 1
Factor -36105/2*f**2 - 34445/2*f**3 - 840*f - 10.
-5*(f + 1)*(83*f + 2)**2/2
Let z(p) be the first derivative of p**6/3 - 76*p**5/5 + 457*p**4/2 - 1216*p**3 + 2304*p**2 + 375. Factor z(a).
2*a*(a - 16)**2*(a - 3)**2
Let o = -263 - -301. Suppose -40*f + 4 = -o*f. Find l, given that -2/13*l**3 + 0*l + 0 + 2/13*l**f = 0.
0, 1
Let l be 2/(-17) - (70/(-17) - -2). Suppose 0*h**l + 6/7 - 9/7*h + 3/7*h**3 = 0. Calculate h.
-2, 1
Suppose -3/5*g**4 - 48/5*g + 192/5 - 33/5*g**3 - 108/5*g**2 = 0. Calculate g.
-4, 1
Let y be (-140)/(-28) + -3 + 0. Let g(o) be the second derivative of 2*o - 1/4*o**4 + o**3 + 0 - 3/2*o**y. Factor g(s).
-3*(s - 1)**2
Let u(h) be the first derivative of -h**4/18 + 2*h**3/27 + 8*h**2/9 - 8*h/3 - 75. Factor u(y).
-2*(y - 2)**2*(y + 3)/9
Suppose 4*v - 13*g - 18 = -14*g, 2*g + 12 = 4*v. Factor 1/10*h**2 - 1/10*h**v - 1/10*h**5 + 0 + 1/10*h**3 + 0*h.
-h**2*(h - 1)*(h + 1)**2/10
Let h be (-45)/84*(-432)/270. Let n(b) be the first derivative of 5 + 12/7*b + h*b**2 - 15/7*b**3. Solve n(a) = 0 for a.
-2/5, 2/3
Let r = 9097/45 + -1805/9. Factor -6/5 - 2/5*k + r*k**2.
2*(k - 1)*(4*k + 3)/5
Let j(t) = -2*t**5 + 14*t**4 - 28*t**3 + 32*t**2 - 20*t + 4. Let w(v) = -v**4 + v + 48*v**3 - 48*v**3. Let z(h) = -j(h) - 2*w(h). Factor z(b).
2*(b - 2)*(b - 1)**4
Factor 315 + 140*m - 5*m**2 + 313 + 375 - 703.
-5*(m - 30)*(m + 2)
Let g(t) be the second derivative of 1/27