- 2/5*u**5 + 16 + 2/3*u**3 - 1/4*u**4 + 0*u. Find l such that m(l) = 0.
-1, 0, 1, 2
Let q(m) be the second derivative of m**6/60 + 3*m**5/40 + m**4/24 - m**3/4 - m**2/2 + 162*m. Factor q(v).
(v - 1)*(v + 1)**2*(v + 2)/2
Let r be 79/6*-19 - (-9)/54. Let s = -250 - r. Determine z, given that 0 + z**4 + 0*z**2 - 1/3*z**5 - 2/3*z**3 + s*z = 0.
0, 1, 2
Let j(s) = -s**3 + 9*s**2 + 38*s + 25. Let p be j(12). Let i = p - 193/4. Determine u so that -9/8*u**3 - i*u**2 + 0 + 0*u - 3/8*u**4 = 0.
-2, -1, 0
Let h(k) be the third derivative of k**5/300 + k**4/60 - 43*k**2 + 2. Solve h(b) = 0 for b.
-2, 0
Let f(u) = -2*u**3 + u + 1. Let v(n) = -38*n**3 + 50*n**2 + 5*n + 3. Let r(z) = -14*f(z) + 2*v(z). Let r(h) = 0. What is h?
-1/4, 1/3, 2
Let c = -5093/2 + 2216. Let n = c + 334. Factor n*y + 3/2*y**2 + 1.
(y + 2)*(3*y + 1)/2
Factor -8/3 + 2/9*o**3 + 10/9*o**2 - 16/9*o.
2*(o - 2)*(o + 1)*(o + 6)/9
Let z = -2705 - -81151/30. Let m(j) be the second derivative of 0 + 1/50*j**5 - 2/15*j**3 + z*j**4 + 0*j**2 + 12*j. Factor m(r).
2*r*(r - 1)*(r + 2)/5
Suppose 124*s + 273 = 412 + 481. Find z such that 0 - 22/9*z**2 - 10/9*z**s - 4/9*z - 14/3*z**3 - 34/9*z**4 = 0.
-1, -2/5, 0
Let c = 150 + -291/2. Let l be 584/200 - ((-4)/125)/(62/155). Determine t so that -l*t + 1/2*t**2 + c = 0.
3
Let y(u) = -2*u**3 + 25*u**2 - 7*u + 27. Let n be y(12). Let s be (2/14)/(n/406). Factor 4/3*q + 2/3*q**4 + 0*q**2 - s - 4/3*q**3.
2*(q - 1)**3*(q + 1)/3
Let g(z) be the first derivative of -1/9*z**4 + 0*z**3 + 2/9*z**2 + 2/9*z - 2/45*z**5 - 1. Solve g(d) = 0 for d.
-1, 1
Let k be (1/(-8))/((-140)/32 + 4). Factor -1/3*y**5 + 2/3*y**3 - 1/3*y + k*y**4 + 1/3 - 2/3*y**2.
-(y - 1)**3*(y + 1)**2/3
Let v be 2*(-2)/(-20)*(-90)/(-72). Let w(p) be the third derivative of -1/12*p**6 + 0 - 1/70*p**7 - 1/6*p**3 + 0*p - 1/5*p**5 - v*p**4 + 8*p**2. Factor w(d).
-(d + 1)**3*(3*d + 1)
Let t(p) = -p**5 + p**2 - p + 1. Let a(i) be the first derivative of -5*i**6/3 + 5*i**4 + 5*i**3 - 10*i**2 - 5*i + 14. Let l(z) = a(z) - 5*t(z). Factor l(c).
-5*(c - 2)*(c - 1)*(c + 1)**3
Let p(b) be the first derivative of b**5/5 - 2*b**3 + 4*b**2 - 3*b + 67. Factor p(j).
(j - 1)**3*(j + 3)
Let y be (8 - 3)*(2 + (-12)/10). Let l = 11 + -8. What is a in -a - a**2 + l*a - y + 3 = 0?
1
Suppose 4*v - 2*v - 882 = 0. Factor 10*a**3 + 30*a**2 + 20 - 5*a**3 + v*a - 396*a.
5*(a + 1)**2*(a + 4)
Suppose 2*k + k**3 - 5*k**3 + k**3 + k**5 - k**2 + 3970*k**4 - 3969*k**4 = 0. Calculate k.
-2, -1, 0, 1
Let p(f) = -f - 1. Let l(d) = -5*d**3 - 5*d**2 + 26*d + 22. Let b(u) = -l(u) - p(u). Let i(m) be the first derivative of b(m). Factor i(k).
5*(k - 1)*(3*k + 5)
Let d be -11 - (0 + -4 + -1). Let j(x) = 14*x**3 - 20*x**2 + 4*x + 8. Let v(u) = -13*u**3 + 19*u**2 - 4*u - 7. Let y(g) = d*v(g) - 5*j(g). Solve y(l) = 0 for l.
-1/4, 1
Suppose 3 = 4*w - 3*w. Suppose 64*v + 21*v**3 + 4*v**4 + 30*v**w - 96*v**2 - 8*v**4 - 15*v**3 = 0. Calculate v.
0, 1, 4
Let m(s) be the first derivative of 2*s**3/3 - 8*s**2 - 18*s - 174. Factor m(d).
2*(d - 9)*(d + 1)
Solve -2*c - 383*c**4 + c**2 - 383*c**4 + 2*c**3 + 765*c**4 = 0 for c.
-1, 0, 1, 2
Let s = 29 + -12. Factor -20 + 190*l**2 - 87*l - 290*l**2 - s*l - 16*l**3.
-4*(l + 1)*(l + 5)*(4*l + 1)
Factor 11*k + 56*k**2 + 63*k + 26*k + 48 + 4*k**3.
4*(k + 1)**2*(k + 12)
Let b(r) be the third derivative of 1/168*r**8 + 0 - 1/60*r**6 + 1/6*r**3 + 26*r**2 - 1/15*r**5 + 0*r + 1/70*r**7 + 0*r**4. Find u, given that b(u) = 0.
-1, 1/2, 1
Let f(b) be the third derivative of -b**8/112 - b**7/35 - 8*b**2 + b. Factor f(r).
-3*r**4*(r + 2)
Let m(n) be the first derivative of 0*n**2 - 5/63*n**7 + 0*n**5 - 6*n + 0*n**4 + 0*n**3 - 3 - 2/45*n**6. Let j(h) be the first derivative of m(h). Factor j(k).
-2*k**4*(5*k + 2)/3
Let s = 28 - 26. Suppose s + 2 = h. Factor 0 + 2/7*c**h - 2/7*c**5 - 2/7*c**2 + 0*c + 2/7*c**3.
-2*c**2*(c - 1)**2*(c + 1)/7
Let l be (6/5 + 0/151)/(42/20). Solve 0*t**4 + 2/7*t**5 + 2/7*t + 0 - l*t**3 + 0*t**2 = 0.
-1, 0, 1
Let h(w) be the second derivative of 11*w + 2*w**2 - 1/21*w**7 + 2/5*w**6 + 8/3*w**4 - 7/5*w**5 - 3*w**3 + 0. Suppose h(l) = 0. Calculate l.
1, 2
Let v(q) be the first derivative of q**4 - 56*q**3/3 - 138*q**2 - 216*q + 169. Solve v(t) = 0 for t.
-3, -1, 18
Let c(s) be the third derivative of 0*s**3 + 0*s - 6/25*s**5 - 34*s**2 - 4/175*s**7 + 0 + 1/560*s**8 + 11/100*s**6 + 9/40*s**4. Factor c(q).
3*q*(q - 3)**2*(q - 1)**2/5
Let f(g) be the first derivative of 2*g**5/19 - 9*g**4/19 - 2*g**3/19 + 32*g**2/19 + 24*g/19 + 139. What is c in f(c) = 0?
-1, -2/5, 2, 3
Let k = -35459/13 + 2743. Factor k*c**2 + 18/13 + 120/13*c.
2*(10*c + 3)**2/13
Let r(q) = -6*q**2 - 144*q - 327. Let x(i) = -3*i**2 - 72*i - 168. Let d(h) = -4*r(h) + 7*x(h). Factor d(p).
3*(p + 2)*(p + 22)
Suppose -41*y = -24*y. Let q(c) be the second derivative of y + 7*c - 1/3*c**4 + 2*c**2 + 0*c**3. Suppose q(j) = 0. Calculate j.
-1, 1
Determine p, given that -9/5*p + 6/5*p**2 + 8/5*p**3 - 6/5*p**4 + 0 + 1/5*p**5 = 0.
-1, 0, 1, 3
Let d = 8690 - 5213999/600. Let u(v) be the third derivative of -d*v**6 + 1/300*v**5 - 2*v**2 + 0*v**3 + 1/60*v**4 + 0*v + 0. Factor u(b).
-b*(b - 2)*(b + 1)/5
Factor 1/6*p**2 + 22 - 34/3*p.
(p - 66)*(p - 2)/6
Factor -1/2*a + 1/2*a**3 + 1/2*a**2 - 1/2.
(a - 1)*(a + 1)**2/2
Let f be 18/(-15)*6/(-9)*3. Factor -f + 3/5*o**2 + 0*o.
3*(o - 2)*(o + 2)/5
Let v(x) = x**3 - 3*x**2 - 6*x + 4. Let w be v(5). Let a be (1/3 - (-22)/w)/1. Suppose 5/4*f**4 - a*f**2 + 0 - 5/2*f + 5/2*f**3 = 0. Calculate f.
-2, -1, 0, 1
Let z(d) be the third derivative of d**6/120 - 13*d**5/60 - 2*d**4 - 268*d**2. Solve z(t) = 0 for t.
-3, 0, 16
Let z(b) = -2*b + 7*b**2 - 3*b + 0*b + 3*b. Let x(p) = -3*p**2 + p. Suppose -18 = -3*n - 0*n. Let f(c) = n*z(c) + 15*x(c). Factor f(u).
-3*u*(u - 1)
Let t(u) be the third derivative of 0 + 25/1008*u**8 + 2/21*u**7 + 0*u**4 + 0*u + 1/8*u**6 + 0*u**3 - 20*u**2 + 1/18*u**5. Factor t(y).
5*y**2*(y + 1)**2*(5*y + 2)/3
Factor 0 + 0*g + 0*g**2 + 400/3*g**3 + 1/3*g**5 - 40/3*g**4.
g**3*(g - 20)**2/3
Let v be 5/(-2)*((-224)/(-75) - 3). Let a(g) be the second derivative of -2/15*g**3 + 2*g - v*g**4 + 0 - 1/5*g**2. Factor a(f).
-2*(f + 1)**2/5
Let s(d) = -4*d**3 - 44*d**2 + 224*d - 232. Let q(z) = -2. Let p(j) = 4*q(j) + s(j). Factor p(x).
-4*(x - 2)**2*(x + 15)
Determine v so that 1/4*v**3 + 8835/4*v - 187/4*v**2 - 8649/4 = 0.
1, 93
Suppose 0 = 394*i - 406*i + 24. Solve 4/11*g - 2/11*g**i - 2/11 = 0 for g.
1
Suppose 36/7*m - 2/7*m**2 - 22 = 0. What is m?
7, 11
Let h(i) be the second derivative of 2*i**2 + 0 + 1/6*i**4 - 7/10*i**5 + 7/3*i**3 - 1/5*i**6 - 24*i. Suppose h(b) = 0. What is b?
-2, -1, -1/3, 1
Factor -2/5*m**3 + 2382032/5 - 67416/5*m + 636/5*m**2.
-2*(m - 106)**3/5
Let p(g) be the first derivative of -g**3/4 + 15*g**2/8 - 3*g + 31. Factor p(r).
-3*(r - 4)*(r - 1)/4
Let a(d) be the first derivative of -4*d**5/5 + 11*d**4 - 12*d**3 - 22*d**2 + 40*d + 344. Factor a(y).
-4*(y - 10)*(y - 1)**2*(y + 1)
Let g(u) be the third derivative of u**8/20160 + u**7/1260 + u**6/180 - u**5/20 - 21*u**2. Let w(p) be the third derivative of g(p). Factor w(v).
(v + 2)**2
Let i = 44 - 42. Factor 115*y - 3*y**2 - 123*y - y**i.
-4*y*(y + 2)
Suppose 5*a + 65 = -3*k, -29 = 2*k + 4*a + 11. Let g be ((-63)/k)/(-7)*10/(-12). Find i, given that 1/2 + i**2 - g*i**3 - 5/4*i = 0.
1, 2
Let r(i) be the second derivative of -i**7/63 + 7*i**6/15 - 13*i**5/10 + 19*i**4/18 - 438*i. Factor r(p).
-2*p**2*(p - 19)*(p - 1)**2/3
Let v be (1/4)/(-8 - (9 + -19)). Let y(i) be the second derivative of -7/24*i**3 - 9*i - v*i**2 - 1/30*i**6 - 13/80*i**5 + 0 - 5/16*i**4. Solve y(k) = 0 for k.
-1, -1/4
Factor 3*y**3 + 35*y + 30*y + 36*y - 113*y.
3*y*(y - 2)*(y + 2)
Determine j, given that 2/3*j**2 - 98/3 + 32*j = 0.
-49, 1
Suppose 82*d - 71 - 158 = 17. Factor 0 + 0*f - 2/11*f**2 - 6/11*f**d - 6/11*f**4 - 2/11*f**5.
-2*f**2*(f + 1)**3/11
Factor -9/2*b**2 + 0*b + 1/4*b**4 + 3/4*b**3 + 0.
b**2*(b - 3)*(b + 6)/4
Let v(s) = 2*s**2 + 5*s + 3. Let r be 0/1 + -2 - 2. Let f(d) = 176 + d**2 - 349 + 3*d + 175. Let l(x) = r*v(x) + 7*f(x). Solve l(g) = 0 for g.
-1, 2
Let k be 0*(1 + -2)/(-1) - -2. Let f be -3*((-466)/66 + 7). Factor 2/11*h - 2/11*h**4 - f*h**3 + 0 + 2/11*h**k.
-2*h*(h - 1)*(h + 1)**2/11
Let p(h) be the second derivative of -1/24*h**4 + 0 - 4*h*