*o**2. Let c(v) = 1. Let y(b) = 4*c(b) + t(b). Suppose y(g) = 0. What is g?
38
Suppose 0 = -4*h - 16, -4*o = -3*o + h - 8. Let x = 35 - 22. Factor x*f**3 - o*f**3 - 2*f - f**5 - 3*f**2 + 2*f**5 + 3*f**4.
f*(f - 1)*(f + 1)**2*(f + 2)
Let i(w) be the third derivative of w**5/450 + 31*w**4/15 + 371*w**3/45 - 1113*w**2. What is x in i(x) = 0?
-371, -1
Let h(i) be the third derivative of 2/35*i**7 + 8/15*i**5 - 7/30*i**6 + 17*i**2 - 1/168*i**8 - 3/4*i**4 + 2/3*i**3 + 0*i + 0. Determine m, given that h(m) = 0.
1, 2
Let k(u) be the third derivative of u**6/480 - 17*u**5/120 - 37*u**4/32 + 2*u**2 + 102*u. Suppose k(t) = 0. Calculate t.
-3, 0, 37
Let g(f) be the second derivative of 0 + 1/90*f**6 - 90*f - 2/3*f**2 + 2/9*f**3 + 1/12*f**4 - 1/15*f**5. Factor g(w).
(w - 2)**2*(w - 1)*(w + 1)/3
Suppose -1686*b - 46*b - 707*b = -4878. Factor 2/11*w + 6/11 - 8/11*w**b.
-2*(w - 1)*(4*w + 3)/11
Suppose -5*j - 12 = -7, -t = -2*j - 425. Solve -b**4 + 7*b**2 - 10 - 403*b - 2*b**3 + 22 + t*b = 0 for b.
-2, -1, 3
Determine z, given that -272*z**2 + 11560/11*z + 146/11*z**3 - 2/11*z**4 + 0 = 0.
0, 5, 34
Solve 95/6*u + 5 + 5/3*u**2 - 5/2*u**3 = 0.
-2, -1/3, 3
Solve 7243151*l**3 - 7243223*l**3 - 4*l**4 + 41*l**2 + 35*l**2 = 0 for l.
-19, 0, 1
Let p(j) = 2*j**3 - 17*j**2 - 206*j + 242. Let z(m) = m**3 + 5*m**2 + m. Let n(d) = -p(d) + 3*z(d). Factor n(a).
(a - 1)*(a + 11)*(a + 22)
Let x = -122 + 124. Suppose x = -q + 7. What is k in 5*k**4 - 5*k**2 - 3*k**3 - 11*k**5 + 33*k**q - 17*k**5 - 2*k**3 = 0?
-1, 0, 1
Let d(v) = 8*v**3 + v**2 - v + 1. Let x(m) = 435*m**3 - 10*m**2 - 170*m. Let i(y) = -55*d(y) + x(y). Let i(a) = 0. Calculate a.
-11, -1
Let i(s) = -12*s**2 + 117*s - 355. Let k(g) be the first derivative of -23*g**3/3 + 233*g**2/2 - 712*g - 38. Let h(f) = -5*i(f) + 3*k(f). Factor h(o).
-(3*o - 19)**2
Let i(n) = -3*n**3 + 24*n**2 - 55*n - 7. Let a = -841 + 855. Let j(m) = -m**3 + 8*m**2 - 18*m - 2. Let t(r) = a*j(r) - 4*i(r). Factor t(l).
-2*l*(l - 4)**2
Let y(n) be the third derivative of -2*n**2 + 13/30*n**5 + 9 + 0*n + 1/30*n**6 - 67/12*n**4 + 10*n**3. Find t, given that y(t) = 0.
-10, 1/2, 3
Suppose -7*t - 106*t**3 - 35*t - 72 + 51*t**3 - 5*t**4 + 34*t**2 + 3*t**4 + 57*t**3 = 0. Calculate t.
-4, -1, 3
Let o(n) be the first derivative of 2/7*n**2 + 2/7*n + 37 + 2/21*n**3. Determine h, given that o(h) = 0.
-1
Let f(i) be the second derivative of i**4/6 + 71*i**3/3 + 138*i**2 - 28*i - 17. Factor f(u).
2*(u + 2)*(u + 69)
Factor 0 + 38/5*b**2 + 2/5*b**3 - 184/5*b.
2*b*(b - 4)*(b + 23)/5
Suppose 2 - 4 = -m. Let -18 + 0*z**4 - 21*z + 22*z**2 + 17*z**3 + 15*z**m - 18*z**2 - z**4 + 4*z**4 = 0. Calculate z.
-3, -2/3, 1
Let x(z) be the second derivative of -z**6/20 + 49*z**5/60 - 13*z**4/3 + 8*z**3/3 + 57*z**2 + 139*z. Let o(y) be the first derivative of x(y). Factor o(n).
-(n - 4)**2*(6*n - 1)
Suppose 11*u - 9*u = -66. Let b be -1*(-6)/(-33) + (-105)/u. Factor 2*o**3 - 2*o**2 + 6*o**4 - 5*o**b - o**2.
3*o**2*(o - 1)*(2*o + 1)
Let d(f) = 1603*f + 33665. Let g be d(-21). Factor 1/3*a**3 - 2/3*a**g + 0*a + 0 + 1/3*a**4.
a**2*(a - 1)*(a + 2)/3
Let o = -461 - -489. Factor 0*y**4 - 374*y**2 + 54*y + 437*y**2 + 3*y**4 - 4*y**3 + o*y**3.
3*y*(y + 2)*(y + 3)**2
Let z(l) = -34*l**2 + 873*l + 1684. Let j(p) = -15*p**2 + 435*p + 842. Let w(u) = 9*j(u) - 4*z(u). Factor w(a).
(a + 2)*(a + 421)
Let t(y) be the second derivative of -y**7/336 + y**6/160 + y**5/10 + 2*y**4 + 9*y. Let k(n) be the third derivative of t(n). Determine x, given that k(x) = 0.
-1, 8/5
Let d(s) = s**2 + 11*s + 13. Let p be d(-9). Let a(l) = 0*l**2 + 6*l**2 - 5 + 2*l**2. Let h(n) = -15*n**2 + 10. Let v(z) = p*a(z) - 3*h(z). Factor v(x).
5*(x - 1)*(x + 1)
Let u = 337 + -349. Let h(a) = -19*a**3 + 733*a**2 - 5650*a + 1795. Let x(l) = 48*l**3 - 1832*l**2 + 14124*l - 4488. Let p(f) = u*h(f) - 5*x(f). Factor p(g).
-4*(g - 15)**2*(3*g - 1)
Let z(d) = -53*d**2 + 2334*d - 1361887. Let y(m) = -26*m**2 + 1. Let r(g) = 2*y(g) - z(g). What is v in r(v) = 0?
1167
Let g(p) be the third derivative of 1/2*p**4 - 1/80*p**5 + 0*p + 15*p**2 - 1/160*p**6 - 5/2*p**3 - 1. Factor g(t).
-3*(t - 2)**2*(t + 5)/4
Let n(j) = 45*j + 98. Let q be n(-2). Suppose x = -4*w + 12, -4*w - 4 = 3*x - q. Find f such that -10*f**w - 5*f**2 + 0*f + 0 + 5/2*f**5 + 25/2*f**3 = 0.
0, 1, 2
Let n(k) be the first derivative of 256*k - 180*k**3 + 88/5*k**5 + 32*k**2 + 157 - k**6 - 127/2*k**4. Solve n(l) = 0 for l.
-1, 2/3, 8
Factor 0 - 4/5*s**3 - 4256/5*s**2 - 1132096/5*s.
-4*s*(s + 532)**2/5
Let i(b) = -92*b + 567. Let c be i(6). Let o be ((-1)/c)/((-10)/(-10 - -40)). What is d in 0 + 1/5*d**3 + 0*d + 1/5*d**2 - o*d**5 - 1/5*d**4 = 0?
-1, 0, 1
Let a(x) be the second derivative of -x**4/6 + 33*x**3 - 194*x**2 - 700*x. Factor a(k).
-2*(k - 97)*(k - 2)
Let v(b) be the first derivative of 1/4*b**4 + 12*b + 2*b**2 - 12 - 7/3*b**3. Let v(l) = 0. Calculate l.
-1, 2, 6
Suppose -2/9*k**3 + 46/9*k**2 - 2/9*k**4 - 26/3*k + 4 = 0. What is k?
-6, 1, 3
Let f(o) be the second derivative of o**5/15 + 4*o**4/3 - 98*o**3/9 - 40*o**2 + o - 229. Factor f(y).
4*(y - 4)*(y + 1)*(y + 15)/3
Let b(f) be the first derivative of f**6/12 + 23*f**5/10 + 51*f**4/8 - 69*f**3/2 - 135*f**2 - 899. Let b(i) = 0. Calculate i.
-20, -3, 0, 3
Factor 18374*o**3 + 61*o - 76 - 8*o**2 + 24*o**2 - 36744*o**3 + 18369*o**3.
-(o - 19)*(o - 1)*(o + 4)
Suppose 3*q - 32 = -3*o + o, 4*o = q - 34. Suppose 2*g + 2*d = -6, -q*g + 12*g + 9 = -d. Factor -4/9*w**3 + 0*w**g + 0 + 0*w**4 + 2/9*w**5 + 2/9*w.
2*w*(w - 1)**2*(w + 1)**2/9
Let y = -522413/3 + 174223. Solve -224/3*r + y - 31/3*r**2 - 1/3*r**3 = 0 for r.
-16, 1
Let n(v) be the second derivative of v**4/3 - 670*v**3 + 2008*v**2 - 13573*v. What is b in n(b) = 0?
1, 1004
Let u(g) be the first derivative of g**5/15 + 5*g**4/2 - 31*g**3/9 - 97. Solve u(f) = 0 for f.
-31, 0, 1
Let d(v) be the third derivative of 1/840*v**6 + 4/21*v**3 - 1/84*v**5 + v + 1/84*v**4 + 3*v**2 + 0. Find k, given that d(k) = 0.
-1, 2, 4
Let x = 127 - 120. Let b(h) = -9*h**2 - 59*h - 54. Let o(f) = 17*f**2 + 117*f + 107. Let j(u) = x*b(u) + 4*o(u). Find y such that j(y) = 0.
-10, -1
Let g(n) be the first derivative of -n**6/6 - 5*n**5 - 99*n**4/4 + 25*n**3/3 + 50*n**2 + 2019. Suppose g(w) = 0. Calculate w.
-20, -5, -1, 0, 1
Let b(a) = 4*a**3 - a**2 + 2*a - 1. Let w be b(1). Let n(f) = 5*f**2 - 17*f + 16. Let g be n(1). Factor 9*t**2 - 7*t**w + 7*t**2 + 3*t**3 - 4*t - 9*t**g + t**3.
-4*t*(t - 1)*(t + 1)*(4*t - 1)
Let n(d) be the third derivative of 0*d - 1/12*d**3 + 1/24*d**4 - 1/160*d**5 + 15*d**2 + 0 - 1/480*d**6 + 1/1680*d**7. Let n(u) = 0. Calculate u.
-2, 1, 2
Let c(a) = -17*a**4 + 33*a**3 - 23*a**2 - 8*a. Let h(u) = -2*u**4 - u**2. Let g(r) = -2*c(r) + 10*h(r). Factor g(k).
2*k*(k - 4)*(k - 1)*(7*k + 2)
Suppose 8 = 2*v - 4. Let w be ((-12)/v)/((-4)/82). What is o in w*o**3 + 32*o**3 + 20*o**2 - 78*o**3 - 15*o = 0?
0, 1, 3
Let t(d) be the second derivative of -d**4/72 + 15*d**3/4 + 34*d**2/3 - d - 339. Factor t(a).
-(a - 136)*(a + 1)/6
Let o(x) be the second derivative of -5*x**4/48 + 85*x**3/24 - 75*x**2/2 + 101*x - 6. Factor o(k).
-5*(k - 12)*(k - 5)/4
Factor 0 + 107*y**2 + 0*y + 1/8*y**3.
y**2*(y + 856)/8
Let z(v) be the first derivative of v**5/40 - v**4/12 - v**3/12 + v**2/2 - 9*v + 47. Let f(x) be the first derivative of z(x). Factor f(m).
(m - 2)*(m - 1)*(m + 1)/2
Suppose -5*u + 2*t + 21 = 0, 0 = -2*t - 3 + 7. Suppose -j = 5*y - 4*y - 2, 4*j = u*y + 35. Factor 0*s - 6/7*s**2 + 6/7*s**4 + 0 - 6/7*s**3 + 6/7*s**j.
6*s**2*(s - 1)*(s + 1)**2/7
Let j = 66251/55 + -6021/5. Let c(p) be the first derivative of 6/11*p + j*p**2 - 1 + 2/33*p**3. Factor c(a).
2*(a + 1)*(a + 3)/11
Let s(h) = -h**2 - 6*h + 29. Let a be s(-9). Factor 12*j**4 - 36*j + 11*j**a - 47*j**2 + 15*j**2 + 45*j**3.
3*j*(j - 1)*(j + 4)*(4*j + 3)
Suppose -13*j + 31*j + 22 = 29*j. Determine h, given that 3/2*h**3 + 3*h + 13/4*h**j + 1 + 1/4*h**4 = 0.
-2, -1
Let t(q) be the first derivative of -q**6/40 + 53*q**5/240 + 17*q**4/48 + 5*q**3/24 - 167*q**2/2 + 14. Let j(u) be the second derivative of t(u). Factor j(h).
-(h - 5)*(3*h + 1)*(4*h + 1)/4
Suppose -100 = -23*q - 2*q. Solve -3*o**2 + 14*o + q*o**2 - o**2 + 0*o**2 - 2*o**2 = 0.
0, 7
Let w = -192 + 273. Let g = w + -81. Factor 2/5*b**3 + 0 + 0*b**2 + g*b.
2*b**3/5
L