*r**4 - 250 - 1275*r - 1835*r**2 + 392*r**4 + 222*r**4 = 0. Calculate r.
-1, -1/2, -2/5, 5
Factor 1616/15 + 8/15*g**2 + 6466/15*g.
2*(g + 808)*(4*g + 1)/15
Let k(d) be the second derivative of -1083/2*d**2 + 0 + 19*d**3 - 1/4*d**4 + 73*d. Find s, given that k(s) = 0.
19
Let q(a) = -6*a + 44. Let s be q(7). Suppose -s*z - 3*z = 3*z. Determine g, given that 2/7*g**2 - 2/7 + z*g = 0.
-1, 1
Let g be 39/(-52)*(110/(-15) + 7). Let j(z) be the first derivative of g*z - 1/6*z**2 - 31 + 1/36*z**3. Factor j(d).
(d - 3)*(d - 1)/12
Let t = -137 - -236. Factor -78*h**2 + 44*h**2 + 24 + 46*h**2 + t*h.
3*(h + 8)*(4*h + 1)
Let p be (-32)/(-4) - 45012/(-33). Suppose 0 = -1370*s + p*s - 4. Factor -8/5*t - 1/5*t**s + 9/5.
-(t - 1)*(t + 9)/5
Suppose -26*a + 240 = -20*a. Solve a + 25*c**2 - 27*c**2 + 18*c - 56*c = 0 for c.
-20, 1
Let s(v) be the first derivative of 1/4*v**3 - 9 + 0*v + 1/4*v**2. Factor s(h).
h*(3*h + 2)/4
Suppose -11 - 15 = -2*o. Suppose 0 = -a + o - 7. Factor -a*x**3 + 3*x**3 + 24*x - 12*x.
-3*x*(x - 2)*(x + 2)
Let g(c) = -c**3 - c**2 + c - 1. Let d(i) = 2*i**4 + 2*i**3 - 2*i + 2. Let t = -156 - -152. Let a(u) = t*g(u) - 2*d(u). Determine r, given that a(r) = 0.
-1, 0, 1
Suppose 5*y + 13 = j, j - 985*y + 987*y + 1 = 0. Let f(p) be the second derivative of 0 + 1/16*p**4 + 9/8*p**2 + 30*p + 1/2*p**j. Determine d so that f(d) = 0.
-3, -1
Let m = -198 + 178. Let j(s) = s**5 - s**4 + 2*s**2. Let x(i) = 75*i**5 + 100*i**4 + 75*i**3 + 50*i**2. Let d(v) = m*j(v) + x(v). Factor d(o).
5*o**2*(o + 1)**2*(11*o + 2)
Let r be ((-30)/(-135) - 20/9)/4*0. Determine v so that 3/5*v - 3/5*v**4 - 9/5*v**2 + 9/5*v**3 + r = 0.
0, 1
Suppose -44/5*j**4 + 4/5*j**5 + 52/5 - 8/5*j**2 + 20*j - 104/5*j**3 = 0. What is j?
-1, 1, 13
Let b be 48735/120 + (-2)/16. Factor b - 2381 + 248*s - 4*s**2 - 1869.
-4*(s - 31)**2
Solve -1/6*a**4 + 15/2*a**2 + 1/6*a**5 + 0*a - 7/2*a**3 + 0 = 0.
-5, 0, 3
Let g(t) be the second derivative of t**7/168 + 61*t**6/30 + 3025*t**5/16 + 14641*t**4/24 + 6604*t. Suppose g(q) = 0. Calculate q.
-121, -2, 0
Let q(n) be the third derivative of -n**5/12 - 625*n**4/3 - 625000*n**3/3 + n**2 - 35*n. Let q(z) = 0. Calculate z.
-500
Let x(a) be the first derivative of -4*a**3/3 - 100*a**2 - 196*a - 108. Factor x(k).
-4*(k + 1)*(k + 49)
Suppose 15*r - 44 = -2*g + 11*r, -4*r = -20. Find h, given that -g*h**3 - 83 - 6*h**3 - 202*h + 47 - 184*h**2 = 0.
-9, -1, -2/9
Let f(w) = 1536*w + 43011. Let l be f(-28). Determine x, given that 5/6*x**2 - 8 + 1/6*x**l - 4/3*x = 0.
-4, 3
Let a(n) be the first derivative of -n**3/30 + 9*n**2/5 - 162*n/5 - 1174. Factor a(y).
-(y - 18)**2/10
Let h(k) be the third derivative of k**5/12 - 4465*k**4/12 + 3987245*k**3/6 + 2336*k**2. Factor h(l).
5*(l - 893)**2
Suppose 0 = 3*z - 11 - 1. Let j(l) = -9*l + 20. Let w be j(2). Factor w*d**3 - 6*d**z + 2*d**4 - 2*d**5 + d**2 + d**2 + 2*d**4.
-2*d**2*(d - 1)*(d + 1)**2
Let o(h) = h**3 - 11*h**2 + 36*h - 5. Let v be o(7). Let p = -6 + 8. Factor 30*j - 4*j**3 - 4*j**4 + 2 - v*j + p*j**2 - j**5 + 26*j.
-(j - 1)*(j + 1)**3*(j + 2)
Let f(h) = -2*h - 57. Let a be f(-30). Let t(w) be the first derivative of 1/11*w**4 - 2/55*w**5 - 2/33*w**a + 0*w + 0*w**2 - 28. Solve t(n) = 0.
0, 1
Let j(p) be the third derivative of -p**5/30 - 11*p**4/12 + 80*p**3/3 + 4*p**2 + 250. Solve j(m) = 0 for m.
-16, 5
Let z = 47 + -33. Suppose 8*q - z*q + 18 = 0. Factor -12*w**4 - 9*w**5 - 8*w**q + 0*w**4 + 5*w**5.
-4*w**3*(w + 1)*(w + 2)
Let f(t) be the second derivative of -t**4/4 + 11*t**3 - 63*t**2/2 + 876*t. Suppose f(o) = 0. Calculate o.
1, 21
Let f(g) be the second derivative of 0 + 17/24*g**3 + 11/48*g**4 + 39*g + 3/4*g**2. Factor f(q).
(q + 1)*(11*q + 6)/4
Let a(w) = 3*w**2 - w. Let g be a(-1). Suppose 5*z - g = 16. Let 3*x**2 + 2*x**4 - 4 + z - 4*x**3 - x**4 = 0. What is x?
0, 1, 3
Suppose 376*x = -418*x. Suppose -7/4*d - 1/4*d**2 + x = 0. What is d?
-7, 0
Let p(g) be the third derivative of -26*g**5/105 - 103*g**4/84 + 2*g**3/21 + 871*g**2. Factor p(y).
-2*(y + 2)*(52*y - 1)/7
Let p(l) be the first derivative of -11*l + 6*l**2 + 81 - 1/3*l**3. Determine i so that p(i) = 0.
1, 11
Let h(v) = 3*v + 14. Let d(y) = 7*y + 25. Let s(z) = -4*d(z) + 9*h(z). Let p be s(24). Find m such that 0*m + 8/15 - 2/15*m**3 - 2/5*m**p = 0.
-2, 1
Let n be 3/((-6)/12 + (-25)/(-20)). Determine q so that 0*q**5 + 81*q - 14*q**5 - 173*q**4 + 5*q**5 + 5*q**n - 65*q**3 + 158*q**2 - 7*q**5 + 10 = 0.
-10, -1, -1/4, 1
Suppose -3*z = -4*g - 179, 4*g = -62*z + 57*z - 139. Let k = -36 - g. Factor -1/5*c**4 + 0 + 0*c**3 + 1/5*c**k + 0*c + 0*c**2.
c**4*(c - 1)/5
Let k = 645 - 642. Factor 176*c - 3958*c**3 + 3814*c**k - 194*c**2 - 46*c**2 + 968 + 396*c.
-4*(c - 2)*(6*c + 11)**2
Let c = -173 - -201. Factor 16*k - 17*k**2 - 9*k**2 + 128 + c*k**2 - 14*k + 30*k.
2*(k + 8)**2
Let m(t) be the third derivative of t**6/30 - 139*t**5/15 - 70*t**4/3 + 447*t**2. Suppose m(g) = 0. What is g?
-1, 0, 140
Let a(g) be the second derivative of g**7/21 - 333*g**6/5 + 249999*g**5/10 - 249001*g**4/6 + 4*g - 82. Solve a(f) = 0 for f.
0, 1, 499
Let z = -14505 - -29011/2. Let w(s) be the first derivative of 0*s**3 - 1/16*s**4 + z*s**2 + 0*s + 10. Factor w(u).
-u*(u - 2)*(u + 2)/4
Let n be 2/11 - 7910/(-539) - 5. Let y = -131/14 + n. Let 1/4*x**2 + y + 3/4*x = 0. What is x?
-2, -1
Find i, given that 3 - 3/2*i**2 + 161/6*i = 0.
-1/9, 18
Let t(x) be the third derivative of 3/40*x**6 - 3/8*x**4 - 1/20*x**5 + x - 14*x**2 + 1/70*x**7 + 0*x**3 + 0. Factor t(b).
3*b*(b - 1)*(b + 1)*(b + 3)
Let s(z) = -4*z - 4. Let d(x) = 3*x + 5. Let g(f) = 5*d(f) + 4*s(f). Let w be g(6). Factor -3*q**4 + 3*q**4 + 3*q**4 - 6*q - 11*q**w - q**3 + 15*q**2.
3*q*(q - 2)*(q - 1)**2
Let p = 251/906 - -84/151. Let l(f) be the second derivative of 0 + p*f**2 + 1/12*f**4 - 1/60*f**5 + 18*f + 1/2*f**3. Factor l(b).
-(b - 5)*(b + 1)**2/3
Solve 1418/5*s + 59/5*s**2 + 48/5 = 0.
-24, -2/59
Factor 32 + 0*q**4 + 22*q**2 + 7*q**3 + 31*q**2 + q**5 + 2*q**3 - 82*q + 4*q**3 - 17*q**4.
(q - 16)*(q - 1)**3*(q + 2)
Suppose 0 = -44*j + 42*j - 3*u, -6 = 3*u. Factor -4/3*m**j + 9*m + 9 + 0*m**2.
-(m - 3)*(2*m + 3)**2/3
Suppose 4*w - 2*o = 16 - 0, 4*w + 2*o = 8. Let f(z) be the first derivative of z**3 - 12 + 192*z + 10 - 34 - 24*z**2 + 0*z**w. Find g such that f(g) = 0.
8
Let m(p) be the third derivative of p**8/112 + 39*p**7/70 + 34*p**6/5 + 194*p**5/5 + 126*p**4 + 248*p**3 - 669*p**2 - 2. Determine h so that m(h) = 0.
-31, -2
Let q(t) = -2403*t + 93717. Let o be q(39). Determine c so that o + 2448/7*c**2 - 2312/7*c + 2/7*c**4 - 138/7*c**3 = 0.
0, 1, 34
Find d such that 472*d**2 + 128*d**3 + 143*d**2 - 6400 + 12*d**3 + 5*d**4 - 5920*d = 0.
-16, -1, 5
Let a(m) = -6*m**2 - 734*m + 4. Let z(t) = 4*t**2 + 727*t - 3. Let n(u) = -3*a(u) - 4*z(u). Determine s, given that n(s) = 0.
0, 353
Let d(z) be the third derivative of -z**7/840 + z**6/30 - 49*z**5/240 - 11*z**4/16 + 1119*z**2. Factor d(y).
-y*(y - 11)*(y - 6)*(y + 1)/4
Let a(h) be the first derivative of -21/10*h**4 - 6/5*h - 16/5*h**3 + 188 - 18/25*h**5 - 27/10*h**2 - 1/10*h**6. Find j, given that a(j) = 0.
-2, -1
Let p(y) be the third derivative of -5*y**2 + 1/25*y**6 - 1/350*y**7 + 3 + 0*y**4 + 0*y - 4/25*y**5 + 0*y**3. Factor p(n).
-3*n**2*(n - 4)**2/5
Let n(q) = -q**4 + q**2 - q - 1. Let u(z) = 17*z**4 - 12*z**3 - 17*z**2 + 14*z + 2. Suppose -40 = -11*c - 62. Let k(w) = c*n(w) - u(w). Solve k(l) = 0 for l.
-1, 0, 4/5, 1
Let c(z) be the second derivative of 17/6*z**3 + 1/72*z**6 + 5*z - 5/12*z**4 + 0 + 1/24*z**5 + 0*z**2. Let g(t) be the second derivative of c(t). Factor g(y).
5*(y - 1)*(y + 2)
Let q(o) be the second derivative of 49*o**5 + 2275*o**4/12 - 715*o**3/3 + 100*o**2 + 72*o - 2. Suppose q(u) = 0. Calculate u.
-20/7, 1/4, 2/7
Let a = 191/291 + 1/97. Factor -26/3*m**2 - 32*m - a*m**3 - 24.
-2*(m + 1)*(m + 6)**2/3
Let j(g) = 6*g**4 - 9*g**3 - 13*g**2 + 21*g + 15. Let l(i) = i**4 - i**2 + i. Let q(n) = j(n) - 4*l(n). Factor q(f).
(f - 5)*(f + 1)**2*(2*f - 3)
Find y such that 27/2*y**3 + 786*y + 156 + 381*y**2 = 0.
-26, -2, -2/9
Let h(b) be the second derivative of 3*b**5/220 + 59*b**4/132 - 136*b**3/33 + 142*b**2/11 + 3027*b. Let h(v) = 0. Calculate v.
-71/3, 2
Suppose -883*c + 3748 = -33*c + 87*c. Factor k**3 + 4/5*k**2 + 2/5*k**c + 0 + 1/5*k.
k*(k + 1)**2