1/6*m**2 + x*m + 1 + 1/3*m**3. Determine n so that s(n) = 0.
-1, 0, 1/3, 1
Suppose 5*h - 3 = -3*f, h = 5*f + 4 - 9. Let i(b) be the second derivative of -2*b - 1/78*b**4 + 0*b**3 + h + 1/13*b**2. Find q such that i(q) = 0.
-1, 1
Let t(r) be the first derivative of 0*r - 1/4*r**4 + 1/40*r**6 + 0*r**3 + 8 + 1/20*r**5 + 6*r**2. Let q(f) be the second derivative of t(f). Solve q(m) = 0.
-2, 0, 1
Let m = 105 + -68. Let c be (-188)/(-60) - 3 - m/(-60). Factor 1/2*j**2 - c*j**3 - 1/2 + 3/4*j.
-(j - 1)*(j + 1)*(3*j - 2)/4
Let a(o) be the first derivative of -2*o**3/27 - 4*o**2/3 - 70*o/9 + 23. Factor a(n).
-2*(n + 5)*(n + 7)/9
Let y(b) = b**2 + 62*b + 915. Let v be y(-38). Factor 4/15 - 2/3*u + 4/15*u**v + 2/15*u**2.
2*(u - 1)*(u + 2)*(2*u - 1)/15
Suppose -8 + 26/3*b**2 + 2*b**3 + 16/3*b = 0. What is b?
-3, -2, 2/3
Let r(o) = -o**2 - 202*o + 10203. Let q(h) = -4*h**2 - 606*h + 30610. Let z(i) = 2*q(i) - 7*r(i). Factor z(f).
-(f - 101)**2
Let h(v) be the first derivative of 15 + 3/4*v**4 + 12*v - 1/2*v**6 + 9/5*v**5 + 0*v**2 - 7*v**3. Solve h(w) = 0 for w.
-1, 1, 2
Suppose -5*r + 2*a = -40, 35 = 4*r - r + a. Factor -19*u + 2*u - 14*u**2 - r + 8 + 8.
-(2*u + 3)*(7*u - 2)
Let z(d) be the second derivative of d**7/189 - 29*d**6/135 + 25*d**5/9 - 293*d**4/27 + 533*d**3/27 - 169*d**2/9 - 360*d. Determine w so that z(w) = 0.
1, 13
Let g = 10 - 3. Let m = 9 - g. Factor -30*j**2 - 15*j**2 + 7*j**m + 48*j + 2*j**2 - 16.
-4*(3*j - 2)**2
Suppose -42 - 39*r**2 + 3/2*r**3 - 165/2*r = 0. Calculate r.
-1, 28
Let v be (-103)/(-2)*2*6/30. Let w = 21 - v. Determine k, given that 0 + 2/5*k + w*k**2 = 0.
-1, 0
Let q be (2/(-10))/((-456)/150 + 3). Suppose -8*h + 2*p = -q*h + 4, 10 = 5*p. Solve 28/3*n**5 - 9*n**4 + 0*n + h + 2/3*n**2 - n**3 = 0 for n.
-2/7, 0, 1/4, 1
Suppose -3*s + 142 = 2*y, y - 69 = s - 3*s. Find w such that 25*w**4 - 68*w**3 - 9*w**4 - y*w + 25*w**2 + 39*w**2 + 65*w = 0.
0, 1/4, 1, 3
Let p(w) be the first derivative of 1/2*w**2 + 1/15*w**3 + 51 + 6/5*w. Find j such that p(j) = 0.
-3, -2
Let j be (32/14)/(1200/112 - 11) + 10. Factor -625/6*y**5 + 50*y**3 + 100/3*y**j - 125/3*y**4 + 16/3*y + 0.
-y*(5*y - 4)*(5*y + 2)**3/6
Let b(m) be the first derivative of -5*m**3/9 + 65*m**2/6 + 70*m/3 + 2. Factor b(z).
-5*(z - 14)*(z + 1)/3
Let v = 45223/45 + -1005. Let p = v + 74/45. Let -p + 6*s**2 + 8/5*s**3 + 24/5*s = 0. What is s?
-2, 1/4
Let p(x) be the third derivative of -4*x**7/1575 + x**6/300 + 17*x**5/450 - x**4/15 - 4*x**3/45 - 140*x**2. Suppose p(h) = 0. What is h?
-2, -1/4, 1, 2
Let j be 8 - 77/14 - -10. Suppose -j*m + 5*m**2 + 5 = 0. What is m?
1/2, 2
Let p(z) = -z**3 - 8*z**2 - 16*z + 1. Let q be p(-5). Solve -9*j**4 + 15*j + 19*j**2 + 17*j**2 - 5*j**4 - q + 3*j**3 + 2*j**4 = 0 for j.
-1, 1/4, 2
Let i(k) be the first derivative of -6/5*k**5 + 1/2*k**6 - 26 + 0*k + 8*k**3 + 0*k**2 - 3*k**4. Factor i(m).
3*m**2*(m - 2)**2*(m + 2)
Let l(h) = 9*h + 57. Let d be l(-6). Factor -54*u**2 + 18 + 44*u**2 - 3*u + 9*u + 2*u**d.
2*(u - 3)**2*(u + 1)
Let v(c) = -c**4 + c**3 - c**2 + c + 1. Let i(x) = 36*x**3 - 9*x**2 - 327*x + 429. Let j(h) = i(h) + 3*v(h). Factor j(o).
-3*(o - 12)*(o - 2)**2*(o + 3)
Let q(b) be the third derivative of 1/30*b**6 + 0*b - 1/2*b**4 + 0*b**5 - 4/3*b**3 + 53*b**2 + 0. Determine a, given that q(a) = 0.
-1, 2
Solve 6/7 + 186/7*u**2 - 46/7*u**3 - 146/7*u = 0.
1/23, 1, 3
Let u(m) be the first derivative of 2*m**5/5 - 61*m**4 + 7682*m**3/3 - 7320*m**2 + 7200*m - 194. Factor u(v).
2*(v - 60)**2*(v - 1)**2
Find n, given that 7*n**4 - 48*n**2 - 2893 + 92*n + 2845 - n**4 - n**3 - n**5 = 0.
-3, 1, 2, 4
Suppose 2*j + 40 = -5*q, 4*j - 3*q = -5*q - 80. Let n be (6/j)/((-108)/2250). Factor -n*u**2 + 5*u + 5 - 15/4*u**3.
-5*(u - 1)*(u + 2)*(3*u + 2)/4
Suppose 8*t - 15 = 3*t. Factor 2*w**3 - 35*w**2 + 0*w**4 + w**t - w**4 + 2*w + 40*w**2 - w**5.
-w*(w - 2)*(w + 1)**3
Let d(m) = m**3 - m**2 - 62*m + 140. Let h be d(7). Factor -2/11*r**2 + h*r + 0 + 3/11*r**3 + 2/11*r**4.
r**2*(r + 2)*(2*r - 1)/11
Suppose 0 = 4*i + a - 0 - 16, 2*i + 5*a + 10 = 0. Factor 6*c**4 + 2*c**5 + c**i - 3*c**4.
3*c**4*(c + 1)
Let z = 1595/6 + -30269/114. Factor 0*q + 0 + z*q**4 - 2/19*q**2 - 4/19*q**3.
2*q**2*(q - 1)*(3*q + 1)/19
Factor 7*x**4 - 7*x**2 - 4*x**5 + 3*x**5 - 18*x**3 - 5*x + 27*x**2 - 3*x.
-x*(x - 2)**3*(x - 1)
Let u(r) be the third derivative of -1/12*r**4 + 0*r + 0 - 4*r**2 - 1/360*r**6 - 1/40*r**5 + 11/6*r**3. Let a(h) be the first derivative of u(h). Factor a(w).
-(w + 1)*(w + 2)
Let q(l) = -38*l + 45. Let c be q(1). Let o(n) be the first derivative of 0*n + c + 2/7*n**2 + 6/7*n**3. Suppose o(j) = 0. What is j?
-2/9, 0
Factor 3/2*o**3 - 3456 + 3600*o - 291/2*o**2.
3*(o - 48)**2*(o - 1)/2
Let j(d) be the second derivative of 0 - 1/30*d**5 + 0*d**2 - 7*d + 5/6*d**3 + 1/4*d**4 - 1/180*d**6. Let m(s) be the second derivative of j(s). Factor m(x).
-2*(x - 1)*(x + 3)
Suppose 1734 = 705*r - 127*r. What is s in -38/3*s + 6 - 2/3*s**r + 22/3*s**2 = 0?
1, 9
Let t be 1 - ((-2256)/(-9))/(-1). Let y = t + -249. Factor -y - 10/3*w**2 - 14/3*w**3 + 32/3*w.
-2*(w - 1)*(w + 2)*(7*w - 2)/3
Let p(d) be the first derivative of -3*d**5/5 - 3*d**4/4 + 3*d**3 + 3*d**2/2 - 6*d - 305. Factor p(u).
-3*(u - 1)**2*(u + 1)*(u + 2)
Let w = -157/158 + 118/79. Find s, given that 1/4*s**2 - w*s + 0 = 0.
0, 2
Let o = -7814 - -85958/11. Factor o*m**2 + 8/11*m**3 + 5/11*m**4 + 0 + 0*m + 1/11*m**5.
m**2*(m + 1)*(m + 2)**2/11
Let g(u) = 7*u**2 - 3*u + 4. Let p be g(6). Factor p*r**3 - 3*r - 243*r**3 + 20*r**2 - 12*r.
-5*r*(r - 3)*(r - 1)
Let s(p) = -p**2 + 1. Let q(y) be the first derivative of 3*y**4 - 10*y**2 - 8*y + 14. Let f(u) = -q(u) - 16*s(u). Factor f(t).
-4*(t - 2)*(t + 1)*(3*t - 1)
Let t(h) = 30*h - 28. Let g be t(1). Let b(m) be the second derivative of 5/2*m**3 + 2*m + 0 + 3/2*m**g + m**4. Solve b(u) = 0.
-1, -1/4
Find y such that -104/5*y**2 - 16*y - 16/5*y**3 - 12/5 + 4*y**4 = 0.
-1, -1/5, 3
Let y(p) = 3*p**3 + p**2. Let w be y(-1). Let r be (-10)/(-6)*(-6)/w. Find k such that 5*k - r*k + 2*k**4 + 4*k**3 + 2*k**2 = 0.
-1, 0
Let b(y) be the third derivative of 1/630*y**7 - 2*y**2 + 0 + 1/120*y**6 + 0*y**3 + 0*y + 1/72*y**4 + 1/60*y**5. Factor b(r).
r*(r + 1)**3/3
Let k be 10/(-16)*(-116)/145. Let w(f) be the first derivative of k*f**4 + 0*f + 0*f**2 - 1 - 1/3*f**6 - 2/3*f**3 + 2/5*f**5. Determine s, given that w(s) = 0.
-1, 0, 1
Let 14*q + 84*q - 28 - 4*q**2 - 69 - 63 - 10*q = 0. Calculate q.
2, 20
Let x(i) be the first derivative of -i**3/3 - 11*i**2/2 - 30*i - 4. Solve x(g) = 0 for g.
-6, -5
Let v(p) be the third derivative of -p**8/336 - p**7/35 + p**6/60 + p**5/5 - p**4/24 - p**3 + 4*p**2 + 8. Factor v(u).
-(u - 1)**2*(u + 1)**2*(u + 6)
Let d(n) = 9*n**3 - 13*n**2 + n + 5. Let q(r) = -36*r**3 + 51*r**2 - 3*r - 21. Let h be (-14)/(-6) + 24/(-72). Let g(y) = h*q(y) + 9*d(y). Factor g(s).
3*(s - 1)**2*(3*s + 1)
Suppose 6*r = -99 + 99. Let l(d) be the second derivative of 3*d**2 - 1/4*d**4 + r + 3*d - 1/2*d**3. Suppose l(z) = 0. Calculate z.
-2, 1
Let t be (-29)/(-3) + 378/(-252). What is j in -t - 1/6*j**2 + 7/3*j = 0?
7
Let h(z) be the third derivative of z**9/15120 - z**8/2520 - 17*z**5/60 - 38*z**2. Let g(o) be the third derivative of h(o). Factor g(c).
4*c**2*(c - 2)
Let m(w) = -2*w**2 + 50*w - 6. Let d(r) = 4*r**2 - 99*r + 11. Let z(c) = 6*d(c) + 11*m(c). Suppose z(a) = 0. What is a?
0, 22
Let b(g) be the second derivative of -g**9/3024 + g**8/1680 + g**7/840 - g**6/360 + g**3/3 + g. Let a(k) be the second derivative of b(k). Solve a(r) = 0 for r.
-1, 0, 1
Let f = -147 - -152. Let v(x) be the first derivative of 0*x + 3/2*x**4 - x**3 + 4 - 3/5*x**f + 0*x**2. Solve v(a) = 0 for a.
0, 1
Let l(s) = -12*s**4 + 24*s**3 + 112*s**2 + 106*s + 26. Let r(y) = 25*y**4 - 48*y**3 - 226*y**2 - 213*y - 50. Let o(a) = 5*l(a) + 2*r(a). Solve o(t) = 0.
-1, -3/5, 5
Let j be (-1)/((-6)/(-14) - (-416)/(-448)). Factor 0 - 9/4*r + 1/4*r**3 - 2*r**j.
r*(r - 9)*(r + 1)/4
Suppose 15*y - 36 = 3*y. Factor 12*t**y - 41*t**2 + 15*t**5 + 7*t**3 + 32*t**4 + 43*t**2.
t**2*(t + 1)**2*(15*t + 2)
Factor -h**3 - 387*h**2 - 678*h - 3885*h + 270*h**2 - 59319.
-(h + 39)**3
Let -1/7*r**3 - 4/7*r**2 + 4/7 + 1/7*r = 0. What is r?
-4, -1, 1
Let n(j) be the third derivative of 1/60*j**6 + 0*j**4 + 1/840*j**8 - 1/75*j**5 + 0