*(n + 2)/7
Let b(n) be the second derivative of 3*n**5/100 - n**4/60 - 7*n. Determine k so that b(k) = 0.
0, 1/3
Let w be 4/2 + 0 - -2. Let 6*m**w + 3*m - 4*m**4 - 7*m - 6*m**2 = 0. What is m?
-1, 0, 2
Let g = 281/133 - 27/95. Let o = g + -10/7. Factor 8/5*s**2 + o*s + 8/5*s**4 + 0 + 12/5*s**3 + 2/5*s**5.
2*s*(s + 1)**4/5
Factor 0 + 0*v + 4/15*v**2 - 2/15*v**3.
-2*v**2*(v - 2)/15
Suppose -3*j + 4*j + 3*c = 6, 2*j = 3*c + 3. Let h = j - -1. Find a, given that h*a - 5*a**2 + 11*a**2 - 4 + 4 = 0.
-2/3, 0
Suppose -69 + 537 = 3*q. Let o = 1718/11 - q. Factor -o*g**4 + 0*g**3 + 0 + 2/11*g**2 + 0*g.
-2*g**2*(g - 1)*(g + 1)/11
Suppose 1 = 4*y - 7. Let p(a) = -a + 11. Let z be p(9). Factor -2*d**2 + 4*d + 2 - y - z.
-2*(d - 1)**2
Let m(n) be the second derivative of n**4/36 + n**3/18 + 6*n. Factor m(j).
j*(j + 1)/3
Let i(x) be the third derivative of x**8/1344 - x**7/420 + x**6/480 - 2*x**2. What is s in i(s) = 0?
0, 1
Let n(q) be the second derivative of 1/2*q**2 + 0 - 4/5*q**5 - 32/15*q**6 - 11/6*q**3 - 4*q + 3*q**4. Factor n(c).
-(c + 1)*(4*c - 1)**3
Let f(u) be the second derivative of -u**6/105 + 3*u**5/35 - 13*u**4/42 + 4*u**3/7 - 4*u**2/7 - 8*u. Factor f(q).
-2*(q - 2)**2*(q - 1)**2/7
Let y(n) be the second derivative of -n**6/50 + n**4/10 - 3*n**2/10 + 13*n. Let y(q) = 0. Calculate q.
-1, 1
Let a = 2/59 + 23/1062. Let x(y) be the second derivative of 0 + a*y**4 - 2/3*y**2 + 3*y - 1/9*y**3. Suppose x(l) = 0. Calculate l.
-1, 2
Let f = 7 + 1. Suppose 0 = 7*u - 3*u - f. Let 3 - 3 - u*b**2 = 0. Calculate b.
0
Let d(s) = s**3 + s**2 - s + 1. Let w(x) = 12*x**3 + 10*x**2 - 16*x + 8. Let y(r) = 22*d(r) - 2*w(r). Factor y(t).
-2*(t - 3)*(t + 1)**2
What is i in -16*i**2 - 16*i - 8*i**5 + 12*i**3 + 4*i**5 + 23*i**4 + 8*i**5 - 7*i**4 = 0?
-2, -1, 0, 1
Determine f, given that -5*f + 2 + 18*f + 2 - 1 + 4*f**2 = 0.
-3, -1/4
Let w(a) be the third derivative of a**8/24 + 4*a**7/35 - a**6/15 - 7*a**5/15 - a**4/4 + 2*a**3/3 - 30*a**2. Solve w(i) = 0.
-1, 2/7, 1
Let s(d) be the second derivative of -d**4/3 - 8*d. Determine p so that s(p) = 0.
0
Let v(k) be the first derivative of 0*k + 0*k**2 + 0*k**3 + 2/25*k**5 + 1/10*k**4 - 8. Factor v(j).
2*j**3*(j + 1)/5
Let n(v) be the first derivative of 0*v + 0*v**2 + 0*v**4 - 1/24*v**6 + 0*v**3 + 2 + 1/20*v**5. Suppose n(k) = 0. What is k?
0, 1
Suppose -3*i + 20 = i, 0 = -p + i + 33. Factor 0*d + p*d**5 + 8*d**5 + 60*d**3 + 112*d**4 + d + 13*d**2 + 18*d**5.
d*(d + 1)*(4*d + 1)**3
Let k = 330/7 + -3560/77. Factor k*w - 8/11 - 2/11*w**2.
-2*(w - 4)*(w - 1)/11
Let x(d) be the first derivative of -d**7/1050 + d**6/300 - d**4/60 + 2*d**3/3 + 3. Let c(q) be the third derivative of x(q). Suppose c(o) = 0. Calculate o.
-1/2, 1
Let k(u) be the second derivative of u**5/50 - 2*u**4/15 + u**3/3 - 2*u**2/5 + 8*u. Determine n so that k(n) = 0.
1, 2
Suppose 10 - 25 = -5*r. Solve -26*k**2 - 64*k**3 + 21*k**5 - 8*k + 6*k**3 - 21*k**2 - k**4 + r*k**2 = 0 for k.
-1, -2/3, -2/7, 0, 2
Let f(z) be the second derivative of -5*z**6/6 - 2*z**5 - 5*z**4/12 + 5*z**3/3 + 24*z. Factor f(d).
-5*d*(d + 1)**2*(5*d - 2)
Suppose 1 = -2*j + 5. Factor 0*l - l + 2*l**4 + 2*l**2 - 4*l**j + l**5.
l*(l - 1)*(l + 1)**3
Let i(v) = -v**2 - 11*v - 7. Let z be i(-10). Determine q so that 9*q**z - 6*q**3 - q**5 + 2*q**4 - q**3 - 3*q**3 = 0.
0, 1
Let s(r) = -25*r**2 + 14. Let f(x) = -5*x**2 + 3. Let b(l) = 11*f(l) - 2*s(l). Factor b(y).
-5*(y - 1)*(y + 1)
Let d(x) be the second derivative of -1/33*x**3 + 0*x**2 + 0 + 1/66*x**4 - 4*x. Factor d(c).
2*c*(c - 1)/11
Let z = -43 - -70. Suppose -4*n + 6*n - 5*u - z = 0, 3*n + 5*u + 22 = 0. What is c in 0 - c**2 + 2 - n = 0?
-1, 1
Suppose 10*i + 50 = 90. Determine q, given that 0*q + 0 + 1/2*q**i - 1/2*q**3 - q**2 = 0.
-1, 0, 2
Let t(g) be the first derivative of -g**6/180 + g**5/15 - g**4/3 - g**3 - 5. Let p(y) be the third derivative of t(y). Factor p(q).
-2*(q - 2)**2
Let p(g) be the third derivative of g**8/120 - g**7/105 - g**6/150 + 8*g**2. Factor p(f).
2*f**3*(f - 1)*(7*f + 2)/5
Let x be (-2)/10 + 847/35. Let c be 1/3 - (-4)/x. Factor 1 + c*m**4 + 5/2*m**3 + 9/2*m**2 + 7/2*m.
(m + 1)**3*(m + 2)/2
Let c(j) = -9*j**2 + j. Let a(u) = 3*u**2 + 6*u. Let p(k) = -7*k**2 - 11*k. Let t(w) = 11*a(w) + 6*p(w). Let r(m) = -3*c(m) + 2*t(m). Let r(f) = 0. What is f?
0, 1/3
Let t(u) = -u**3 + 6*u**2 - 3*u - 7. Suppose -2*b = 2*l - 5*b - 22, -4*b = 16. Let v be t(l). Factor -4*c + 6*c**4 + 4*c**2 - 10*c**v + 4*c.
2*c**2*(c - 1)*(3*c - 2)
Let u(t) = 3*t**3 + t**2 - 5. Let a(b) = 2*b**3 - 4. Let z(n) = -4*a(n) + 3*u(n). Let f(j) be the first derivative of z(j). Let f(m) = 0. What is m?
-2, 0
Let f = 43/11970 - 1/2394. Let t(b) be the third derivative of 0*b**3 - f*b**7 + 0 + 0*b**4 + 0*b**5 - 1/1008*b**8 + 0*b - 1/360*b**6 + 2*b**2. Factor t(u).
-u**3*(u + 1)**2/3
Let c(z) be the second derivative of 3*z - z**2 + 11/6*z**3 - 1/5*z**5 - 7/6*z**4 + 0 - 1/6*z**7 + 8/15*z**6. Suppose c(s) = 0. What is s?
-1, 2/7, 1
Let b(s) be the second derivative of -s**4/16 - s**3/4 + 9*s**2/8 - 12*s. Suppose b(x) = 0. Calculate x.
-3, 1
Find h such that 3/5*h + 9/5*h**3 + 0 - 9/5*h**2 - 3/5*h**4 = 0.
0, 1
Let z(n) = -13*n**4 - 2*n**3 + 2*n**2 + 2*n + 11. Let j = -17 + 11. Let x(u) = -7*u**4 - u**3 + u**2 + u + 6. Let r(d) = j*z(d) + 11*x(d). Solve r(o) = 0.
-1, 0, 1
Let t be (-760)/(-6)*(-12)/8. Let x = t + 956/5. Suppose -x*c**2 - 1/5*c**4 - 4/5*c - 1/5 - 4/5*c**3 = 0. What is c?
-1
Let l = -10/21 - -4/3. Determine c so that -2/7 - l*c**2 + 2/7*c**3 + 6/7*c = 0.
1
Let c(x) be the third derivative of -x**6/24 + x**5/12 + 37*x**2. Suppose c(z) = 0. Calculate z.
0, 1
Let x = -32 + 37. Let o(f) be the third derivative of -1/24*f**3 + 0*f + 0 - 1/96*f**4 + 1/480*f**6 + 1/240*f**x - 3*f**2. Let o(t) = 0. What is t?
-1, 1
Find h such that 10/9*h - 2/9*h**2 - 2/3 - 2/9*h**3 = 0.
-3, 1
Let x(s) be the first derivative of -15*s**4/16 + 3*s**3 - 3*s**2/2 - 42. Determine u so that x(u) = 0.
0, 2/5, 2
Let q(u) be the first derivative of -u**4/18 - u**3/9 - 6*u - 3. Let h(k) be the first derivative of q(k). Find d, given that h(d) = 0.
-1, 0
Let t(x) be the second derivative of x**5/5 + x**4 - 29*x. Determine r, given that t(r) = 0.
-3, 0
Let x be 6/(-21) + (-64)/266. Let v = x - -146/133. Factor 0*l**2 - 4/7*l + v*l**3 + 2/7*l**4 - 2/7.
2*(l - 1)*(l + 1)**3/7
Let h(r) = -2*r**2 + 9. Suppose -4*j = -0*j - 3*n - 19, 3*n - 30 = -3*j. Let f(k) = k**2 - 6. Let u(b) = j*f(b) + 5*h(b). Factor u(l).
-3*(l - 1)*(l + 1)
Let z(i) be the first derivative of 2*i**5/35 - 4*i**3/21 + 2*i/7 - 2. What is p in z(p) = 0?
-1, 1
Factor -6*o - 5*o**2 + 0*o - 26 + 6 - 14*o.
-5*(o + 2)**2
Factor 12/5 + 2/5*m - 2/5*m**2.
-2*(m - 3)*(m + 2)/5
Suppose -5 = -2*n + 4*y - 17, -2*y + 10 = -3*n. Let t be -10*(-1)/(-5)*n. Factor 3*w**3 + 0 + w + t*w**2 + 0.
w*(w + 1)*(3*w + 1)
Let p(b) be the second derivative of -b**4/102 - 4*b**3/17 - 11*b**2/17 - 25*b. Determine o, given that p(o) = 0.
-11, -1
Let a = 4/19 - 13/152. Let h(x) be the second derivative of -1/48*x**4 + 0*x**3 + a*x**2 + 0 - x. Factor h(n).
-(n - 1)*(n + 1)/4
Let a = 3 + -1. Suppose -3*d - d = -4*g, 0 = 5*d - 2*g. Determine o so that d - 5/2*o**a - o + 7/2*o**3 = 0.
-2/7, 0, 1
Let q(a) be the first derivative of -84*a**5/5 + 171*a**4/4 - 28*a**3 - 9*a**2/2 + 6*a - 8. What is w in q(w) = 0?
-1/4, 2/7, 1
Let s be (-63)/(-12) + 10/(-8). Determine b, given that -2/3*b - 2/3*b**s - 2/3*b**5 - 2/3 + 4/3*b**3 + 4/3*b**2 = 0.
-1, 1
Let v = 921796 - 904281664/981. Let c = v + 2/327. Factor c*r**3 + 0 - 2/9*r**2 + 0*r.
2*r**2*(r - 1)/9
Let t(o) = -5*o**3 - 14*o**2 + 11*o + 8. Let d(y) = -3*y**3 - 9*y**2 + 7*y + 5. Let k(s) = -8*d(s) + 5*t(s). Solve k(w) = 0.
0, 1
Factor -1/4*m - 1/4*m**3 + 1/2*m**2 + 0.
-m*(m - 1)**2/4
Let k = -25 + 481/19. Let f = k - -7/38. Factor -1/2*r**3 + 1/2 + 1/2*r - f*r**2.
-(r - 1)*(r + 1)**2/2
Let p(s) be the second derivative of -3*s**5/140 + s**4/7 - 3*s**3/14 + 38*s. Factor p(v).
-3*v*(v - 3)*(v - 1)/7
Let i = 132 - 130. Factor 0 - 3/2*t + 3/4*t**i + 9/4*t**3.
3*t*(t + 1)*(3*t - 2)/4
Let k(o) be the second derivative of o**7/3360 - o**6/480 + o**5/160 + 7*o**4/12 + 3*o. Let x(z) be the third derivative of k(z). Factor x(j).
3*(j - 1)**2/4
Suppose 115 = -3*d - 4*b, 2*b = b + 5. Let u be (15/(-10))/(d/12). 