 3
Let p(l) = 3*l - 15. Let y be p(8). Suppose 8*u + 3 = y*u. Find j such that 3/7*j**5 - 3/7 - 6/7*j**u - 3/7*j**4 + 6/7*j**2 + 3/7*j = 0.
-1, 1
Let u(k) be the second derivative of k**6/1980 - 2*k**3 - 3*k. Let h(s) be the second derivative of u(s). Factor h(q).
2*q**2/11
Let g(q) = q**3 + 33*q**2 + 58*q - 3. Let x be g(-31). Let v = x + -119. Factor 12/5*j + 8/5 + 4/5*j**v.
4*(j + 1)*(j + 2)/5
Factor -8 - 15/2*b + 1/2*b**2.
(b - 16)*(b + 1)/2
Let n be (0 + (-2)/(-5))*2120/212. Factor -1/7*z**3 - 4/7 - 9/7*z**2 - 11/7*z + 1/7*z**n.
(z - 4)*(z + 1)**3/7
Let a be (675/(-6))/((-9)/12). Suppose 0*h - a = -5*k - 2*h, -5*h = -5*k + 150. Find s, given that -6*s**2 - 15 - 48*s - 1 - k*s**2 = 0.
-2/3
Let s(z) be the first derivative of 5 + 0*z - 2*z**4 + 20/3*z**3 - 4*z**2. Factor s(y).
-4*y*(y - 2)*(2*y - 1)
Let d(r) be the first derivative of -4/9*r + 4/27*r**3 + 1 - 1/9*r**2 + 1/18*r**4. Suppose d(k) = 0. Calculate k.
-2, -1, 1
Let s(j) be the second derivative of -j**4/16 - j**3/8 + 3*j**2/4 - 58*j. Factor s(n).
-3*(n - 1)*(n + 2)/4
Let o = 59 + -64. Let a(h) = 12*h**2 - 4. Let p(v) = -8*v**2 + 3. Let y(f) = o*a(f) - 8*p(f). Suppose y(g) = 0. Calculate g.
-1, 1
Let v(u) be the third derivative of u**8/462 + 41*u**7/1155 + 23*u**6/110 + 92*u**5/165 + 49*u**4/66 + 5*u**3/11 - 161*u**2 - 2*u. Find b, given that v(b) = 0.
-5, -3, -1, -1/4
Let z(p) be the third derivative of p**6/220 - 49*p**5/110 + 46*p**4/11 - 180*p**3/11 - 332*p**2. Factor z(l).
6*(l - 45)*(l - 2)**2/11
Suppose 5*i - 46 - 59 = 0. Factor 19 + p**3 + 29 - i*p**2 + 24*p + p**3 + p**3.
3*(p - 4)**2*(p + 1)
Let j(n) = 11*n**2 - 166*n + 17. Let q be j(15). Factor 3/5*t**q + 0*t - 3/5*t**4 + 0*t**3 + 0.
-3*t**2*(t - 1)*(t + 1)/5
Suppose 0 - 10/7*q**2 + 18/7*q**4 - 51/7*q**3 + 3/7*q = 0. What is q?
-1/3, 0, 1/6, 3
Let g(h) be the second derivative of 0 + 0*h**2 - 1/14*h**7 - 1/5*h**6 + 1/2*h**4 + 0*h**5 + 1/2*h**3 - 4*h. Factor g(b).
-3*b*(b - 1)*(b + 1)**3
Let d(r) be the third derivative of 5/3*r**3 + 0*r + 1/4*r**5 - 5*r**2 + 1/36*r**6 + 1 - 85/72*r**4. Factor d(m).
5*(m - 1)*(m + 6)*(2*m - 1)/3
Let z(n) be the third derivative of 9/8*n**4 - 10*n**2 - 9/40*n**6 + 1/10*n**5 + 0 + 0*n - 2/35*n**7 + n**3. Determine g, given that z(g) = 0.
-2, -1, -1/4, 1
Let w(c) be the third derivative of -1/4*c**4 + 1/168*c**8 + 0*c**7 + 3*c**2 - 1/10*c**6 - 4/15*c**5 + 0*c + 0 + 0*c**3. Factor w(u).
2*u*(u - 3)*(u + 1)**3
Let a be (24/20)/((-4)/(-10)). Let t be (-76)/(-10) + (-48)/80. Factor -t*h + h - 4*h**2 + a*h - 5*h - 4.
-4*(h + 1)**2
Let n(c) be the third derivative of -2*c**7/105 - 7*c**6/30 + 2*c**5 - 88*c**2. Factor n(y).
-4*y**2*(y - 3)*(y + 10)
Let t(o) be the third derivative of -o**6/600 + 3*o**5/50 - 47*o**4/120 + o**3 + 121*o**2. Factor t(g).
-(g - 15)*(g - 2)*(g - 1)/5
Let q be -1 - (-37)/(3885/126). Factor -4/5*d + q*d**2 - 12/5.
(d - 6)*(d + 2)/5
Suppose -10 = -7*g + 2*g. Solve -11*w + 4 + 4*w**g - 4*w**2 - 3*w + 6*w**2 = 0.
1/3, 2
Let v = -1294/5 - -260. Suppose 0 + v*w - 3/5*w**4 - 9/5*w**3 + 3/5*w**2 + 3/5*w**5 = 0. What is w?
-1, 0, 1, 2
Let n(p) be the second derivative of -2*p**7/21 + 2*p**6/15 + p**5/5 - p**4/3 - 2*p - 18. Find t, given that n(t) = 0.
-1, 0, 1
Factor 0*q**2 + 0*q + 0 + 2/3*q**4 + 22/3*q**3.
2*q**3*(q + 11)/3
Determine w so that -6*w**3 - 2492*w**2 + 2530*w**2 + 4*w**3 = 0.
0, 19
Let f = -19 - -21. What is i in 12 + i**3 - 5*i**3 + 0*i**3 + 7*i**2 + 20*i - 3*i**f = 0?
-1, 3
Let p(w) be the third derivative of w**7/105 - w**6/60 - w**5/15 - 61*w**2. Let p(h) = 0. What is h?
-1, 0, 2
Let v(z) = -7*z**2 - z - 9. Let i(q) = 6*q**2 + 8. Let h(a) = 6*i(a) + 5*v(a). Let r be h(5). Factor -33 - 27*g**2 + 81*g + 2*g**3 + g**3 - r - 45.
3*(g - 3)**3
Let d(y) be the first derivative of -2*y**6/3 + 29*y**5/5 - 79*y**4/4 + 98*y**3/3 - 26*y**2 + 8*y + 104. Determine v, given that d(v) = 0.
1/4, 1, 2
Let w be (6 + 220/(-35))*-77. Suppose -4*p = -5*b - 10, -3*p + w - 7 = 0. Factor -b*s**4 + 22/9*s**2 - 4/9*s + 0 - 8/3*s**3.
-2*s*(s + 2)*(3*s - 1)**2/9
Let j = 4122 - 4118. Find n such that 4*n**3 + 1 - 7/4*n**4 - j*n + 3/4*n**2 = 0.
-1, 2/7, 1, 2
Let g(q) be the second derivative of 0*q**3 + 1/16*q**4 + 0*q**2 - 25*q - 3/40*q**5 + 0 + 1/40*q**6. Find x, given that g(x) = 0.
0, 1
Let g(k) be the second derivative of -1/91*k**7 + 0*k**2 + 2*k + 0*k**3 - 2/195*k**6 + 5 + 1/39*k**4 + 3/130*k**5. Solve g(i) = 0 for i.
-1, -2/3, 0, 1
Let b(n) be the third derivative of 0 - 14*n**2 + 0*n - 5/12*n**4 + 1/30*n**5 + n**3 + 1/60*n**6. Find s, given that b(s) = 0.
-3, 1
Suppose -38*k + 34 + 80 = 0. Let r(o) be the first derivative of 9/10*o**2 + 0*o + k - 1/5*o**3. Determine d, given that r(d) = 0.
0, 3
Let 288 + 20*g**2 - 2*g**2 - 7*g**2 - 15*g**2 + 284*g = 0. What is g?
-1, 72
Let v = 2212/5 + -442. Let h(w) be the first derivative of 2 - 14/15*w**3 + v*w**2 + 0*w. Let h(y) = 0. What is y?
0, 2/7
Let y(n) be the second derivative of n**6/180 - 7*n**5/60 + 61*n**4/72 - 7*n**3/3 + 3*n**2 + 265*n + 1. Factor y(m).
(m - 6)**2*(m - 1)**2/6
Let t = -6 - -27. Suppose 3*l = 5*f + 24, -5*l + t = -l - 3*f. Factor -b + b**2 + 0*b**3 - b**l + 1 - 2 + 2*b.
-(b - 1)**2*(b + 1)
Suppose -3*q = -11 - 1. Suppose -5 = -q*b + 3. Factor -2*u**5 + 4*u**5 + b*u**4 + 4*u**2 - 4*u**2.
2*u**4*(u + 1)
Let h(m) be the first derivative of 8/55*m**5 + 0*m - 5/22*m**4 + 0*m**2 - 1/33*m**6 + 4/33*m**3 - 5. Factor h(a).
-2*a**2*(a - 2)*(a - 1)**2/11
Let o(m) be the second derivative of -2*m**2 + 0 - 1/3*m**4 - 2/5*m**5 + 4/15*m**6 + 3*m + 5/3*m**3 - 1/21*m**7. Let o(j) = 0. What is j?
-1, 1, 2
Let k(u) be the second derivative of u**9/7560 - u**7/1260 + 17*u**4/12 - 10*u. Let a(x) be the third derivative of k(x). Factor a(t).
2*t**2*(t - 1)*(t + 1)
Let o = 14 + -14. Suppose o = -0*t + 9*t - 27. Factor 0 + 1/5*j**4 + 0*j + 1/5*j**5 + 3/5*j**2 - j**t.
j**2*(j - 1)**2*(j + 3)/5
Let o(j) be the first derivative of -4/9*j**3 - 1/12*j**4 - 13 - 7/12*j**2 + 1/36*j**6 - 1/3*j + 1/15*j**5. Factor o(l).
(l - 2)*(l + 1)**4/6
Let d be (-3)/(-5 + 6/(-4) - 7). Solve -2/9*m + 0 + d*m**2 = 0.
0, 1
Let t = -7019/3 + 2340. Factor t*g + 1/3*g**2 - 1/3*g**4 + 0 - 1/3*g**3.
-g*(g - 1)*(g + 1)**2/3
Let t(o) = -2*o**3 + 2*o**2 + 1. Let p(j) = -7*j**3 + 7*j**2 - 5*j + 11. Let s(d) = -p(d) + 6*t(d). Suppose s(u) = 0. What is u?
-1, 1
Suppose -11 = -6*n + 13. Find r, given that 7*r**3 + 33*r**n + 16*r**4 + 4*r**2 + 13*r**3 - 33*r**4 = 0.
-1, -1/4, 0
Determine y, given that -24*y**3 - 309*y + 4 + 333*y - 20*y**4 + 23*y**2 - 7*y**2 = 0.
-1, -1/5, 1
Let i(w) be the third derivative of w**7/1995 - w**6/380 + w**5/190 - w**4/228 - 555*w**2. Factor i(q).
2*q*(q - 1)**3/19
Suppose 3*a - 3 = 2*k + 2, -3*a = -4*k - 1. Factor k*c + 21*c**2 - 20*c**2 - c**3 - 2*c.
-c**2*(c - 1)
Let s(m) be the first derivative of m**6/12 + m**5/2 + 3*m**4/4 - m**3/3 - 7*m**2/4 - 3*m/2 - 38. Let s(x) = 0. What is x?
-3, -1, 1
Suppose 2/15*v**4 + 28/15*v**3 + 76/5*v + 42/5 + 128/15*v**2 = 0. What is v?
-7, -3, -1
Let m be (-8)/20 + (-27)/(-5). Let h be (1 - -3) + ((-372)/48)/(-31)*0. Suppose -6/11*l**h + 0 - 4/11*l + 2/11*l**m + 2/11*l**3 + 6/11*l**2 = 0. What is l?
-1, 0, 1, 2
Let i = -138 + -22. Let k = i - -241. Factor -k - 2*h**2 + 81.
-2*h**2
Suppose -4*a + 58 = -34. Suppose 2*k**2 - a - k**2 - 27 - 4*k + 54 = 0. Calculate k.
2
Let a = -32 - -40. Suppose 5*z**3 + 4 - 15*z**4 + 5*z**5 + 7*z**2 - 10*z - 4 + a*z**2 = 0. Calculate z.
-1, 0, 1, 2
Let u(b) = 2 + 5*b**2 + 4*b + 4*b**3 + 6*b**3 - 5*b**3 - 4*b**3. Let j be u(-4). Factor 4/5*n + 2/5*n**j + 0.
2*n*(n + 2)/5
Let p be (-4)/3*(-6)/4. Suppose -p*i = 2 - 6. Let 3*k**i + 2*k - 3*k + 2*k - 4*k**2 = 0. What is k?
0, 1
Let y(a) = 6*a**3 + 2*a**2 + 10*a. Suppose 5*f = 4*l - 23, -11*f + 7*f = 4*l + 40. Let d(w) = 5*w**3 + 2*w**2 + 9*w. Let b(q) = f*d(q) + 6*y(q). Factor b(v).
v*(v - 3)*(v + 1)
Suppose -2*o = -d + 2*o, -3*o = 3*d - 30. Find m such that -71*m**2 + 38*m**2 + d*m + 31*m**2 + 2*m = 0.
0, 5
Let o(a) be the first derivative of -5*a**4/4 + 40*a**3/3 - 105*a**2/2 + 90*a + 86. What is c in o(c) = 0?
2, 3
Let h(a) be the second derivative of a**7/56 - a**6/40 - 9*a**5/80 + 5*a**4/16 - a**3/4 - 359*a. Factor h(t).
3*t*(t - 1)**3*(t + 2)/4
Let f(a) be the third derivative of -a**7/1260 + a**6/144 - a**5/40 + 7*a**4/14