-3*u*(u + 1)*(u + 21)/8
Factor 76 + 58 - 161 + 27*h - 115*h**2 + 346*h**2 - 441*h**3 + 18*h.
-3*(3*h + 1)*(7*h - 3)**2
Find y, given that -487*y**3 + 1963*y**2 - 1360 - 771*y**4 - 115*y**5 - 69*y**5 + 664*y + 175*y**5 = 0.
-85, -4/3, 1
Let a = 2259 + -2253. Let i(g) be the third derivative of 1/30*g**a - 1/3*g**5 + 2*g**2 + 1/2*g**4 + 0*g + 0 + 0*g**3 + 2/105*g**7. Factor i(f).
4*f*(f - 1)**2*(f + 3)
Let q(z) be the third derivative of 7/12*z**4 - 2*z**3 - 1/30*z**5 - 182*z**2 + 0 + 0*z. Solve q(r) = 0.
1, 6
Let y(k) = 63*k**2 - 861*k + 156. Let m(t) = -62*t**2 + 863*t - 158. Let j(b) = -12*m(b) - 13*y(b). Let j(u) = 0. What is u?
4/25, 11
Let b(q) be the first derivative of 53 - 25/2*q - q**3 + 45/8*q**2 + 1/16*q**4. Factor b(s).
(s - 5)**2*(s - 2)/4
Suppose -2*z = -0*z + 3*q + 73, 193 = -5*z - 4*q. Let l = z - -54. Suppose 0 - l*f**2 - 2*f - 3 + 14*f**2 = 0. Calculate f.
-1, 3
Let a(s) be the third derivative of -s**5/30 - 26*s**4 - 1232*s**3/3 - 13*s**2 + 39. Factor a(o).
-2*(o + 4)*(o + 308)
Let n be (-16)/(-12)*-32*(515/(-30) + 17). Solve 22/3*f + n + 2/9*f**2 = 0.
-32, -1
Let y be (-25 - -11) + 18 + (-84)/22. Let m(g) be the second derivative of -9/11*g**2 + 0 + y*g**3 + 1/22*g**4 - 27*g. What is f in m(f) = 0?
-3, 1
Suppose -115*x + 3 = -1 + 4. Let o(v) be the third derivative of 0 - 25*v**2 + 0*v**4 + x*v**3 + 0*v**5 - 1/60*v**6 + 0*v. What is u in o(u) = 0?
0
Let n(j) be the first derivative of -j**4/4 + j**3/2 + 3*j**2 - 58*j - 78. Let q(t) be the first derivative of n(t). Factor q(b).
-3*(b - 2)*(b + 1)
Suppose 0 = -4*w - 16, w - 22 = -t + 5*w. Suppose -2*b + 6*b + t*b = 0. Let -5/3*s**2 + b*s + 5/3 = 0. What is s?
-1, 1
Suppose 3*d + 5 = -2*d. Let w be d - -7 - (1 + 2). Factor -30*r**w + 2*r**4 + 15*r**3 - 12*r + 3*r**4 + 24*r**2 - 2*r**4.
3*r*(r - 2)**2*(r - 1)
Let v be (-3124)/(-602) + 6700/(-144050). Factor 120/7*j + 2/7*j**3 + v*j**2 - 400/7.
2*(j - 2)*(j + 10)**2/7
Let l(o) be the second derivative of 65*o**4/12 + 35*o**3/6 - 50*o**2 - o + 95. Factor l(b).
5*(b - 1)*(13*b + 20)
Let u be 40/(-850)*(-2058)/16 - 6. Let x(s) be the second derivative of 4/255*s**6 + 0*s**2 - u*s**5 + 1/51*s**4 + 0*s**3 + 0 - 4*s. Factor x(o).
2*o**2*(o - 2)*(4*o - 1)/17
Factor 2/15*k**2 + 6 + 28/15*k.
2*(k + 5)*(k + 9)/15
Let t be -53 + 40 - 355*(-3)/75. Solve -3/5*b**5 - 2/5 + t*b**3 - 3/5*b - 2/5*b**4 + 4/5*b**2 = 0 for b.
-1, -2/3, 1
Let r = 346 - 345. Let d(u) = -10*u**2 + 5*u. Let f(y) = -y**3 + 2*y**2. Let h(p) = r*d(p) + 5*f(p). Suppose h(l) = 0. What is l?
-1, 0, 1
Suppose 0 = 2*z + 547 - 93. Let m = -656/3 - z. Factor -5/3*h**3 - m*h - 5/2 - 15/2*h**2.
-5*(h + 1)*(h + 3)*(2*h + 1)/6
Suppose 73*u - 78*u + 21 = x, 3*x + 9 = 3*u. Suppose -3 = u*q - 5*k + 9, k = q + 2. Find n, given that -12/7*n + 0 - 4/7*n**q = 0.
-3, 0
Let k be 4 + -5 + (-5 - 32/(-2)). Suppose 4 = -3*v - 5*u + k*u, 4*v - 16 = -4*u. Solve -2/5*c + 1/5*c**v + 0 = 0 for c.
0, 2
Let h = 43039/3442 + -7/1721. Let b(t) be the first derivative of 5*t + 50/3*t**3 - h*t**4 - 5/6*t**6 - 25/2*t**2 + 5*t**5 + 19. Factor b(s).
-5*(s - 1)**5
Let v(t) be the first derivative of 19*t**6/21 - 34*t**5/35 - 59*t**4/14 + 26*t**3/21 + 40*t**2/7 + 8*t/7 + 5344. Determine y so that v(y) = 0.
-1, -2/19, 1, 2
Solve 12*g**2 + 3*g**4 + 15*g**2 + 12*g - 11*g**2 - 8*g**4 + 6*g**4 + 7*g**3 = 0 for g.
-3, -2, 0
Let s(l) be the third derivative of -43/42*l**4 + 0 - 234*l**2 + 85/21*l**3 + 1/210*l**5 + 0*l. Factor s(v).
2*(v - 85)*(v - 1)/7
Let i(g) be the third derivative of 0*g + 13/12*g**4 - 1/30*g**5 - g**2 + 40 + 14/3*g**3. Determine k so that i(k) = 0.
-1, 14
Let x(q) = 68*q**2 + 748*q + 768. Let m(c) = 9*c**2 + 2. Let s(u) = -8*m(u) + x(u). Let s(h) = 0. What is h?
-1, 188
Factor 272*o**3 + 55804*o**2 - 2*o**4 - 127232*o**2 + 62458*o**2 - 19044*o.
-2*o*(o - 69)**2*(o + 2)
Suppose 2*w + 8*l - 3*l = 18, 2*w + 2 = 5*l. Find s such that 12385*s**3 + 4 - 12241*s**3 - 11*s - 52*s - 72*s**5 + 4*s**w - 9*s - 8*s**2 = 0.
-1, 1/18, 1
Suppose 94*a = -598*a + 283*a - 1161*a. Factor -1/5*u**5 + 0*u**2 + 3/5*u**4 + a*u - 2/5*u**3 + 0.
-u**3*(u - 2)*(u - 1)/5
Suppose 18 - 50 = -3*s - 23. Let c(p) be the first derivative of -4 + 2/5*p**2 + 4/5*p + 1/15*p**s. Factor c(q).
(q + 2)**2/5
Let m(a) be the third derivative of -2*a**7/105 - 9*a**6/10 - 10*a**5/3 + 1365*a**2 - 2*a. What is z in m(z) = 0?
-25, -2, 0
Factor 22*g**3 + 10*g**2 - 36*g**2 - 201 + 15 + 12*g**3 - 33*g**3 - 149*g.
(g - 31)*(g + 2)*(g + 3)
Let b = -18349 + 807243/44. Let a = -20/11 - b. Determine h so that -a*h**2 - 4/3 - 2*h - 1/12*h**3 = 0.
-4, -1
Let v(x) be the third derivative of x**6/900 + x**5/75 + x**4/15 + 47*x**3/3 - 11*x**2 + 2. Let y(t) be the first derivative of v(t). What is a in y(a) = 0?
-2
Let h(q) = -q**2 + 6*q + 5. Let y(x) = x + 1. Let u(g) = h(g) - 5*y(g). Let v(i) = -8*i**2 + 84*i - 76. Let f(n) = 12*u(n) - v(n). Factor f(d).
-4*(d - 1)*(d + 19)
Let o = 1040302/5 + -208054. Factor 44/5*r**2 - o*r**3 + 52/5*r - 24/5.
-4*(r - 2)*(r + 1)*(8*r - 3)/5
Let j(r) be the second derivative of 3*r**6/70 + 57*r**5/140 + 4*r**4/7 - 8*r + 10. Factor j(n).
3*n**2*(n + 1)*(3*n + 16)/7
Suppose -10*a = -18*a - 64. Let o(d) = 2*d**3 + 17*d**2 + 9*d + 10. Let z be o(a). Solve h**3 + z*h**2 - 5336*h + 5336*h - h**4 = 0 for h.
-1, 0, 2
Let t(c) be the first derivative of c**3/3 - 303*c**2 + 91809*c + 1696. Factor t(r).
(r - 303)**2
Let r be (740/(-1650) - 2/(-11))*(-140)/21. Let f(q) be the second derivative of r*q**3 + 1/120*q**5 + 0 - 18*q + 2/9*q**4 + 0*q**2. Factor f(c).
c*(c + 8)**2/6
Let q(o) be the first derivative of -17*o + 4/5*o**2 + 35 + 1/30*o**4 + 1/3*o**3. Let a(g) be the first derivative of q(g). What is n in a(n) = 0?
-4, -1
Factor -94/7 - 2/7*s**3 + 2/7*s + 94/7*s**2.
-2*(s - 47)*(s - 1)*(s + 1)/7
Let m(o) = -4*o**2 - 1240*o + 8. Let k(y) = -y + 1. Let r(s) = 8*k(s) - m(s). Factor r(a).
4*a*(a + 308)
Suppose -9216 - 25/4*b**2 + 480*b = 0. What is b?
192/5
Let n be (91/(-14) + 7)*0. Let j(d) be the second derivative of 1/4*d**4 + 3*d + n - 4*d**2 - 5/3*d**3. Find p, given that j(p) = 0.
-2/3, 4
Let o be (-2)/26*2 - (-101)/((-65650)/(-1400)). Suppose 0*z**o + 5/6*z**3 + 0 - 5/6*z = 0. Calculate z.
-1, 0, 1
Let r(d) be the second derivative of d**5/120 - d**4/3 + 16*d**3/3 + 179*d**2/2 - 224*d. Let l(q) be the first derivative of r(q). Factor l(a).
(a - 8)**2/2
Let y(m) be the third derivative of m**7/840 - 205*m**6/6 + 420250*m**5 - 8615125000*m**4/3 + 35322012500000*m**3/3 - 6158*m**2. Factor y(g).
(g - 4100)**4/4
Solve 56 + 2/9*s**2 - 22/3*s = 0.
12, 21
Let t = 890 + -884. Let b(o) be the first derivative of t + 1/20*o**4 + 1/5*o**2 - 1/5*o**3 + 0*o. Solve b(r) = 0 for r.
0, 1, 2
Suppose 2*w - 10*n - 129 = -13*n, 4*n = 2*w - 108. Suppose -80*m**4 + 134*m**4 - 119*m**4 - 20*m**2 + w*m**5 - 100*m**3 = 0. Calculate m.
-2/3, -1/4, 0, 2
Let j(c) = -6*c**2 - 1120*c + 16. Let y(q) = -q**2 - 218*q + 3. Let d(w) = -3*j(w) + 16*y(w). Let d(z) = 0. What is z?
0, 64
Let j(a) = -a**2 - 7*a - 10. Let f be j(-4). Factor 7*t**2 - 3*t**3 - 10*t - 6*t**f - 4*t**3 + 10*t.
-t**2*(7*t - 1)
Let v(d) be the third derivative of 0 + 7/60*d**4 - 7/300*d**6 + 1/30*d**5 - 2*d**2 + 1/525*d**7 - 54*d - 2/5*d**3. Factor v(x).
2*(x - 6)*(x - 1)**2*(x + 1)/5
Let a be (-271)/(-50) + (-32 - 20852/(-650)). Factor 1/4*v**2 + 13/4*v + a.
(v + 2)*(v + 11)/4
Let v(y) be the first derivative of -y**5 + 155*y**4/4 - 1220*y**3/3 + 1110*y**2 + 3600*y + 242. Suppose v(f) = 0. Calculate f.
-1, 6, 20
Let b(v) be the first derivative of -v**4/5 - 8*v**3/15 - 2*v**2/5 - 615. Let b(n) = 0. What is n?
-1, 0
Let j be 1056/21 - (-14)/(-49). Suppose 44*u**3 - 65*u**2 - 35*u**4 + 5*u**5 + j*u**3 + 20*u - 19*u**3 = 0. What is u?
0, 1, 4
Let p(a) be the first derivative of a**5/12 + 95*a**4/24 + 15*a**3 - 9*a**2 + 235. Let y(g) be the second derivative of p(g). Factor y(x).
5*(x + 1)*(x + 18)
Suppose 0*q - 2*q = -5*w + 10, 0 = 5*q. Let y(u) be the second derivative of -15*u**w + 65/6*u**3 - 5/6*u**4 + 2*u - 6. Let y(o) = 0. Calculate o.
1/2, 6
Let p(x) be the first derivative of 17*x**3/3 - 868*x**2 + 204*x + 2157. Factor p(v).
(v - 102)*(17*v - 2)
Let v(t) be the third derivative of -t**6/24 - 2*t**5/3 + 25*t**4/6 - 171*t**2. Factor v(a).
-5*a*(a - 2)*(a + 10)
Let v(p) be the first de