. Find s, given that q(s) = 0.
-2, -1, 0
Let p(t) be the first derivative of 8 - 5/2*t**3 - 9/20*t**5 + 3/2*t**2 + 7/4*t**4 + 5*t. Let q(n) be the first derivative of p(n). Find g such that q(g) = 0.
1/3, 1
Let z(l) be the third derivative of l**5/300 + 2*l**4/15 - 17*l**3/30 - 118*l**2. Suppose z(x) = 0. What is x?
-17, 1
Suppose -135*c + 222*c = -394*c. Factor 1/3*l**4 + c*l**3 + 0 - 16/3*l - 4*l**2.
l*(l - 4)*(l + 2)**2/3
Let r(g) be the first derivative of 5*g**9/6048 + g**8/420 + g**7/1680 - g**6/360 + 2*g**3 + 13. Let t(p) be the third derivative of r(p). Factor t(l).
l**2*(l + 1)**2*(5*l - 2)/2
Let i = -54 + 57. Let x(m) = -5*m**3 - 11*m**2 - 8*m + 3. Let h(j) = 24*j + 2 + 32*j**2 + 14*j**3 - 7 - 3. Let a(u) = i*h(u) + 8*x(u). Solve a(l) = 0.
-2, 0
Let f = 1430 + -1427. Let h(w) be the first derivative of -8*w - 4/3*w**f + 5 + 6*w**2. Factor h(x).
-4*(x - 2)*(x - 1)
Let p(w) = w**3 + 91*w**2 + 179*w + 91. Let o be p(-89). Factor -12/7*h - 3/7*h**5 + 18/7*h**4 + 0 + 36/7*h**o - 39/7*h**3.
-3*h*(h - 2)**2*(h - 1)**2/7
Let h be (-42)/(-66) + (-60)/220. Let a(c) = -c**2 - 8*c. Let d be a(-8). Factor d - h*g**2 - 2/11*g.
-2*g*(2*g + 1)/11
Let o(m) be the first derivative of 4/9*m**3 - 2 + 0*m + 1/3*m**2 + 1/6*m**4. Factor o(g).
2*g*(g + 1)**2/3
Determine v, given that -4/3*v**2 - 1/9*v**5 + 0 + 2/9*v**3 + 1/3*v**4 + 8/9*v = 0.
-2, 0, 1, 2
Let l be 76/80 + 12/(-16). Factor 2/5*w - l*w**2 - 1/5.
-(w - 1)**2/5
Let g(x) = 19*x**4 - 2*x**3 + 3*x**2 - 8*x - 8. Let m(j) = -7*j**4 + j**3 - j**2 + 3*j + 3. Let w(y) = -3*g(y) - 8*m(y). Factor w(n).
-n**2*(n + 1)**2
Let s(d) be the first derivative of -5/2*d**2 + 0*d - 2/3*d**3 + 0*d**4 + 4 + 1/60*d**5. Let m(c) be the second derivative of s(c). Factor m(y).
(y - 2)*(y + 2)
Let h(q) be the first derivative of -26 + 12*q**3 - 16*q + 12*q**2 + 5/2*q**4. Let h(x) = 0. Calculate x.
-2, 2/5
Suppose 63 - 59 = d. Suppose d*k - 2*k - 5*k = 0. Factor 0 + k*q**2 + 1/5*q**3 - 1/5*q.
q*(q - 1)*(q + 1)/5
Let s be (-7)/(0 - 0 - (-9)/(-3)). Let u(a) be the first derivative of 4/3*a**3 + s*a**6 + 0*a**2 - 5 + 32/5*a**5 + 11/2*a**4 + 0*a. Factor u(q).
2*q**2*(q + 1)**2*(7*q + 2)
Let b be (-4)/14 - -652*(-3)/210. Let s = 10 + b. Let -1/5*a + s*a**2 + 0 - 1/5*a**3 = 0. What is a?
0, 1
Let -249*n + 21*n**2 + 465*n + 12*n**2 - 228*n = 0. What is n?
0, 4/11
Let i(d) = -60*d**3 - 987*d**2 + 219*d - 21. Let u(w) = 12*w**3 + 197*w**2 - 44*w + 4. Let t(j) = -4*i(j) - 21*u(j). Factor t(z).
-3*z*(z + 16)*(4*z - 1)
Let s = -263 + 284. Let m be 3/s + ((-30)/14 - -2). Factor -8/7*v**3 - 162/7*v**5 + 0*v**2 + m*v - 72/7*v**4 + 0.
-2*v**3*(9*v + 2)**2/7
Let m(s) = -5*s**2 - 7 + 15*s**2 - 8*s - s**3 + 0*s**3. Let g be m(9). Factor -k + 7*k**g + 3*k**4 - 6*k**2 - 5*k**3 + 2*k.
k*(k - 1)**2*(3*k + 1)
Suppose -8*g = -4*q - 9*g + 21, 5*q - 10 = 2*g. Let i(s) be the second derivative of -5*s + 1/4*s**2 + 0 - 1/6*s**3 + 1/24*s**q. What is b in i(b) = 0?
1
Let w(c) = -3*c**3 + c**2. Let u be w(-1). Suppose -6*y - 13 = -3*r - u*y, 4*r - 10 = -y. Factor r - z + 0*z**2 - 3*z**2 + 4*z - 3*z**3.
-3*(z - 1)*(z + 1)**2
Let 10/9 + 1/3*k - 1/9*k**2 = 0. Calculate k.
-2, 5
Factor -23 - 10*h**3 - 5*h**5 + 71*h**2 + 35*h**3 + 25*h**4 - 263*h - 57 - 196*h**2 + 63*h.
-5*(h - 4)**2*(h + 1)**3
Factor -13961*y + 13956*y - 65 + 370*y**2 + 5*y**3 - 305.
5*(y - 1)*(y + 1)*(y + 74)
Let h(g) = -11*g + 17. Let d be h(-2). Determine r so that -6*r**4 + 0*r**3 + 28*r**2 - 16 - d*r + 2*r**3 + 31*r = 0.
-2, -2/3, 1, 2
Let o = -233 + 4195/18. Let n(q) be the second derivative of 0*q**2 + 0 - 1/45*q**6 - 1/15*q**5 + 0*q**3 + q - o*q**4. Factor n(w).
-2*w**2*(w + 1)**2/3
Let x(p) be the third derivative of 1/120*p**6 - 1/24*p**4 - 20*p**2 + 0 + 0*p + 1/20*p**5 - 1/2*p**3. Solve x(n) = 0 for n.
-3, -1, 1
Let c(h) be the third derivative of -5*h**8/336 - h**7/21 + 7*h**6/24 - h**5/3 + 544*h**2. Solve c(n) = 0.
-4, 0, 1
Let k(o) be the first derivative of -o**4/2 - 8*o**3 - 36*o**2 - 64*o + 716. Determine t so that k(t) = 0.
-8, -2
Let h be (9/6)/((-3)/(-72)) - 4. Factor -4*y**3 - 36*y - 14*y**2 + h + 38*y**2 - 12*y.
-4*(y - 2)**3
Suppose 38/11*o**3 + 42/11*o**4 + 0 + 0*o - 4/11*o**2 = 0. Calculate o.
-1, 0, 2/21
Let o(r) = 15*r**3 - 144*r + 129. Let z(t) = -4*t**3 + 8 - 9*t + t**3 + 2*t**3 + 2*t**3. Let v(h) = -2*o(h) + 33*z(h). Factor v(u).
3*(u - 1)**2*(u + 2)
Let i(w) = -9*w**4 + w**3 + 4*w**2. Let g(z) = 2*z**4 + z**3 + z**2. Let o(v) = 10*g(v) + 2*i(v). What is k in o(k) = 0?
-3, 0
Factor 0*h + 12*h**3 - 32/3*h**2 - 4/3*h**4 + 0.
-4*h**2*(h - 8)*(h - 1)/3
Let y be (-104)/(-364)*7/1. Let g be y - (0 + -6 + 6). Factor 1/4*q**g + 3/4*q + 1/2.
(q + 1)*(q + 2)/4
Let k(v) be the second derivative of -1/126*v**7 + 1/54*v**3 + 0*v**4 + 0*v**2 - 1/30*v**5 + 4/135*v**6 - 23*v + 0. Determine y, given that k(y) = 0.
-1/3, 0, 1
Let g be (((-24)/15 - 2) + 3)/((-136)/85). Factor -1/8*t**2 - 1/4 - g*t.
-(t + 1)*(t + 2)/8
Let b = 55957810/470799 - -2/67257. Let t = 119 - b. What is o in -t*o**3 - 3/7*o**2 - 1/7 - 3/7*o = 0?
-1
Factor 58*k**2 + 64*k**3 - 32*k**2 + 15*k**4 + 6*k**2 - 4*k**5 + 48*k**2 - 11*k**4.
-4*k**2*(k - 5)*(k + 2)**2
Factor -2*d**4 - 6*d**4 - 6*d**4 - 5*d**4 + 25*d**2 + 14*d**4 - 20*d**3.
-5*d**2*(d - 1)*(d + 5)
Find s, given that 20*s + 7*s**2 + 5*s**2 - 3*s**2 + 6*s**2 = 0.
-4/3, 0
Let k(m) be the second derivative of 0 + 0*m**2 + 2/75*m**6 + 0*m**5 - 4/15*m**3 - 1/5*m**4 - 6*m. Determine y, given that k(y) = 0.
-1, 0, 2
Let v be 1360/(-21) + (-16)/4 + 8. Let q = v - -184/3. Solve 0 + 6/7*i**4 - 10/7*i**5 + 2*i**3 - 6/7*i**2 - q*i = 0 for i.
-1, -2/5, 0, 1
Suppose 6*z - 61*z = 0. Let k(c) be the third derivative of 10*c**2 - 1/1155*c**7 + 0 + 0*c**4 + 1/330*c**5 + z*c + 0*c**3 + 0*c**6. Factor k(f).
-2*f**2*(f - 1)*(f + 1)/11
Let x(h) be the second derivative of -h**7/14 + 8*h**6/5 - 117*h**5/10 + 28*h**4 - 49*h**3/2 + 7*h + 2. Determine p so that x(p) = 0.
0, 1, 7
Let s(a) be the first derivative of -a**6/200 - a**5/15 - 9*a**4/40 - a**3/3 + 13*a**2/2 + 22. Let t(y) be the second derivative of s(y). Factor t(h).
-(h + 1)*(h + 5)*(3*h + 2)/5
Let z(l) be the first derivative of l**7/525 + l**6/300 - l**5/150 - l**4/60 + 17*l**2/2 + 28. Let p(i) be the second derivative of z(i). Factor p(k).
2*k*(k - 1)*(k + 1)**2/5
Let t = 291 - 291. Let i(g) be the second derivative of -1/24*g**4 + 0*g**2 + t*g**3 + 0 - 3*g. Factor i(n).
-n**2/2
Let f(d) = -8*d + 59. Let m be f(7). Let n(k) be the first derivative of 0*k**m + 0*k**2 + 5 - 1/2*k**4 - 1/5*k**5 + 0*k. Factor n(i).
-i**3*(i + 2)
Let b be 174/(-36) - 25/(-5). Let g(j) be the first derivative of 1/9*j**3 + 0*j - b*j**2 + 1/6*j**4 + 3. Factor g(p).
p*(p + 1)*(2*p - 1)/3
Let d(g) be the second derivative of -22*g - 1/20*g**5 + 1/30*g**6 + 0 + 0*g**2 - 1/12*g**4 + 1/6*g**3. Factor d(j).
j*(j - 1)**2*(j + 1)
Let l(k) be the second derivative of -k**7/21 + 4*k**6/35 + 193*k**5/70 - 169*k**4/21 - 32*k**3 - 160*k**2/7 + 8*k + 24. Determine j so that l(j) = 0.
-5, -1, -2/7, 4
Let m(s) = -12*s**3 - 12*s**2 - 38*s + 7. Let v(l) = -l**3 - 2*l**2 - l - 1. Let q(x) = -2*m(x) + 22*v(x). Factor q(w).
2*(w - 6)*(w - 3)*(w - 1)
Suppose 0*g + 49 = 2*v + 3*g, -2*v - g + 43 = 0. Suppose -48 = -4*d - v*d. Determine q so that 2/3*q**2 + d*q + 4/3 = 0.
-2, -1
Let k be (-1)/1 + (-18)/6. Let j(b) = b**3 + b**2. Let p(z) be the second derivative of -z**4/12 - z**3/6 + z. Let i(y) = k*p(y) - 4*j(y). Factor i(g).
-4*g*(g - 1)*(g + 1)
Suppose 46 + 24 = 5*k. Factor 1 + k*j**2 - 1 - 12*j**2 + 2*j.
2*j*(j + 1)
Let s(a) = -535*a + 6422. Let v be s(12). Factor 2/3*u**3 - 2/3*u + 0 - u**v + u**4.
u*(u - 1)*(u + 1)*(3*u + 2)/3
Let k(p) = -2*p**2 - p. Let d(g) = 18*g**2 + 2*g - 8. Let x(a) = d(a) + 8*k(a). Factor x(w).
2*(w - 4)*(w + 1)
Factor 228/23*g - 6498/23 - 2/23*g**2.
-2*(g - 57)**2/23
Solve -82 - 23*p**2 - 10*p - 39 + 153*p + p**3 = 0 for p.
1, 11
Let x(s) be the second derivative of -s**4/4 + 9*s**3 - 51*s**2/2 + 38*s - 1. Factor x(r).
-3*(r - 17)*(r - 1)
Let m be (-6)/(-75)*(8 - 3). Suppose m*v**3 - 4/5*v + 6/5*v**2 + 2/5*v**5 - 6/5*v**4 + 0 = 0. Calculate v.
-1, 0, 1, 2
Let q(h) be the first derivative of -1/15*h**3 - 36/5*h + 7 - 6/5*h**2. Suppose q(c) = 0. What is c?
-6
Let t(z) be the third derivative of -z**7/84 + 7*z**6/240 - z**5/60 - 