 Let q be s/(-2)*(-10 - -10). Find p, given that q + 0*p + 3*p**2 + 1/3*p**4 + 2*p**3 = 0.
-3, 0
Suppose -10*h = -4*h - 12. Factor 5*b**2 + 100*b**3 - 4*b + b**h - 102*b**3.
-2*b*(b - 2)*(b - 1)
Suppose -2*g - 10 = -m, -4*m + 2*g = -55 + 3. Let x be (16/m)/((-2)/(-7)). What is a in a**4 + 2 - 2*a**2 + 0*a**x - 1 + 0*a**4 = 0?
-1, 1
Suppose -10*q - 6*q - 64 = 0. Let o be 2/(-6)*-3 + 3 + q. Factor -1/2*y + 1/4*y**2 + 1/2*y**3 + o - 1/4*y**4.
-y*(y - 2)*(y - 1)*(y + 1)/4
Let i(g) = -4*g**2 - 2*g - 1. Let v(t) = -t**2 + 0*t**2 - 12*t + 11*t. Let z(q) = -6*i(q) + 21*v(q). Let z(p) = 0. What is p?
1, 2
Let k(x) be the second derivative of 3/2*x**2 + 0 + 4*x + 0*x**3 + 0*x**5 + 1/10*x**6 - 1/2*x**4. Determine g so that k(g) = 0.
-1, 1
Let b(k) be the third derivative of -k**6/300 - 7*k**5/75 + 23*k**4/20 - 18*k**3/5 - 1001*k**2. Determine i so that b(i) = 0.
-18, 1, 3
Let j(a) be the third derivative of a**6/90 - 10*a**5/9 + 625*a**4/18 + 2*a**2 + 9*a. Factor j(b).
4*b*(b - 25)**2/3
Factor 323984*p - 2763*p**4 + 410*p**3 + 628864 + 25097*p**2 + 332624*p + 3055*p**2 + 2765*p**4.
2*(p + 1)*(p + 68)**3
Let k(g) be the second derivative of 2*g**6/105 + 12*g**5/35 + g**4 + 20*g**3/21 + g - 40. Factor k(z).
4*z*(z + 1)**2*(z + 10)/7
Let g be 357/33 + -11 - 24/(-11). Factor 0 - 1/5*f**3 + 1/5*f**5 + 0*f**g + 0*f**4 + 0*f.
f**3*(f - 1)*(f + 1)/5
Let m = 719/4440 + 7/111. Let p(r) be the third derivative of 0 - m*r**6 + 0*r**3 + 0*r + 7*r**2 + 3/5*r**5 - 1/2*r**4. Determine i so that p(i) = 0.
0, 2/3
Factor -10*f**3 - 33/2*f**2 - 1 - 15/2*f.
-(f + 1)*(4*f + 1)*(5*f + 2)/2
Let f(b) be the second derivative of 5/6*b**4 - 5/2*b**2 - 5*b + 0 + 5/6*b**3. Factor f(u).
5*(u + 1)*(2*u - 1)
Let k(z) be the second derivative of 0 - 1/4*z**5 + 0*z**3 - 5/12*z**4 - 6*z + 0*z**2. Find w, given that k(w) = 0.
-1, 0
Let y(n) be the second derivative of -n**8/1344 + n**7/168 + n**6/80 + 21*n**2 + 4*n. Let b(x) be the first derivative of y(x). Factor b(t).
-t**3*(t - 6)*(t + 1)/4
Let g(f) be the second derivative of 0 + f**2 + 20*f + 7/10*f**5 + 4/3*f**4 + 3/2*f**3 + 1/42*f**7 + 1/5*f**6. Suppose g(v) = 0. What is v?
-2, -1
Let q(k) = -k**2 - 5*k + 5. Let m be q(-5). Let f = m + 9. Determine z so that -10*z + f*z + z**2 - 2 - 2*z**2 - z**2 = 0.
1
Let w(c) = -c**3 - 8*c**2 - 17*c - 1. Let f be w(-4). Factor 5*g**3 - g**f + 13*g**2 - 7*g**2 + 12*g - 3*g**3 + 8.
(g + 2)**3
Let m = 29 - 28. Let l(z) = 7*z**4 + 11*z**3 - 5*z**2 - 9*z. Let y(w) = w**3 + 1. Let u(j) = m*l(j) - 2*y(j). Let u(o) = 0. Calculate o.
-1, -2/7, 1
Let q(a) = 10*a**3 - 5*a**2 - 5*a + 15. Let v(l) = -5*l**3 + 3*l**2 + 3*l - 7. Let o = 17 - 15. Let s(y) = o*q(y) + 5*v(y). Factor s(b).
-5*(b - 1)**2*(b + 1)
Let a(d) be the first derivative of -d**5/4 + 5*d**3/2 + 5*d**2 + 4*d + 2. Let x(m) be the first derivative of a(m). Solve x(p) = 0 for p.
-1, 2
Let b be 1/(-2) + (-1)/(-2). Let y be (b + -2)*(-21)/2. Factor -4*k**3 + y*k**2 - 7*k**4 - 8*k + 0*k**3 + 2*k**3 - 4.
-(k - 1)**2*(k + 2)*(7*k + 2)
Factor -20 - 5/2*n**2 + 45/2*n.
-5*(n - 8)*(n - 1)/2
Let 2/5*y**2 + 0*y**3 + 0*y + 0 - 2/5*y**4 = 0. Calculate y.
-1, 0, 1
Let q(a) be the third derivative of -3/40*a**6 + 0*a - 25*a**2 + 1/24*a**4 + 1/3*a**3 + 0 - 3/10*a**5. Suppose q(j) = 0. Calculate j.
-2, -1/3, 1/3
Let h(f) be the first derivative of f**6/32 + 7*f**5/80 - f**4/4 - f**3/2 - f**2 - 2. Let n(i) be the second derivative of h(i). Factor n(v).
3*(v - 1)*(v + 2)*(5*v + 2)/4
Let c(j) = -j**2 - 6*j + 10. Let z be c(-7). Suppose -z*s + 12 = -0*s. Factor 2*u**4 + 293*u + 2*u**2 - 293*u - s*u**3.
2*u**2*(u - 1)**2
Let p be (-15)/50*((-134)/36 - (-8)/(-18)). Solve 0*y + 0*y**2 + 0 - y**5 - 1/4*y**3 - p*y**4 = 0 for y.
-1, -1/4, 0
Let u(i) be the first derivative of 3*i**3/7 - 48*i**2/7 - 15*i + 96. Let u(n) = 0. Calculate n.
-1, 35/3
Let z(i) be the second derivative of -3*i**5/20 + i**4/6 + 2*i**3 - 4*i**2 + 72*i. Determine m so that z(m) = 0.
-2, 2/3, 2
Let j = -27 - -31. Factor -12*a**3 - 8*a**4 + 9*a**j - 4*a**4 - 15*a**2 - 6*a.
-3*a*(a + 1)**2*(a + 2)
Suppose -14*k + 15 + 13 = 0. Factor -k*m + 1/2*m**3 + 2 - 1/2*m**2.
(m - 2)*(m - 1)*(m + 2)/2
Let -2/9*x**3 - 2/3*x**2 + 4/9 + 2/9*x + 2/9*x**4 = 0. Calculate x.
-1, 1, 2
Let u(l) be the first derivative of -3*l**4/16 - 7*l**3/4 + 3*l**2 + 51. Factor u(b).
-3*b*(b - 1)*(b + 8)/4
Let v(d) be the second derivative of -d**6/300 + 6*d**5/25 - 24*d**4/5 + 7*d - 2. Factor v(g).
-g**2*(g - 24)**2/10
Let g(z) be the third derivative of -z**7/504 - z**6/720 - 2*z**4 + z**2 - 4. Let r(b) be the second derivative of g(b). Factor r(a).
-a*(5*a + 1)
Suppose -32 = 3*j - b - 10, 4*j - 2*b + 32 = 0. Let u(w) = w**3 + 7*w**2 + 6*w + 4. Let n be u(j). Factor -4/9*l**2 + 2/9*l**n + 0*l**3 + 0*l + 2/9.
2*(l - 1)**2*(l + 1)**2/9
Let m be (2 + 14)*(7 + -5 + -4). Let a be 2 + m/6 - (3 + -7). Suppose 2/3*t - a*t**2 + 0 = 0. What is t?
0, 1
Let i(y) be the third derivative of 0*y**3 + 0*y - 1/12*y**6 + 1/12*y**5 + 0 + 5/12*y**4 - 1/42*y**7 + 28*y**2. Let i(w) = 0. Calculate w.
-2, -1, 0, 1
Factor 7 - 10 + 14*q + 22*q**2 - 11 + 2*q**3 - 8 - 16*q.
2*(q - 1)*(q + 1)*(q + 11)
Let k = 20 - 40. Let n(s) = -s - 1. Let j(m) = 5*m**2 + 25*m + 10. Let v(o) = k*n(o) - j(o). Factor v(u).
-5*(u - 1)*(u + 2)
Let j(b) = -b**2 + 93*b - 98. Let i(s) = -s**2 - 2. Let v(r) = 6*i(r) - 3*j(r). Let v(t) = 0. What is t?
-94, 1
Find i, given that -4*i**3 + 11*i**2 - 20*i**2 + 6*i**2 - 47*i**2 - 44*i + 2*i**2 = 0.
-11, -1, 0
Let n = -11 + 10. Let k be (126/4)/(n/(-2)). Solve -v**2 - 7*v**4 - 3*v**5 - k*v - 5*v**3 + 63*v = 0 for v.
-1, -1/3, 0
Let b(t) = -3*t + 14. Let h be b(4). Factor 0*j**3 + 4*j + 3*j**h - 2*j**3 - 3*j**4 - 7*j**3 + 3*j**5 + 2*j.
3*j*(j - 2)*(j - 1)*(j + 1)**2
Let y(c) be the first derivative of -4*c**3/3 + 12*c**2 + 28*c - 90. Factor y(w).
-4*(w - 7)*(w + 1)
Factor -1024/3 - 1/3*l**5 + 4*l**4 + 256*l - 32/3*l**3 - 128/3*l**2.
-(l - 4)**4*(l + 4)/3
Let l(a) be the second derivative of a**7/189 + 17*a**6/135 + 53*a**5/45 + 145*a**4/27 + 325*a**3/27 + 125*a**2/9 + 384*a. Factor l(t).
2*(t + 1)**2*(t + 5)**3/9
Suppose -6 = -8*f + 5*f, -3*f = 2*t - 10. Factor 8/3*o**3 + 4*o**t + 2/3*o**4 + 8/3*o + 2/3.
2*(o + 1)**4/3
Let s = -268 - -256. Let q(x) = x**3 + 11*x**2 - 15*x - 36. Let m be q(s). Determine k, given that -2*k + 2*k**2 + 3/2*k**3 + m = 0.
-2, 0, 2/3
Let r(a) be the third derivative of -1/2*a**4 - 2/5*a**5 - 1/70*a**7 - 1/8*a**6 + 0*a - 18*a**2 + 0*a**3 + 0. Factor r(t).
-3*t*(t + 1)*(t + 2)**2
Let g(n) be the first derivative of -3*n**4/4 - 42*n**3/5 - 273*n**2/10 - 18*n + 306. Factor g(c).
-3*(c + 3)*(c + 5)*(5*c + 2)/5
Let u(g) = -7*g**5 - 29*g**4 + 58*g**3 - 34*g**2 + 9*g + 7. Let p(w) = 4*w**5 + 29*w**4 - 57*w**3 + 35*w**2 - 8*w - 6. Let s(v) = 4*p(v) + 3*u(v). Factor s(f).
-(f - 3)*(f - 1)**3*(5*f + 1)
Let u(d) be the third derivative of -11*d**2 + 0*d**4 + 2*d**3 + 0 - 1/20*d**5 + 0*d. Factor u(g).
-3*(g - 2)*(g + 2)
Let s(i) = 11*i + 53. Let j be s(-5). Let u be j/75*-1*(-14 - -24). Factor 2/15*z + u - 2/15*z**2.
-2*(z - 2)*(z + 1)/15
Suppose -12 = -5*a - 2. Suppose -8*m**a - 5*m + 3*m**2 + 2*m**3 + 2 + 6*m**2 = 0. What is m?
-2, 1/2, 1
Suppose 3*s - 9*s = 0. Let y = 755/4 + -188. Factor s - 3*l - 3*l**2 - y*l**3.
-3*l*(l + 2)**2/4
Determine r so that -18*r + 22*r**2 - 21*r**2 - 4*r**2 = 0.
-6, 0
Let p be (2 - (6 + -2)) + 958/18. Let t = -51 + p. Factor 0*a + 0*a**3 + t*a**5 + 0*a**2 + 0 - 2/9*a**4.
2*a**4*(a - 1)/9
Let a(u) be the first derivative of 1/12*u**4 + 0*u**2 - 1/18*u**6 - 19 + 0*u**5 + 0*u**3 + 0*u. Factor a(h).
-h**3*(h - 1)*(h + 1)/3
Let a(j) be the third derivative of 1 + 0*j**3 - 1/180*j**6 - 4/9*j**4 - 8*j**2 + 4/45*j**5 + 0*j. Factor a(z).
-2*z*(z - 4)**2/3
Let a(g) = -g**2 + 41*g - 206. Let k be a(6). Let w(m) be the first derivative of -2/5*m**5 + 6 + 5*m**2 + 4*m - 1/2*m**k + 2*m**3. Factor w(s).
-2*(s - 2)*(s + 1)**3
Let n(c) = c**3 - 7*c**2 + 12*c + 3. Let m be n(3). Factor -2*w**5 - 12*w**m - 302*w**2 + 302*w**2 - 14*w**4.
-2*w**3*(w + 1)*(w + 6)
Let j = 121359/13 - 9331. Let -122/13*r**2 + j*r + 8/13*r**5 - 8/13 + 116/13*r**3 - 50/13*r**4 = 0. Calculate r.
1/4, 1, 2
Let k be -4*(-2)/(-36) + (-10494)/405. Let b = 139/5 + k. Determine r, given that 0 + b*r**2 - 2/3*r = 0.
0, 2/5
Factor -3*c**2 + 29*c