2, 0, 1
Let d(l) = -23*l**4 - l**3 - 2*l**2 + 2*l. Let u(p) = 139*p**4 + 6*p**3 + 13*p**2 - 13*p. Let w(h) = 26*d(h) + 4*u(h). Determine n, given that w(n) = 0.
-1/21, 0
Suppose -512*u - 1089 = -511*u. Let w = -1088 - u. Solve -5/4*b**3 + 1/4*b**5 + b + 5/4*b**2 - 1/4*b**4 - w = 0 for b.
-2, -1, 1, 2
Suppose -b + 2 = -8. Factor n - 8*n**2 - 8*n**3 - 21 + 9 - 23*n + b*n**3.
2*(n - 6)*(n + 1)**2
Let k be 5/(-3) - 495/(-135). Factor -1 + 3*z**2 - 2*z**2 + 61 + 62*z + 2*z**2 - z**k.
2*(z + 1)*(z + 30)
Let f(v) be the first derivative of -v**6/135 + 2*v**5/45 - 2*v**4/27 - 58*v - 53. Let l(b) be the first derivative of f(b). Find c such that l(c) = 0.
0, 2
Let o(f) = f**2 + 4*f - 3. Let p be o(-5). Suppose 2*b - b = p. Solve 7*n**2 - 130*n + 130*n - 4*n**b = 0 for n.
0
Let -144*s + 7747*s**5 - 172*s**3 + 2*s**4 + 284*s**2 + 29*s**4 - 7746*s**5 = 0. What is s?
-36, 0, 1, 2
Factor -249*q**2 + 618*q**2 - 303*q**2 - q**3 + 648 + 238*q + 185*q.
-(q - 72)*(q + 3)**2
Suppose 0 = -3*w, 0 = -b - w + 1 + 4. Let o(s) = -485*s**3 + 280*s**2 - 45*s. Let x(n) = 242*n**3 - 140*n**2 + 23*n. Let a(u) = b*x(u) + 3*o(u). Factor a(z).
-5*z*(7*z - 2)**2
Let a(c) be the third derivative of 0 + 1/4*c**3 + 1/24*c**6 + 1/12*c**5 + 13*c**2 + 1/224*c**8 - 13/48*c**4 + 0*c - 13/420*c**7. Suppose a(h) = 0. What is h?
-1, 1/3, 1, 3
Let b(i) be the third derivative of -1/60*i**6 + 0*i**3 - 5*i**2 + 1/3*i**5 + 0 + 0*i**4 + 0*i. Solve b(d) = 0 for d.
0, 10
Find a such that 10/7*a**3 - 464/7 - 1384/7*a - 556/7*a**2 = 0.
-2, -2/5, 58
Let p(r) = r**4 + r**2 - r - 1. Suppose -20*j + 16*j = 0. Suppose j*i = -2*i - 2. Let y(t) = 2*t**3 - 6*t**2 + 2*t + 2. Let s(a) = i*y(a) - 2*p(a). Factor s(g).
-2*g**2*(g - 1)*(g + 2)
Determine c so that -4882/11 + 444*c - 2/11*c**2 = 0.
1, 2441
Let w(l) be the first derivative of l**5/15 + 11*l**4/6 + 12*l**3 + 111*l**2/2 - 222. Let f(q) be the second derivative of w(q). Factor f(c).
4*(c + 2)*(c + 9)
Suppose 2*s = 4*s. Factor 2*p + 0*p**3 - 7*p**4 - 3*p**5 - 27*p**2 + 30*p**2 + s*p - 3*p**3.
-p*(p + 1)**3*(3*p - 2)
Let d(g) be the first derivative of 5*g**3 - 7330*g**2 + 4885*g + 3483. What is m in d(m) = 0?
1/3, 977
Let o(t) be the second derivative of t**4/6 - 2*t**3 - 280*t**2 - 1789*t. Factor o(k).
2*(k - 20)*(k + 14)
Factor -3*i**3 + 756*i - 1312 + 7*i**3 - 648 - 96*i**2.
4*(i - 10)*(i - 7)**2
Let 22/9*v**2 + 0 + 16/9*v**3 - 2/9*v**4 - 4*v = 0. Calculate v.
-2, 0, 1, 9
Let h(s) be the third derivative of -7/24*s**6 + 24*s**2 - 1/6*s**5 + 35/24*s**4 + 5/3*s**3 + 5 + 0*s. Factor h(d).
-5*(d - 1)*(d + 1)*(7*d + 2)
Let p(h) be the second derivative of 1/5*h**5 + 0*h**2 + 8 + 2/45*h**6 - 2/3*h**3 - 2*h - 1/9*h**4. Let p(g) = 0. Calculate g.
-3, -1, 0, 1
Let -10*u - 1/3*u**3 - 17/3*u**2 + 0 = 0. Calculate u.
-15, -2, 0
Let x be (-18)/(-8)*(7506/(-243) - -31). Factor 7/4*w - x*w**2 - 5/2.
-(w - 5)*(w - 2)/4
Factor -23/2*j**2 + 0 + 25*j - 1/2*j**3.
-j*(j - 2)*(j + 25)/2
Determine x so that -24*x**4 + 33*x**3 + 52*x**2 + 12*x + 14*x**2 - 24 + 17*x**4 - 80*x = 0.
-2, -2/7, 1, 6
Let h(s) be the second derivative of 1/84*s**4 + 5/6*s**3 + 0 - 49*s + 17/7*s**2. Factor h(g).
(g + 1)*(g + 34)/7
Factor 67*w - 57*w + 68*w + 82*w - 4*w**2.
-4*w*(w - 40)
Suppose 2*m = -3*v + 137, -4*m + 14 = v - 15. Let z = 53 - v. Find w, given that 8*w + 0*w**3 - 4*w + z*w**3 + 8*w**2 = 0.
-1, 0
Factor -21*r**3 - 4*r**3 + 2326*r**2 + r**3 + 1778*r**2 + 2097152 + 20*r**3 - 1056768*r.
-4*(r - 512)**2*(r - 2)
Let o be (-19)/6 + (5/5 - -3). Let g(z) be the second derivative of 5*z**2 - 5/12*z**4 - 2*z + 0 + o*z**3. Factor g(v).
-5*(v - 2)*(v + 1)
Let t(r) be the third derivative of 17/14*r**4 + 0*r - 4/105*r**5 - 1/210*r**6 - 60/7*r**3 + 0 - 220*r**2. Factor t(w).
-4*(w - 3)**2*(w + 10)/7
Let k be (-21646)/(-1343) + 1 + -17. Determine s so that k*s**3 + 8/17*s + 0 + 8/17*s**2 = 0.
-2, 0
Let g(p) be the second derivative of -p**5/15 - 55*p**4 - 40672*p**3/3 + 123008*p**2/3 + 119*p + 1. Suppose g(c) = 0. Calculate c.
-248, 1
Suppose -8*r = 34*r + 1134. Let g be r/210*-5*14/12. Let 0 + 3/4*w**4 + 0*w + 3/4*w**3 - g*w**2 - 3/4*w**5 = 0. Calculate w.
-1, 0, 1
Let c(k) be the second derivative of 60*k + 0 + 0*k**2 + 0*k**3 + 1/8*k**4 - 3/40*k**5. Determine g so that c(g) = 0.
0, 1
Let s = -416 - -420. Factor -9*w**s - 160 - 3*w**5 + 160 + 12*w**3 + w**4 - w**5.
-4*w**3*(w - 1)*(w + 3)
Find w such that -51/8*w - 63/4 - 9/8*w**3 + 67/8*w**2 - 1/8*w**4 = 0.
-14, -1, 3
Suppose 0 = 4*z + 16*z - 500. Let -z*a**2 + 12*a**3 + 0*a**3 + 5*a**2 + 8*a + 0*a**2 = 0. Calculate a.
0, 2/3, 1
Suppose 8*m - 3*i + 45 = 11*m, 3*m = 4*i - 46. Suppose 7*r - 1/2*r**m - 49/2 = 0. What is r?
7
Let j(p) be the second derivative of p**6/720 + 3*p**5/80 + 7*p**4/24 + p**3 + p**2/2 - 4*p - 22. Let l(d) be the second derivative of j(d). Factor l(o).
(o + 2)*(o + 7)/2
Factor 13*s**2 - 42*s**2 + 16*s**2 + 8*s**2 - 865*s.
-5*s*(s + 173)
Let t(r) be the first derivative of 8/9*r**2 + 2/27*r**3 + 14/9*r - 25. Factor t(a).
2*(a + 1)*(a + 7)/9
Let o(p) = 5*p**5 - 25*p**4 + 29*p**3 + 153*p**2 + 162*p + 9. Let d(x) = x**5 - 6*x**4 + 7*x**3 + 38*x**2 + 40*x + 2. Let n(a) = -9*d(a) + 2*o(a). Factor n(q).
q*(q - 3)*(q + 2)**2*(q + 3)
Let a(p) = 7342*p - 1. Let v(b) = b**2 + 2*b + 1. Let g be v(-2). Let o be a(g). Determine l so that -8*l**3 - 7341 + 4*l**5 + o + 4*l**4 = 0.
-2, 0, 1
Let d(c) be the second derivative of -23*c - 28*c**2 - 1/35*c**5 - 1 - 2*c**3 + 4/7*c**4. Suppose d(g) = 0. What is g?
-2, 7
Let y(v) be the third derivative of 21*v**2 + 0*v + 0 + 21/8*v**4 - 1/40*v**5 - 441/4*v**3. Factor y(u).
-3*(u - 21)**2/2
Suppose 0 = -46*o + 50*o - 360. Factor -8 + 22*x + 43 - 66 - x**2 - o.
-(x - 11)**2
Let m = 1217/141 + -390/47. Let k(d) be the second derivative of -34*d + 3/10*d**5 - m*d**4 + 0*d**2 + 0 - 2/15*d**6 + 1/6*d**3 + 1/42*d**7. Factor k(t).
t*(t - 1)**4
Let p(g) be the second derivative of -g**6/120 - 21*g**5/80 - 31*g**4/24 + 28*g**3 + 180*g**2 + 697*g + 1. Find j such that p(j) = 0.
-12, -2, 5
Let l(r) = 3*r**3 - 3*r**2 + 45*r. Let w(n) = -3*n**3 + 4*n**2 - 61*n. Let i(d) = 4*l(d) + 3*w(d). Determine o, given that i(o) = 0.
-1, 0, 1
Let f = 5/9022 + 17999/81198. Factor 722/9 + f*o**2 + 76/9*o.
2*(o + 19)**2/9
Let t(z) = -4445*z + 155578. Let n be t(35). What is w in 0*w + 9/4*w**2 + 1/4*w**n + 0 = 0?
-9, 0
Let y(k) be the third derivative of 1/4*k**6 + 0*k + 1/126*k**7 + 250/9*k**3 - 25/2*k**4 + 72*k**2 + 0 + 61/36*k**5. Find m such that y(m) = 0.
-10, 1
Let d be (-65)/(-9) + (-2340)/1053. Suppose 17/4*l + 7/2*l**2 + 0*l**3 - 1/4*l**d - l**4 + 3/2 = 0. Calculate l.
-3, -1, 2
Suppose -104 = 1121949*n - 1122001*n. Determine q, given that 5/7*q - 2/7*q**n - 1/7*q**4 + 3/7 - 6/7*q**3 + 1/7*q**5 = 0.
-1, 1, 3
Let v(w) be the first derivative of w**6/3 + 2*w**5/5 - w**4 + 715. Factor v(g).
2*g**3*(g - 1)*(g + 2)
Let h(f) be the second derivative of 0 - 1600*f**2 - 20*f - 161/24*f**4 + 1640/3*f**3 + 1/40*f**5. Factor h(v).
(v - 80)**2*(v - 1)/2
Let d(z) be the third derivative of z**6/80 + 17*z**5/20 - 3770*z**2. Suppose d(f) = 0. Calculate f.
-34, 0
Let x be (-31)/(-6) + 32/(-192). Factor -x*z**4 + 7*z + 15*z**2 - 34*z + 16*z + 21*z.
-5*z*(z - 2)*(z + 1)**2
Let w(m) = 16*m**3 + 58*m**2 + 242*m + 182. Let c(f) = -87*f**3 - 291*f**2 - 1212*f - 909. Let u(v) = -2*c(v) - 11*w(v). Solve u(p) = 0.
-23, -4, -1
Factor 51/5 + 4*n + 1/5*n**2.
(n + 3)*(n + 17)/5
Suppose u - 3*h - 1 = 4, 1 = -u - 3*h. Suppose 5*o + 3 = 3*y + 7, 2*o + u*y - 8 = 0. Solve -g + 437*g**o - 437*g**2 + g**3 = 0.
-1, 0, 1
Let z(h) be the third derivative of -h**6/120 - h**5/30 + 13*h**4/8 - 12*h**3 + 808*h**2. Determine k so that z(k) = 0.
-8, 3
Let b(p) be the third derivative of 0*p + 7/2*p**3 - 12*p**2 + 10 + 1/4*p**5 - 1/40*p**6 + 13/8*p**4. Let b(d) = 0. Calculate d.
-1, 7
Let 130*p**2 - 748 - 189*p + 946 - 28*p**2 - 114*p = 0. Calculate p.
33/34, 2
Solve 118/7*n**3 + 38/7*n + 4/7 + 62/7*n**4 + 12/7*n**5 + 102/7*n**2 = 0 for n.
-2, -1, -1/6
Let y = 96899 - 96897. Factor 6/5*n**3 - 6/5*n**y + 6/5 - 6/5*n.
6*(n - 1)**2*(n + 1)/5
Let c(i) be the first derivative of -i**5/360 - i**4/48 - i**3/18 + 29*i**2 + 2. Let h(z) be the second derivative of c(z). Suppose h(v) = 0. What is v?
-2, -1
Suppose -4*y + 29 = -5*w, 3*y + 3*w = 2*w - 2. Let c be 44 