n) = 0. What is n?
-2/9, 0, 1
Let k(d) be the first derivative of -5*d**7/42 - d**6/3 - d**5/4 - 10*d - 1. Let w(r) be the first derivative of k(r). Factor w(o).
-5*o**3*(o + 1)**2
Let o(k) be the second derivative of k**7/12600 - k**6/1800 - k**5/200 - k**4/2 + 18*k. Let n(b) be the third derivative of o(b). Factor n(j).
(j - 3)*(j + 1)/5
Let g = 323/2 - 3227/20. Let u(t) be the second derivative of -1/4*t**4 + 0 - g*t**5 - 1/30*t**6 - 1/6*t**3 + 3*t + 0*t**2. Factor u(k).
-k*(k + 1)**3
Let p(v) = v**3 + 3*v**2 - 4*v + 6. Let r be (10 - 4)*8/12. Let l(h) = h**3 + 5*h**2 - 5*h + 7. Let w(m) = r*p(m) - 3*l(m). Factor w(n).
(n - 3)*(n - 1)*(n + 1)
Let v(p) be the first derivative of -12*p**5/5 + 11*p**4 - 16*p**3 + 8*p**2 + 218. Factor v(j).
-4*j*(j - 2)*(j - 1)*(3*j - 2)
Let h = -23 + 43. Factor h*q**3 - 45*q**3 + 10*q**2 + 20*q**3.
-5*q**2*(q - 2)
Let p(j) = -j - 77. Let y be p(-19). Let h = 60 + y. Let 1/6*v**h - 1/2 + 1/3*v = 0. Calculate v.
-3, 1
Let 0 + 1/4*r**3 + 7/2*r + 15/4*r**2 = 0. What is r?
-14, -1, 0
Let l(y) be the first derivative of -2/9*y**2 + 2/27*y**3 + 24 + 2/9*y. Determine m, given that l(m) = 0.
1
Let z(l) be the second derivative of -l**4/66 + 32*l**3/11 - 2304*l**2/11 - 169*l. Factor z(s).
-2*(s - 48)**2/11
Suppose -8*h = -5*h - 4*g - 5, -5*h + 18 = 3*g. Let c be (-1)/(0 - (-1)/(-2)). Factor w**5 - 13*w**h + 16*w**3 + 6*w**4 + c*w**5.
3*w**3*(w + 1)**2
Suppose i - 20 = -4*l, 15 = 4*i - 2*l + 5*l. Let t(q) be the third derivative of -1/480*q**6 - 1/120*q**5 + 2*q**2 + 0 + 0*q + i*q**4 + 0*q**3. Factor t(r).
-r**2*(r + 2)/4
Let y(t) be the third derivative of t**7/1050 - 17*t**6/300 + 289*t**5/300 - 2*t**2 - 57*t. Factor y(k).
k**2*(k - 17)**2/5
Factor -37*m**2 + 47*m + 0*m**3 - 7*m**2 - 9*m**3 + 13*m**3 - 7*m.
4*m*(m - 10)*(m - 1)
Suppose 0 = -3*b - 5*j + 11, 0*j = 3*b + j - 7. Factor -62*t**2 - 20*t**3 + 16 - 35 + 12 + 19 - b*t.
-2*(t + 3)*(2*t + 1)*(5*t - 2)
Let t(r) be the second derivative of -r**7/504 - 11*r**4/6 + 19*r. Let d(x) be the third derivative of t(x). Find w, given that d(w) = 0.
0
Let w(j) be the third derivative of j**8/112 - j**7/1260 - j**6/90 + 19*j**5/60 + 14*j**2. Let q(c) be the third derivative of w(c). Factor q(z).
4*(5*z + 1)*(9*z - 2)
Let a = -11689/105 - -334/3. Let x(n) be the third derivative of 0*n - a*n**7 + 0*n**5 + 0*n**4 + 1/60*n**6 + 0 + 0*n**3 - 4*n**2. Find w such that x(w) = 0.
0, 1
Suppose -4*g = 2*s - 118, 4*s + 4*g - 218 = 5*g. Let d = -51 + s. Determine u so that u**3 - 3/2*u**d + 1/2*u**5 - 3/2*u + 1/2 + u**2 = 0.
-1, 1
Suppose -2*g = w - 3*w - 4, 8 = 4*g + 2*w. Suppose -h**2 + 16*h - 3*h**g - 1 + 21 = 0. What is h?
-1, 5
Let b be (41/(-4) + 5 - -3) + 3. Find v, given that 3/4*v**2 - 3/2*v + b = 0.
1
Let o = 96737/26 - 3720. Let n(a) be the first derivative of 4/13*a + 11/13*a**2 + 2/13*a**5 + 2 + o*a**4 + 14/13*a**3. Factor n(r).
2*(r + 1)**3*(5*r + 2)/13
Let a(j) = -13*j**3 - 217*j**2 - 38*j. Let n(t) = -27*t**3 - 436*t**2 - 74*t. Let y(g) = 9*a(g) - 4*n(g). Factor y(q).
-q*(q + 23)*(9*q + 2)
Let h(d) be the second derivative of -1/4*d**4 + 0*d**2 + 1/10*d**6 - 3/20*d**5 + 7*d + 1/2*d**3 + 0. What is g in h(g) = 0?
-1, 0, 1
Determine z, given that 128*z**2 - 144*z**3 + 0 + 0*z + 33/2*z**4 - 1/2*z**5 = 0.
0, 1, 16
Determine i so that -260*i**2 - 7*i + 42*i + 370*i**2 + 15*i**3 = 0.
-7, -1/3, 0
Let z(l) = 3*l**2 - 6*l + 3. Let t(f) = 2*f**2 - 8*f + 3. Let p(o) = -o**2 + o - 1. Let d(r) = -4*p(r) + t(r). Let w(j) = 3*d(j) - 7*z(j). Factor w(h).
-3*h*(h - 2)
Let p(q) be the second derivative of -56*q**5/55 - 12*q**4/11 - 5*q**3/11 - q**2/11 - 11*q + 18. Factor p(r).
-2*(4*r + 1)**2*(7*r + 1)/11
Let x = -17 - -19. Solve -22*g**2 + g**4 + 21*g**3 + 4*g + g**4 - 7*g**5 + x*g**2 = 0.
-2, 0, 2/7, 1
Find m such that 34/13*m**3 + 0*m + 4/13*m**4 + 16/13*m**2 + 0 = 0.
-8, -1/2, 0
Let b(j) be the third derivative of j**6/300 + 29*j**5/75 - 59*j**4/60 - 12*j**2 + 2. Factor b(c).
2*c*(c - 1)*(c + 59)/5
Let l = -54 + 60. Let z(w) = 14*w**2 + 23*w + 5. Let b(y) = y**3 - y + 1. Let h(v) = l*b(v) + 2*z(v). Factor h(r).
2*(r + 2)**2*(3*r + 2)
Suppose -25 + 5/3*x**2 - 70/3*x = 0. What is x?
-1, 15
Let k(c) = 2*c - 5. Let m(t) = -t + 2. Let y(p) = -3*k(p) - 5*m(p). Let q be y(2). Factor 2/7*a**q + 0 + 0*a**2 + 0*a + 2/7*a**4.
2*a**3*(a + 1)/7
Let g(d) = d**2 + 14*d + 45. Let i(w) = w**2 + 14*w + 44. Let l(h) = 5*g(h) - 4*i(h). Factor l(k).
(k + 7)**2
Suppose 8*c - 3*c = -75. Let o = 17 + c. Factor -a**o + 41*a + 2 - 37*a - 6.
-(a - 2)**2
Let y(i) = -i**2 - 4*i + 5. Let b be y(-4). Suppose -t - b*g + 6 = -4, t - 2 = 3*g. What is s in -48*s + s**4 - 33*s**3 - 5 + t*s**4 + 17 + 63*s**2 = 0?
1/2, 1, 2
Solve 4/3*f**4 + 8*f**3 - 32/3 - 8*f + 28/3*f**2 = 0 for f.
-4, -2, -1, 1
Solve 10*c**2 - 4496 + 4*c**2 + c**2 + 4481 - c + c**3 = 0.
-15, -1, 1
Solve -40/13*n + 0 - 42/13*n**2 - 2/13*n**3 = 0 for n.
-20, -1, 0
Let r = 1146/11 - 317431/3047. Let h = 1381/1108 + r. Suppose -1/2 + h*o**3 - 5/4*o + 3/4*o**4 - 1/4*o**2 = 0. What is o?
-1, -2/3, 1
Let o = -3446/27 - -1150/9. Let j(l) be the second derivative of 1/90*l**5 + 0 + 0*l**2 + 2/27*l**4 + o*l**3 + 11*l. Factor j(g).
2*g*(g + 2)**2/9
Let y be -4*(-5)/(-40)*436. Let d = y + 220. Factor 1/7 + 4/7*q**3 + 6/7*q + 9/7*q**d.
(q + 1)**2*(4*q + 1)/7
Let p = -1/8600 - -34403/25800. Suppose 2*z = 7 - 3. Let -2/3*n**4 + 2*n**z + 10/3*n + p - 2/3*n**3 = 0. What is n?
-1, 2
Let v = -113 - -116. Factor 23*q**3 - q**5 - 12*q**3 - 10*q**v.
-q**3*(q - 1)*(q + 1)
Let f be 189*(1 + 4/(-6)). Let r = -61 + f. Factor -1/3*t**r - 4/3 - 4/3*t.
-(t + 2)**2/3
Let l(b) = b**2 - b + 3. Suppose q = 4*q. Let a be l(q). Factor -u**3 - 6*u**3 + 6*u**a.
-u**3
Let v(y) be the first derivative of -10 - 4/3*y**3 - 6*y**2 + 0*y. Determine l, given that v(l) = 0.
-3, 0
Let c(s) be the second derivative of -3*s**5/100 - s**4/10 + 2*s**3/5 + 12*s**2/5 + 13*s + 1. Factor c(b).
-3*(b - 2)*(b + 2)**2/5
Let r = 17 - 15. Factor -40 - k**2 + 9*k**r + 20*k + 2*k**2 - 5*k**3.
-5*(k - 2)**2*(k + 2)
Let v = 217/40 - 41/8. Let s = 9/20 + v. Let 3/4*b - 3/2*b**2 - 3/2*b**3 + s + 3/4*b**4 + 3/4*b**5 = 0. What is b?
-1, 1
Factor 1024/7 + 128/7*n**3 + 2/7*n**5 - 4*n**4 - 128/7*n**2 - 512/7*n.
2*(n - 4)**4*(n + 2)/7
Let u(z) = z + 13. Let k be u(-9). Suppose 2*n = -k*n + n. Factor 2/7*p**5 + n - 2/7*p**4 + 0*p**3 + 0*p**2 + 0*p.
2*p**4*(p - 1)/7
Let p(k) be the first derivative of k**6/9 - k**4/6 + 132. Let p(u) = 0. Calculate u.
-1, 0, 1
Let m(r) be the second derivative of 57*r**4/4 - 61*r**3/2 + 6*r**2 + 485*r. Suppose m(w) = 0. What is w?
4/57, 1
Suppose 37 = -2*n + 11. Let o(d) = 2*d**2 + 25*d - 13. Let i be o(n). What is t in 2/13*t**3 + i*t**2 + 0 + 0*t - 2/13*t**4 = 0?
0, 1
Let c be 3*8/(-6) - (13/(-1) + 4). Factor 2/13*w**c - 32/13 + 86/13*w**3 - 146/13*w**2 - 22/13*w**4 + 112/13*w.
2*(w - 4)**2*(w - 1)**3/13
Suppose 192*j + 25*j - 702 = -134*j. Factor -16/3 + 0*k + 4*k**j - 4/3*k**3.
-4*(k - 2)**2*(k + 1)/3
Let w(y) be the third derivative of y**8/1260 - y**7/630 + y**3/3 + 2*y**2. Let k(j) be the first derivative of w(j). Suppose k(t) = 0. Calculate t.
0, 1
Let z be -8*((-49)/14 + 4). Let b be z/(-2) + (-48)/28. Factor 6/7*g + b + 6/7*g**2 + 2/7*g**3.
2*(g + 1)**3/7
Let p(b) be the first derivative of b**5/40 + 7*b**4/32 - 182. Suppose p(q) = 0. Calculate q.
-7, 0
Let s be (-1 - -7)/((90/(-6))/(-5)). Let v = -1335/7 + 191. Factor -10/7*z**3 - 2*z + 4/7 + 18/7*z**s + v*z**4.
2*(z - 2)*(z - 1)**3/7
Let h(z) be the first derivative of 26 + 0*z - 4/15*z**3 - 4/5*z**2. What is m in h(m) = 0?
-2, 0
Let u = 20/31 - 4907/62. Let x = u - -80. Let x + 12*s**2 - 21/2*s**3 + 9/2*s**4 - 27/4*s - 3/4*s**5 = 0. Calculate s.
1, 2
Let d(h) be the second derivative of -2/39*h**3 - 2 + 5/78*h**4 - 1/130*h**5 - 7*h - 8/13*h**2. Factor d(b).
-2*(b - 4)*(b - 2)*(b + 1)/13
Factor -l**3 - 576 + 9*l - 258*l - 279*l + 47*l**2.
-(l - 24)**2*(l + 1)
Let r(c) be the first derivative of 3*c**5/5 - 6*c**3 + 12*c**2 - 9*c - 80. Determine a, given that r(a) = 0.
-3, 1
Let w(a) be the second derivative of -22*a + 1/90*a**5 - 1/27*a**3 - 2/27*a**4 + 4/9*a**2 + 1. Factor w(s).
2*(s - 4)*(s - 1)*(s + 1)/9
Let i(t) be the third derivative of t**6/120 - t**4/24 - 9*t**2. Let b(n) = -6*n**3 + n**2 + 5*n. Let p(m) = -5*b(m) - 15*i