**t + 8*a = 0. Calculate a.
3
Factor 446/7*v - 2/7*v**2 + 64.
-2*(v - 224)*(v + 1)/7
Let j = -488 - -500. Suppose j*n = 14*n. Factor 1/4*w**3 + 0*w**2 + 0 - w**4 + n*w.
-w**3*(4*w - 1)/4
Let k be (-918)/(-108)*-6*2/(-34). Factor 0*l**2 + 0 - 1/3*l**4 + 0*l - 1/6*l**5 + 4/3*l**k.
-l**3*(l - 2)*(l + 4)/6
Suppose -380*w - 5*m = -382*w + 3113, 2*m + 4730 = 3*w. Determine a so that 384 + 387/2*a**2 + 6*a**3 + w*a = 0.
-16, -1/4
Suppose y + 4*o + 15 = 0, y - 2*y - 2*o - 7 = 0. Let d be (y - -49)*(-1 - (-27)/15). Solve 30*i**2 + d + 2*i**3 - 60*i + 4*i**3 - 11*i**3 = 0 for i.
2
Let g(u) be the second derivative of u**7/105 + u**6/30 - u**5/10 - 2*u**4/3 - 4*u**3/3 + 56*u**2 - 83*u. Let h(i) be the first derivative of g(i). Factor h(p).
2*(p - 2)*(p + 1)**2*(p + 2)
Find n, given that 356*n**2 - 74273*n + 42005*n + 2*n**3 - 66248 + 47374*n = 0.
-91, 4
Let x = -694 - -681. Let p be x/(-4) + (-39)/156. Find g, given that 0 + 3/2*g**4 + 0*g + 5/2*g**p - 3/2*g**2 - 5/2*g**5 = 0.
-1, 0, 3/5, 1
Let v(m) = -12*m - 106. Let x be v(-9). Factor -7*g**2 - 20*g + 15*g**2 + 7*g**x + 10*g**2 - 5*g**3.
-5*g*(g - 4)*(g - 1)
Let o be (-3)/(14130/(-26))*(60 + 9). Let x = o - -3/157. Factor 2/5 - 2/5*i**2 - 2/5*i + x*i**3.
2*(i - 1)**2*(i + 1)/5
Let m(a) be the first derivative of -a**3/3 + 12*a**2 - 2146. Factor m(z).
-z*(z - 24)
Let q = 22194956/165 + -134514. Let b = 16/15 - q. Determine u, given that -b*u**2 + 6/11 + 4/11*u = 0.
-1, 3
Let y = 90987/440 - 2977/40. Find w such that -y*w + 1568/11 + 10*w**4 - 1678/11*w**2 + 2/11*w**5 + 1454/11*w**3 = 0.
-28, -1, 1
Factor 1/2*z**2 + 99/2*z + 49.
(z + 1)*(z + 98)/2
Let l be 9/(-4)*((-74140)/(-1485) - 50). Suppose 0*j**3 - l*j**4 + 0 - 1/3*j**5 + 0*j**2 + 0*j = 0. What is j?
-1/2, 0
Let c(i) be the second derivative of -1/4*i**4 + 27*i**2 - 2 - 7/2*i**3 + 10*i. Determine p so that c(p) = 0.
-9, 2
Let p(a) be the first derivative of -a**4/16 + 3*a**3/2 + 11*a**2 - 157. Factor p(u).
-u*(u - 22)*(u + 4)/4
Let y(b) be the third derivative of b**2 + 23/960*b**6 + 1/240*b**7 + 17/192*b**4 + 5/24*b**3 + 32 - 19/160*b**5 + 0*b. Find d such that y(d) = 0.
-5, -2/7, 1
Let h(r) = r**2 + 2*r - 1. Let w be h(-3). Suppose 2 = -w*q + 10. Factor 16*d**2 - q - 9*d**2 + d**2 - 4*d**4.
-4*(d - 1)**2*(d + 1)**2
Let c be (((-13)/(-390))/(6/(-10)))/(-1). Let n(r) be the third derivative of -1/90*r**5 + 0 + 7*r**2 - 1/9*r**3 + 0*r + c*r**4. Solve n(m) = 0.
1
Let w(z) = 23*z + 28. Let f be w(-1). Factor -3*d**5 - 18*d**3 + 11*d**4 + 13*d**4 - 4*d - 120*d**2 + f*d - 76*d + 0*d**5.
-3*d*(d - 5)**2*(d + 1)**2
Let m(q) be the second derivative of -q**6/15 + q**5/5 + q**4/2 - 8*q**3/3 + 4*q**2 - 2294*q. Determine b, given that m(b) = 0.
-2, 1, 2
Let j(r) be the second derivative of -r**9/34020 + r**8/3780 - r**7/1890 - 19*r**4/6 + 62*r. Let w(a) be the third derivative of j(a). Factor w(h).
-4*h**2*(h - 3)*(h - 1)/9
Let u(n) = n**2 + 5*n - 10. Let z be u(3). Suppose 3 - 6*k**2 + 15*k**2 - 9 - z*k**2 - 8*k + 3*k**2 = 0. What is k?
-3, -1
Let n(u) be the second derivative of -1/4*u**5 + 0*u**2 - 5/12*u**4 + 1 + 0*u**3 + 4*u. Factor n(y).
-5*y**2*(y + 1)
Suppose -161*n**3 + 12*n**2 - 33*n**2 + 104*n**3 + 148*n - 56 - 41*n**2 + 9*n**4 = 0. What is n?
-2, 2/3, 7
Let g(u) be the third derivative of 1/1680*u**7 + 0 + 0*u + 432*u**3 - 36*u**4 + 9/5*u**5 - 351*u**2 - 1/20*u**6. Factor g(s).
(s - 12)**4/8
Factor -37/6*d - 170/3 - 1/6*d**2.
-(d + 17)*(d + 20)/6
Let x(b) be the first derivative of 284*b**3/3 - 572*b**2 + 32*b + 7786. Determine r, given that x(r) = 0.
2/71, 4
Factor -3/2*z**2 - 99*z - 840.
-3*(z + 10)*(z + 56)/2
Let s = -64 - -45. Let w = -17 - s. Factor -i + w - 5*i**2 + 10*i + 12*i**2.
(i + 1)*(7*i + 2)
Let w be 2 - ((-48)/6)/(-4). Let v be (-68)/(-272) - w/2. Factor 0 + v*j**4 - 1/4*j**3 + j - j**2.
j*(j - 2)*(j - 1)*(j + 2)/4
Let z be 99/6*((-77)/21 + 3). Let w be (-2 - z) + 570/(-76). Determine q, given that -6*q - 9/2*q**4 + 6*q**3 + 3*q**2 + w = 0.
-1, 1/3, 1
Let j(b) be the second derivative of -b**8/4480 - b**7/120 - 11*b**6/160 + b**4/6 + 23*b**2/2 + 21*b - 2. Let l(u) be the third derivative of j(u). Factor l(o).
-3*o*(o + 3)*(o + 11)/2
Suppose -2*u - 3*u - 300 = 0. Let t = u + 80. Solve -t + b**2 - 18*b - 5*b**2 + b**2 + 5 = 0 for b.
-5, -1
Let a(x) be the second derivative of -1/20*x**4 - 2883/10*x**2 - 31/5*x**3 + 1 + 134*x. Factor a(j).
-3*(j + 31)**2/5
Let g = 260 + -258. Factor 16*d**g - 25 + 1798*d - 2*d**3 - 3 - 1808*d.
-2*(d - 7)*(d - 2)*(d + 1)
Let g(p) be the third derivative of p**6/300 + 10*p**5/3 - p**4/60 - 100*p**3/3 - 6970*p**2. Factor g(s).
2*(s - 1)*(s + 1)*(s + 500)/5
Let i(u) = 72*u**4 - 1576*u**3 - 3496*u**2 + 14332*u + 52. Let g(q) = 7*q**4 - 150*q**3 - 333*q**2 + 1365*q + 5. Let a(s) = -52*g(s) + 5*i(s). Factor a(c).
-4*c*(c - 2)*(c + 5)*(c + 17)
Let g = 12/136409 - -272782/409227. Factor 32/3 + 6*b**2 + 16*b + g*b**3.
2*(b + 1)*(b + 4)**2/3
Suppose -2*r = 10 - 14. Factor z - r*z**2 + z**3 - 36338 + 36338.
z*(z - 1)**2
Let l = 437064 + -437064. Factor 2/17*f**4 + 0 - 6/17*f**3 + 4/17*f**2 + l*f.
2*f**2*(f - 2)*(f - 1)/17
Let 14/5*p**3 + 16/5*p**2 + 0*p + 0 - 2/5*p**4 = 0. Calculate p.
-1, 0, 8
Let i(v) = -2*v. Let o(a) = 4*a + 1. Let s(k) = -3*i(k) - 2*o(k). Let q(b) = -34*b**2 + 134*b + 18. Let t(p) = 2*q(p) + 2*s(p). Solve t(d) = 0.
-2/17, 4
Solve -1/2*o**4 - 133/2*o**2 + 33*o + 34*o**3 + 0 = 0.
0, 1, 66
Solve -14884/7 + 244/7*a - 1/7*a**2 = 0 for a.
122
Let g(t) be the second derivative of t**10/45360 - t**9/5670 - t**8/2016 + 11*t**4/2 - 20*t. Let u(m) be the third derivative of g(m). Factor u(r).
2*r**3*(r - 5)*(r + 1)/3
Factor 0 + 41/3*m**2 - 14*m + 1/3*m**3.
m*(m - 1)*(m + 42)/3
Let d(h) be the first derivative of -h**5/3 + h**4/3 + 64*h**3/9 + 8*h**2 - 57*h + 25. Let o(n) be the first derivative of d(n). Find z such that o(z) = 0.
-2, -2/5, 3
Let g(c) be the first derivative of -2*c**3/27 - 11*c**2/9 + 52*c/9 + 714. Factor g(t).
-2*(t - 2)*(t + 13)/9
Let w = 59425/24 - 2476. Let v(s) be the first derivative of 0*s - w*s**6 - 1/12*s**3 - 3/20*s**5 + 0*s**2 - 14 - 3/16*s**4. Suppose v(d) = 0. What is d?
-1, 0
Suppose -s**2 + 18496 + 2*s**2 + 430249*s - 430521*s = 0. What is s?
136
Let l(t) be the second derivative of 5*t**4/21 + 82*t**3/3 + 228*t**2/7 - 3253*t. Let l(k) = 0. What is k?
-57, -2/5
Suppose -s + 0*s - 3*g = -3, 4 = 4*s + 4*g. Suppose -19 = -4*k + 5*u, k + s*u = -u + 7. Factor -166 + 2*x**3 - k*x**3 + 166 - 8*x**2 + 4*x**4.
4*x**2*(x - 2)*(x + 1)
Let z = -9934 + 9954. Let r(u) be the third derivative of -z*u**2 - 8/105*u**5 - 11/420*u**6 + 3/245*u**7 + 1/21*u**4 + 0*u + 0 + 0*u**3. Solve r(w) = 0 for w.
-1, 0, 2/9, 2
Let o(h) be the first derivative of 2*h**5/5 + 25*h**4/4 + 31*h**3/3 - 11*h**2 + 2137. Factor o(s).
s*(s + 2)*(s + 11)*(2*s - 1)
Let c(d) be the second derivative of 1/2*d**3 + 0*d**2 + 0 - 1/6*d**4 - 1/20*d**5 + 86*d. Let c(b) = 0. Calculate b.
-3, 0, 1
Suppose n = 2*t - 3, 8*t - 13 = 3*t - 3*n. Solve 147*x**2 + 0*x**3 + 6 - t*x**3 - 145*x**2 + 10*x = 0.
-1, 3
Let s(h) be the second derivative of h**2 - 20/9*h**3 - 7/15*h**5 + 31/18*h**4 + 1 + 17*h. Factor s(b).
-2*(b - 1)**2*(14*b - 3)/3
Let g(s) be the third derivative of -s**7/70 - 457*s**6/40 + 917*s**5/20 - 459*s**4/8 + 155*s**2 + 3*s. Factor g(f).
-3*f*(f - 1)**2*(f + 459)
Let v(p) = -2*p**2 + 2*p + 26. Let t be v(-3). What is x in 23 + 34 + 31 - 172*x - 8*x**t + 0*x**2 = 0?
-22, 1/2
Let q(m) = -8*m**3 - 6*m**2 - 4*m + 3. Let k(t) = 7*t**3 + 6*t**2 + 3*t - 2. Suppose l - b = 5, 0*b + 3*b = 2*l - 12. Let y(u) = l*k(u) + 2*q(u). Factor y(f).
f*(f + 1)*(5*f + 1)
Suppose -20*m - 44*m - 29*m + 12*m = 0. Let k(j) be the second derivative of m + 32*j + 1/6*j**6 - j**5 + 0*j**2 + 5/4*j**4 + 0*j**3. Factor k(q).
5*q**2*(q - 3)*(q - 1)
Let k(q) be the second derivative of 10*q**6/9 + 724*q**5/3 + 2153*q**4/3 + 6872*q**3/9 + 1144*q**2/3 - 1303*q. Suppose k(f) = 0. Calculate f.
-143, -1, -2/5
Factor 7275*n**3 + 7278*n**3 + 1804720640 + 10680*n**2 - 14558*n**3 - 7604160*n.
-5*(n - 712)**3
Factor -5*f**2 + 3175*f - 54789 + 1190*f + 63539.
-5*(f - 875)*(f + 2)
What is p in -81/4*p**3 + 0*p + 0 + 1/4*p**4 + 79/2*p**2 = 0?
0, 2, 79
Solve -643*g - 270*g**3 - 1037*g**2 - 257*g**3 - 248*g**2 - 114*g**3 + g**4 = 0 for g.
-1, 0, 643
Let r = -