*m**2 - 4/7*m**3 + 8/7*m - 2/7*m**4 - b.
-2*(m - 1)**2*(m + 2)**2/7
Suppose 0*h - 73 = -4*h - 3*a, -4*h = a - 67. Factor -1 - h + 6 + 6*k**2 - k**3 - 21.
-(k - 4)**2*(k + 2)
Let m(d) be the third derivative of d**5/90 + 11*d**4/36 + 10*d**3/9 + 280*d**2 + 1. Factor m(f).
2*(f + 1)*(f + 10)/3
Let h(d) be the third derivative of -d**8/112 + d**7/70 - 11*d**2 + 2. Factor h(f).
-3*f**4*(f - 1)
Let c(u) be the first derivative of 0*u + 0*u**2 + 1/9*u**3 - 7 + 1/12*u**4. Factor c(i).
i**2*(i + 1)/3
Let o(t) be the second derivative of -t**9/1008 - t**8/1344 + t**7/63 - t**6/36 - 4*t**4/3 - 23*t. Let r(g) be the third derivative of o(g). Factor r(v).
-5*v*(v - 1)*(v + 2)*(3*v - 2)
Factor 1 - b**2 + 4 - 9733*b + 9729*b.
-(b - 1)*(b + 5)
Find a such that 350/3*a + 1/3*a**2 + 30625/3 = 0.
-175
Factor -1/4*t**5 - 5/4*t**4 - t**2 - 2*t**3 + 0*t + 0.
-t**2*(t + 1)*(t + 2)**2/4
Factor 70/13*x**3 + 2/13*x**2 + 0 - 12/13*x.
2*x*(5*x - 2)*(7*x + 3)/13
Let f be 2/3 - 2 - (19 + -21). What is k in -3/2*k - 1/6*k**3 + f + k**2 = 0?
1, 4
Let b(o) be the second derivative of -o**4/108 - o**3/18 - o - 259. Factor b(z).
-z*(z + 3)/9
Let s(q) = -2*q**3 - 24*q**2 + 56*q - 35. Let f = -140 + 139. Let a(z) = -z**3 + z - 1. Let g(o) = f*s(o) + 5*a(o). Determine v, given that g(v) = 0.
1, 2, 5
Let x = 6 + 1. Let q(t) = t**2 - 12*t - 23. Let o(h) be the first derivative of 4*h**3/3 - 37*h**2/2 - 68*h - 3. Let w(d) = x*q(d) - 2*o(d). Factor w(k).
-(k + 5)**2
Let l(b) be the second derivative of b**4/60 - b**3/30 - 6*b**2/5 - b + 14. Suppose l(h) = 0. Calculate h.
-3, 4
Suppose -156 + 167/3*p**2 + 8*p**3 + 92*p + 1/3*p**4 = 0. Calculate p.
-13, -6, 1
Let b(i) be the third derivative of 1/15*i**5 + 0*i**3 + 0*i + 0 + 1/60*i**6 - 1/105*i**7 + 0*i**4 + 11*i**2. What is s in b(s) = 0?
-1, 0, 2
Let x(k) be the first derivative of 0*k**4 + 1 - 2/9*k**3 + 0*k**2 + 2/15*k**5 + 0*k. Factor x(m).
2*m**2*(m - 1)*(m + 1)/3
Factor -3/4 - 23/4*g**4 + 17/4*g + 5/4*g**5 - 19/2*g**2 + 21/2*g**3.
(g - 1)**4*(5*g - 3)/4
Let d be ((-99)/(-40) - 3)/((-15)/20). Determine i, given that -1/10*i**3 - 3/2*i - 9/10 - d*i**2 = 0.
-3, -1
Let p(x) be the third derivative of 0*x + 1/2*x**4 + 0 - 29/360*x**6 + 4/9*x**3 + 13*x**2 - 1/30*x**7 + 1/18*x**5 - 1/252*x**8. Solve p(s) = 0 for s.
-2, -1/4, 1
Let u(a) be the first derivative of -a**5 + 25*a**4/4 - 35*a**3/3 + 15*a**2/2 - 12. Factor u(n).
-5*n*(n - 3)*(n - 1)**2
Let h be (-62517)/(-2184) + -1*18. Let n = -743 - -3001/4. Solve 53/4*o**3 - h*o**4 - n*o**2 + 13/8*o - 1/8 + 25/8*o**5 = 0.
1/5, 1
Let w = -1335 - -78769/59. Let g = w - -106/177. Factor u**4 - u**2 + 0 + g*u - 2/3*u**3.
u*(u - 1)*(u + 1)*(3*u - 2)/3
Suppose q + 13 = 5*b, -5*q + 13 = -3*b + 4*b. Let p be (8/(-54))/(66/(-18) - -3). Factor -8/9*l + p*l**q + 8/9.
2*(l - 2)**2/9
Let j = 1149 - 8041/7. Determine y so that -1/7*y**2 - j*y + 0 + 1/7*y**3 = 0.
-1, 0, 2
Suppose -5*p - 25 = -4*a, -3*a + 3*p = -7*a - 15. Suppose -14 = -5*y + q, -3*q + a*q - 12 = -5*y. Factor 2/5*o**y - 6/5*o + 4/5 + 0*o**2.
2*(o - 1)**2*(o + 2)/5
Factor 7*s**3 - 16*s**4 - 238026*s**5 + 238024*s**5 - 21*s**3.
-2*s**3*(s + 1)*(s + 7)
Let i(p) be the second derivative of 2*p**2 + 10/3*p**3 + 0 + 7/4*p**4 - 40*p. Factor i(b).
(3*b + 2)*(7*b + 2)
Let x(z) be the first derivative of 5/7*z + 19 - 1/21*z**3 - 2/7*z**2. Factor x(v).
-(v - 1)*(v + 5)/7
Find y such that 86*y**3 - 142*y**2 - 256 - 66*y**3 + 10*y**2 - y**4 + 320*y = 0.
2, 8
Let g(r) be the first derivative of r**5 - 5*r**4 - 5*r**3/3 + 10*r**2 + 57. Find s, given that g(s) = 0.
-1, 0, 1, 4
Suppose -4*j**3 + 125*j**2 - 63*j**2 - 74*j**2 + 16*j = 0. Calculate j.
-4, 0, 1
Let y(k) be the first derivative of -2*k**5 - 4*k**4 + 88*k**3/3 - 16*k**2 + 395. Find i, given that y(i) = 0.
-4, 0, 2/5, 2
Let a(n) be the first derivative of n**6/6 - 11*n**5/10 - 37*n**4/8 + 191*n**3/6 + 115*n**2/4 - 50*n + 195. Find d, given that a(d) = 0.
-4, -1, 1/2, 5
Factor -249*l - 3*l**3 - 251*l + 500*l - 3*l**4.
-3*l**3*(l + 1)
Suppose 93*q**3 - 36*q + 36*q**2 + 4*q**4 - 8*q**4 - 89*q**3 = 0. What is q?
-3, 0, 1, 3
Suppose -54 + 46 = -2*f - b, -14 = -5*f - b. Find u such that 0 + 1/9*u**f + 1/9*u**3 + 0*u = 0.
-1, 0
Let n = -12 + 14. Suppose 2*k - 2*i - i = 25, -20 = -n*k + 2*i. Factor -4*u**k + u**5 + 2*u**5 + u**4.
-u**4*(u - 1)
Suppose 4 - 16 - 12*b - 3*b**2 + 0*b + 0*b = 0. Calculate b.
-2
Let c(y) = y**3 - 5*y**2 - 47*y + 235. Let h be c(5). Factor 8/5 + h*m - 2/5*m**3 - 6/5*m**2.
-2*(m - 1)*(m + 2)**2/5
Let a = -2927 + 20491/7. Factor -2/7*w - a*w**2 + 4/7.
-2*(w - 1)*(w + 2)/7
Let h = -4 - -5. Let t be h + (12/(-4))/(-3). Factor -6*q - 2*q**2 - 4 - 4*q**t + 3*q**2 + 1.
-3*(q + 1)**2
Let x(s) be the third derivative of -1/360*s**6 + 0 - 6*s**2 - 1/72*s**4 + 0*s - 1/90*s**5 + 0*s**3. Factor x(t).
-t*(t + 1)**2/3
Let w(x) = 5*x**2 + x - 1. Let i(a) = -21*a**2 + 3*a - 8. Let t(k) = -3*i(k) - 12*w(k). Let t(l) = 0. Calculate l.
3, 4
Let o(c) be the second derivative of 2/5*c**2 + 9/5*c**4 + 0 - 31*c + 6/5*c**3 + 27/25*c**5. Determine l so that o(l) = 0.
-1/3
Let i be ((-4)/25)/(2/(-5)). Suppose 3*r - 4*r - 8 = -2*h, h + r + 2 = 0. Solve -i*f - 1/5*f**h - 1/5 = 0 for f.
-1
Suppose -q + 3*q + 62 = 0. Let m = q + 220/7. Factor 6/7 - 6/7*v**2 - 3/7*v**3 + m*v.
-3*(v - 1)*(v + 1)*(v + 2)/7
Find b such that -548*b**4 - 558*b**4 - 48*b + 52*b**3 - 4*b**5 - 4*b**2 + 1110*b**4 = 0.
-3, -1, 0, 1, 4
Let f(z) = 5*z**5 + 11*z**4 - 9*z**3 - 11*z**2 - 6*z + 5. Let x(a) = 5*a**5 + 10*a**4 - 8*a**3 - 10*a**2 - 5*a + 4. Let m(b) = -4*f(b) + 5*x(b). Factor m(n).
n*(n - 1)*(n + 1)**2*(5*n + 1)
Let h(s) = -6*s - 6. Let x(r) = -r - 1. Let l(n) = -h(n) + 5*x(n). Let w be l(1). Factor 4*a**2 - w - 2 - 3*a**2 + 3.
(a - 1)*(a + 1)
Solve -226257*t**2 - 5*t**3 + 226237*t**2 + 2 - 2 = 0 for t.
-4, 0
Let o = 527 - 2633/5. Solve 16/5*h**3 + 0*h + 6/5*h**4 - o + 12/5*h**2 = 0 for h.
-1, 1/3
Determine g so that 528 - 5439*g**4 + 3120*g + 4101*g**2 - 5649/2*g**3 + 1029/2*g**5 = 0.
-4/7, -2/7, 1, 11
Let g = -115 - -118. Let h(u) be the third derivative of 0*u + 3*u**2 + 1/60*u**5 + 0 + 1/120*u**6 - 1/24*u**4 - 1/6*u**g. Determine p so that h(p) = 0.
-1, 1
Let p(s) be the first derivative of 4*s**5/5 + 4*s**4 - 32*s**2 - 64*s - 70. Suppose p(a) = 0. What is a?
-2, 2
Let o(g) be the third derivative of 1/300*g**5 + 0*g + 30*g**2 - 1/30*g**3 + 1/120*g**4 + 0 - 1/600*g**6. Factor o(r).
-(r - 1)**2*(r + 1)/5
Let u(t) be the third derivative of 5/16*t**5 - 7*t**2 + 0 - 125/96*t**4 + 0*t - 1/32*t**6 + 1/840*t**7 + 0*t**3. Factor u(y).
y*(y - 5)**3/4
Let a be ((-42)/(-35))/(-7 + 226/30). Let -3/4*v**3 + 0*v**2 - 3/2 + a*v = 0. What is v?
-2, 1
Let n(r) = 9*r**2 + 13*r + 16. Let q(k) = -2*k**2 - 3*k - 4. Let c be (-27)/(-5) - 15/(-25). Let w(d) = c*n(d) + 26*q(d). Factor w(b).
2*(b - 2)*(b + 2)
Let k(c) be the first derivative of c**6/2 + 9*c**5 + 93*c**4/2 + 34*c**3 - 189*c**2/2 - 147*c - 122. Determine o, given that k(o) = 0.
-7, -1, 1
Let s(x) be the third derivative of -x**8/840 - 2*x**7/525 + x**5/75 + x**4/60 - 2*x**2 + 12. Factor s(l).
-2*l*(l - 1)*(l + 1)**3/5
Let j be (-5 - -11)*(-511)/21. Let y = -583/4 - j. Factor -1 + y*l**2 - 3/4*l.
(l - 4)*(l + 1)/4
Let k be (-3 - (-8 + 5)) + -29. Let h = k - -31. Let 1/2*u**h + 1/2*u - 1/2*u**3 - 1/2*u**4 + 0 = 0. What is u?
-1, 0, 1
Let m(s) = s**2 + 5. Let h(v) = -9*v**2 - 2*v - 40. Let i(j) = 6*h(j) + 51*m(j). Suppose i(g) = 0. What is g?
-5, 1
What is b in -114/7*b**2 + 72/7 + 18/7*b**4 + 24/7*b**3 - 48/7*b = 0?
-3, -1, 2/3, 2
Let b(x) be the first derivative of x**3/3 + 81*x**2/8 + 5*x + 13. Suppose b(f) = 0. What is f?
-20, -1/4
Let j(v) = -6*v - 72. Let l be j(-13). Let i be -6 + l + -6 - -6. Factor -4/5*b**3 + 0*b**2 + 0*b**4 + i + 0*b + 4/5*b**5.
4*b**3*(b - 1)*(b + 1)/5
Let i(p) be the third derivative of 0*p**3 - 1/360*p**6 - 8*p**2 + 0 - 1/30*p**5 - 5/72*p**4 + 0*p. Find x such that i(x) = 0.
-5, -1, 0
Solve -4*m**2 + 376 + 227*m + 156*m - 95*m + 84*m = 0 for m.
-1, 94
Let r = 28 - 20. Factor -4*y + 8*y - r*y**3 + 0*y + 4*y**5.
4*y*(y - 1)**2*(y + 1)**2
Let f(o) be the second derivative of 7*o**4/4 + 15*o**3 + 12*o**2 - 5*o - 17. Factor f(v).
3*(v + 4)*(7*v + 2)
Let i(w) be the third derivative of w**7/42 + w**6/8 + w**5/4 + 5*w**4/24 + 47*w**2. Factor i(y).
5*y*(y +