 2/3*c**3.
-(c - 1)**2*(c + 1)**3/3
Let a(b) be the third derivative of b**8/840 + 2*b**7/525 - b**6/100 - 2*b**5/75 + b**4/15 + 6*b**2 + b. Factor a(s).
2*s*(s - 1)**2*(s + 2)**2/5
Let k(c) be the third derivative of c**7/70 + 31*c**6/40 + 69*c**5/5 + 122*c**4 + 608*c**3 - 258*c**2. Factor k(f).
3*(f + 4)**3*(f + 19)
Let g(k) = -8*k**3 + 95*k**2 - 688*k + 1315. Let o(m) = 26*m**3 - 284*m**2 + 2064*m - 3946. Let c(i) = -10*g(i) - 3*o(i). Factor c(v).
2*(v - 41)*(v - 4)**2
Suppose 6 = -9*w + 123. Let m = -38/3 + w. What is i in 2/3 - i + m*i**2 = 0?
1, 2
Let b be (-3836)/(-819) + -4 + (4 - 58/13). Factor -b*z**2 + 2/9 + 2/9*z**3 - 2/9*z.
2*(z - 1)**2*(z + 1)/9
Let n(h) be the third derivative of -h**6/540 - 7*h**5/90 - 49*h**4/36 - 6*h**3 - 10*h**2. Let r(x) be the first derivative of n(x). What is s in r(s) = 0?
-7
Let q = 169/30 - 28/5. Let p(n) be the second derivative of -5*n + 0*n**2 + q*n**5 + 0 + 0*n**3 - 1/18*n**4. Factor p(g).
2*g**2*(g - 1)/3
Let y(u) be the third derivative of -3*u**6/40 - u**5/4 - u**4/4 + 72*u**2. Factor y(g).
-3*g*(g + 1)*(3*g + 2)
Let l(d) = -2*d**3 + d + 1. Let z(w) = -3*w**4 + 23*w**3 - 27*w**2 + 4*w + 3. Let x(j) = 3*l(j) + z(j). Find o, given that x(o) = 0.
-1/3, 1, 2, 3
Factor 1861*d**2 - 5 + 7*d - 7 + 3*d - 1859*d**2.
2*(d - 1)*(d + 6)
Suppose 6*u - 12*u + 12 = 0. Factor -2*z - 3*z**u - 19 + 7 - 2*z - 11*z.
-3*(z + 1)*(z + 4)
Suppose 12 = 13*z - 7*z. Let y(i) = i**3 + 3*i**2 - 5*i - 1. Let w be y(-4). Let d + w*d - 3*d + d**3 - z*d**3 = 0. Calculate d.
-1, 0, 1
Let h(r) = 3*r**3 - 4*r**2 + 4*r + 1. Let b be h(2). What is d in -b*d + 20*d**4 - 10*d - 75*d**3 + 80*d**2 + 12*d - 10 = 0?
-1/4, 1, 2
Let y(c) = -c**2 + 32*c + 92. Let u be y(30). Let w be (39/26)/(3/u). Solve w*a**3 + 49/4*a - 51*a**2 - 16*a**4 - 1 = 0.
1/4, 4
Let s = -84 - -96. Let t be (6/s)/(-1)*0. Factor t - 4/5*r - 2/5*r**2.
-2*r*(r + 2)/5
Factor 16/5*n**2 + 16/5*n**4 + 0 + 4/5*n**5 + 4/5*n + 24/5*n**3.
4*n*(n + 1)**4/5
Suppose 123 = 2*m + 29. Let n = -27 + m. Let 4*f**5 + 2*f**2 - n*f**3 + 4*f**4 + 5*f**5 + 6*f**2 - f**5 = 0. What is f?
-2, 0, 1/2, 1
Let q(j) = -3*j**5 + 99*j**4 + 183*j**3 + 96*j**2 - 15*j. Let l(g) = g**5 - 25*g**4 - 46*g**3 - 24*g**2 + 4*g. Let p(u) = 15*l(u) + 4*q(u). Factor p(y).
3*y**2*(y + 1)*(y + 2)*(y + 4)
Suppose -60*s - 3*s + 37 + 89 = 0. Find t such that -18/5*t - 1/5*t**s - 81/5 = 0.
-9
Factor 1/4*s**2 + 0 + 55/4*s.
s*(s + 55)/4
Determine g, given that -g**3 + 301*g**2 + 2*g**3 - 312*g**2 = 0.
0, 11
Determine t so that 565 - 322*t + 130*t + 6638 + 3*t**2 - 102*t = 0.
49
Let a(o) be the second derivative of 0 - 15*o + 1/126*o**4 + 4/63*o**3 + 1/7*o**2. Factor a(h).
2*(h + 1)*(h + 3)/21
Let p = 10578 + -52884/5. Let q = -18/5 + 21/5. Determine g so that p*g**2 + 0 - q*g - 6/5*g**4 + 3/5*g**5 + 0*g**3 = 0.
-1, 0, 1
Suppose -4*j - 20 + 47 = 5*p, -2*p - 4*j + 18 = 0. Factor 1/4 + 1/4*k**p - 1/4*k**2 - 1/4*k.
(k - 1)**2*(k + 1)/4
Let z be ((-375)/(-27))/5 + 4/18. Factor -3/5*k**z + 0 - 3/5*k - 6/5*k**2.
-3*k*(k + 1)**2/5
Let z(i) be the first derivative of 3/8*i**2 + 0*i + 1/4*i**3 - 7. Factor z(q).
3*q*(q + 1)/4
Solve 160/17*r + 2/17*r**4 - 150/17 - 16/17*r**3 + 4/17*r**2 = 0 for r.
-3, 1, 5
Let g(w) = 5*w - 3. Let t(m) = 2*m - 1. Let s(b) = -3*g(b) + 8*t(b). Let u be s(6). Solve -f - f**2 - u*f + 7*f**2 + 14*f**2 = 0 for f.
0, 2/5
Let m be -9*(-3 - (-5)/(10/8)). Let q(g) = g**3 + 8*g**2 - 5*g + 41. Let z be q(m). Factor 2/5*h**4 - 8/5 + 2/5*h**z - 2/5*h**2 - 2*h**3 + 16/5*h.
2*(h - 1)**3*(h + 2)**2/5
Let f(q) be the first derivative of -q**6/540 + q**5/36 - q**4/9 + 3*q**3 - 24. Let t(l) be the third derivative of f(l). Find c, given that t(c) = 0.
1, 4
Suppose 0 = -5*c + 17*c - 48. Let c*t**4 + 20*t**2 + 14*t**2 - 35*t**2 = 0. What is t?
-1/2, 0, 1/2
Suppose 0 = -3*n - 4*s + 604, 0*s = 4*n - 3*s - 797. Let c be (n/270)/((-2)/(-3)). Factor c*r**3 + 4/9*r**2 - 10/9*r - 4/9.
2*(r - 1)*(r + 1)*(5*r + 2)/9
Let d(b) be the third derivative of -b**8/336 + b**7/420 + 37*b**6/240 - 43*b**5/60 + 7*b**4/12 + 10*b**3/3 + 27*b**2. Let d(u) = 0. Calculate u.
-5, -1/2, 2
Let s be 1/(-2)*(30 + -2). Let h be ((-2)/(-7))/(0 + (-10)/s). Factor h*t + 2/15*t**2 + 4/15.
2*(t + 1)*(t + 2)/15
Let c(h) be the first derivative of -h**3/5 + 3*h**2/10 - 545. Factor c(o).
-3*o*(o - 1)/5
Let n(l) = l. Let f(y) = 0*y**2 + y**2 + 0 - 2 + 4. Let h(v) = 2*f(v) + 6*n(v). Factor h(m).
2*(m + 1)*(m + 2)
Factor -6 + 36/5*i - 6/5*i**2.
-6*(i - 5)*(i - 1)/5
Let u = -6 + -6. Let x = u + 14. Suppose 3*d - x*d + d**3 + 2*d**2 + 0*d**2 = 0. Calculate d.
-1, 0
Let k(d) be the third derivative of -41*d**2 - 7/720*d**6 + 0*d + 5/18*d**3 + 3/16*d**4 - 1/12*d**5 + 0. Factor k(z).
-(z - 1)*(z + 5)*(7*z + 2)/6
Suppose -o + 3*f + 33 = 0, -o + 0*o + f + 31 = 0. Suppose -i + 224 = 5*n, n - 5*i = -4*n + 200. Factor 1 + 3 + 18*u + n*u**2 - o*u**2.
2*(u + 1)*(7*u + 2)
Suppose 0 = 9*s - 14*s. Suppose s = -3*c - 3*o + 18, -o - 12 = -0*c - c. What is h in 3*h**2 + 7*h - 6*h**2 - 9 + c*h - 4*h = 0?
1, 3
Let l(h) be the first derivative of -3*h**5/40 - h**4/8 + 2*h**3 + 9*h**2 + 20*h - 1. Let c(s) be the first derivative of l(s). Factor c(o).
-3*(o - 3)*(o + 2)**2/2
Suppose 3*v + o + 2 = 17, v - 5*o + 11 = 0. Let j be v/((-1 - -2) + 1). Factor -9*n**3 - 2 + 12*n**j - 29*n**5 - 6*n**4 + 2 + 12*n + 32*n**5.
3*n*(n - 2)**2*(n + 1)**2
Let i(q) be the first derivative of q**3/6 + 25*q**2/4 + 12*q - 326. Solve i(a) = 0 for a.
-24, -1
Factor -4 + 6*b - 9*b**3 - 14*b**3 + 21*b**3.
-2*(b - 1)**2*(b + 2)
Let j(m) be the second derivative of -m**6/15 + 7*m**5/5 - 23*m**4/2 + 140*m**3/3 - 100*m**2 - 2*m - 118. Factor j(t).
-2*(t - 5)**2*(t - 2)**2
Let l be 120/50*(-45)/(-4). Suppose -10*g + l = -g. Solve 0 - 3/2*v - 3/2*v**3 - g*v**2 = 0 for v.
-1, 0
Let s = 3 + 0. Find g, given that 22*g + 0*g**3 - 5*g**s - 17*g = 0.
-1, 0, 1
Let d(w) be the third derivative of -5*w**8/112 + 31*w**7/42 - 35*w**6/24 - 11*w**5/12 + 15*w**4/4 + 437*w**2. Find q such that d(q) = 0.
-2/3, 0, 1, 9
Let i(s) be the third derivative of -s**7/5460 + s**6/585 + s**5/780 - s**4/39 - 16*s**3/3 + 22*s**2. Let j(f) be the first derivative of i(f). Factor j(q).
-2*(q - 4)*(q - 1)*(q + 1)/13
Factor -4*f**3 + f**3 - f**2 + 21*f**2 - f**3 + 16 - 32*f.
-4*(f - 2)**2*(f - 1)
Let a(x) be the second derivative of -2*x + 1/24*x**6 + 259/16*x**4 + 8 - 107/80*x**5 - 2009/24*x**3 + 343/4*x**2. Factor a(c).
(c - 7)**3*(5*c - 2)/4
Let q(g) be the first derivative of 50*g**6/7 - 204*g**5/7 + 807*g**4/28 + 64*g**3/7 - 225*g**2/14 - 54*g/7 + 260. Determine c so that q(c) = 0.
-3/10, 1, 2
Solve 1/6*n**5 + 1/2*n**3 + 1/2*n**4 + 1/6*n**2 + 0 + 0*n = 0 for n.
-1, 0
Let w be ((-2)/(-92))/(0 - (-5)/(-160)). Let q = 388/161 + w. Suppose -q*l**3 + 2/7*l**4 + 0*l + 0 + 18/7*l**2 = 0. What is l?
0, 3
Let g(p) = 25*p**3 - 390*p**2 - 585*p + 870. Let v(n) = -2*n**3 + 30*n**2 + 45*n - 67. Let r(f) = 3*g(f) + 40*v(f). Determine c so that r(c) = 0.
-2, 1, 7
Let g be (-2)/4*(2 - 4). Suppose g - 33 = -4*h. Factor 4*s**5 - 12*s**3 + 6*s + h*s**4 + 4*s**2 - 12*s**4 + 2*s.
4*s*(s - 2)*(s - 1)*(s + 1)**2
Let v(n) = -3*n**2 - 10*n + 9. Let h(a) = -4*a**2 - 11*a + 9. Suppose 0 = -2*t + 2*i, 4*t + 0*t = i - 9. Let o(w) = t*v(w) + 2*h(w). Solve o(m) = 0 for m.
-9, 1
Let m(f) be the third derivative of f**7/630 - f**6/90 - 25*f**4/24 + 21*f**2. Let t(l) be the second derivative of m(l). Let t(j) = 0. What is j?
0, 2
Let b(h) = -h - 1. Let q be (0 + 2)*4/2. Let f be b(q). Let y(s) = 11*s**2 - 23*s - 5. Let p(i) = 39*i**2 - 81*i - 18. Let m(r) = f*p(r) + 18*y(r). Factor m(l).
3*l*(l - 3)
Let a(l) be the first derivative of l**7/84 + l**6/15 + l**5/10 - 6*l + 7. Let b(o) be the first derivative of a(o). Solve b(c) = 0.
-2, 0
Let d(s) be the first derivative of -s**3 - s**2 + s + 4. Let f(h) = -h**2 - h. Let v(q) = d(q) - 4*f(q). Factor v(a).
(a + 1)**2
Let f(y) = -61*y + 3. Let n be f(-3). Let a = 188 - n. Solve 3/4*v**a + 9/4*v**3 + 3 - 6*v = 0 for v.
-2, 2/3, 1
Let f(a) = 14*a**2 + 94*a - 83. Let t(g) = -11*g**2 - 93*g + 84. Let q(p) = 4*f(p) + 5*t(p). Find k, given that q(k) = 0.
1, 88
Let m(l) be the third derivative of -l**8/10080 - l**7/1260 - l**6/360 + 19*l**5/60 - 16*l**2. Let w(j) be the third derivative of m(j). Factor w(q).
-2*(q + 1)**2
Let j(o) 