et l(m) = m**3 - 26*m**2 - 25*m - 51. Let q be l(27). Let b be (-54)/81 - (-2)/q. Factor 0 + 1/5*c**4 + 0*c**3 + b*c**2 + 0*c.
c**4/5
Let n be (-1 + 16 - -1)/(2 - 0). Suppose -4*w = 5*r - n, -5*w = -3*r - 4 - 6. Solve -3 + 104*p - 2*p**w - 111*p - 2*p**2 = 0.
-1, -3/4
Suppose -107*o + 1313 + 394 = -647. Let w(h) be the second derivative of 0*h**2 + o*h - 1/6*h**3 - 1/20*h**5 + 0 - 1/6*h**4. Find i, given that w(i) = 0.
-1, 0
Let v be ((-168)/20)/(2/10). Let c = v + 177/4. Let -c*k**3 - 21/4*k**2 + 9/4 + 21/4*k = 0. What is k?
-3, -1/3, 1
Let k = -95425/4 - -23905. Let k*t + 1/4*t**3 - 27/4*t**2 - 169/4 = 0. Calculate t.
1, 13
Let c(z) be the third derivative of -z**9/40320 + 73*z**8/80640 - z**7/1680 + 11*z**5/20 + z**2 - 134. Let x(n) be the third derivative of c(n). Factor x(k).
-k*(k - 12)*(6*k - 1)/4
Let s(w) be the second derivative of -2*w**7/105 - 161*w**6/75 + 81*w**5/50 - 6597*w. Factor s(t).
-2*t**3*(t + 81)*(2*t - 1)/5
Factor -572/3 - 4294/9*d - 10/9*d**2.
-2*(d + 429)*(5*d + 2)/9
Let i(t) be the second derivative of -t**5/16 + 25*t**4/3 - 7585*t**3/24 - 8405*t**2/4 + 3*t - 855. Let i(v) = 0. What is v?
-2, 41
Factor 173*o + 52*o**3 + 230 + o**4 + 98*o + 120*o**2 + o**4 - 675*o.
2*(o - 1)**2*(o + 5)*(o + 23)
Let t(c) = 2*c**2 - 27*c - 46. Let g(h) = -2*h**2 + h - 2. Let s(x) = 2*g(x) + t(x). Find f such that s(f) = 0.
-10, -5/2
Suppose 0 = -10*n + 7*n + 6. Let u = 8 + -4. Factor -10*s + 2*s - 4 + 16*s - u*s**n.
-4*(s - 1)**2
Let s = -66/29675 + 60472/504475. Factor 12/17*o**2 - 18/17*o - s*o**3 + 0.
-2*o*(o - 3)**2/17
Factor -336*k**2 + 121*k**2 - 20*k + 113*k**2 + 106*k**2 - 1200.
4*(k - 20)*(k + 15)
Let f(t) be the third derivative of 1/270*t**5 - 17/108*t**4 - 2/3*t**3 + 0 - 2*t**2 - t. Factor f(q).
2*(q - 18)*(q + 1)/9
Solve -3/8*j + 0 + 3/8*j**3 - 1/2*j**4 + 1/2*j**2 = 0 for j.
-1, 0, 3/4, 1
Factor -33*i**2 + 1903*i - 845*i**2 + 214*i**2 + 565*i + 760 + 28*i**3.
4*(i - 19)*(i - 5)*(7*i + 2)
Let k(d) be the second derivative of d**6/225 + d**5/6 + 23*d**4/90 - 5*d**3/9 - 8*d**2/5 - 1860*d. Suppose k(s) = 0. What is s?
-24, -1, 1
Let o be 2703/106 + 3*-6. Factor -3/4*f**2 + 0*f - 33/4*f**3 - o*f**4 + 0.
-3*f**2*(f + 1)*(10*f + 1)/4
Let c(x) be the third derivative of x**9/15120 + x**8/1680 - x**6/45 + x**5/15 - 103*x**2. Let v(a) be the third derivative of c(a). Solve v(b) = 0.
-2, 1
What is o in -860*o**4 + 36855*o + 342*o**5 - 177*o**2 - 135*o**5 - 9585*o**3 - 113*o**5 - 5403*o**2 + 39690 - 114*o**5 = 0?
-21, -3/2, 2
Suppose 6 = -5*g - 5*a + 26, -5*g = -2*a + 8. Suppose g = -8*s + 218 - 218. Solve 0*b**4 - 3/2*b**5 + 0*b**3 + 0*b + s + 0*b**2 = 0 for b.
0
Let q(v) be the first derivative of -v**4/4 - 520*v**3/3 - 67077*v**2/2 + 136242*v + 4927. Factor q(w).
-(w - 2)*(w + 261)**2
Factor -4*t**3 - 44*t**2 + 1349*t - 2020*t**2 + t + 4136 + 726*t.
-4*(t - 2)*(t + 1)*(t + 517)
Let p(v) be the third derivative of 0 + 0*v + 1/12*v**5 + 25/3*v**3 + 35/24*v**4 + 10*v**2. Factor p(g).
5*(g + 2)*(g + 5)
Suppose -20 = 74*s - 79*s, 18 = -d - s. Let o be (-52)/12 + (-154)/d. Factor -5/6*h**3 - 13/6*h - 1/3 - o*h**2.
-(h + 1)*(h + 2)*(5*h + 1)/6
Factor 2/13*r**2 + 134*r + 0.
2*r*(r + 871)/13
Suppose -1152*x + 1250 + 1054 = 0. Solve -2312/5 + 136/5*l - 2/5*l**x = 0.
34
Suppose -482851 = 68*p - 483803. Factor 2/3*v**3 - p*v + 6*v**2 + 22/3.
2*(v - 1)**2*(v + 11)/3
Let s = -2/21751 + 304532/195759. Let l be (-100)/(-42) - (-2)/7. Suppose -4/9 + 2/3*w + l*w**2 + s*w**3 = 0. Calculate w.
-1, 2/7
Let a(r) = -6*r**3 + 2584*r**2 - 17*r. Let c(z) = -z**3 + 431*z**2 - 3*z. Let x(u) = 6*a(u) - 34*c(u). Determine n, given that x(n) = 0.
0, 425
Let p(s) = 6*s - 66. Let j be p(13). Determine h, given that -j*h + 4*h**2 + 4*h + 23 - 15 - 2*h**2 = 0.
2
Suppose -6*s + 2*x + 52 = 0, 31 = 17568*s - 17564*s - x. Factor 7/2*l**2 + 0*l + 5/2*l**4 + 0 - 1/2*l**s + 13/2*l**3.
-l**2*(l - 7)*(l + 1)**2/2
Let a(w) be the second derivative of w**5/80 + 17*w**4/32 - 17*w**2/2 + 12*w. Let f(l) be the first derivative of a(l). Determine c so that f(c) = 0.
-17, 0
Suppose -c - 49 = -71. Let 12 - 23/2*b**3 + 5/2*b**4 + c*b - 25*b**2 = 0. What is b?
-2, -2/5, 1, 6
Let v(c) be the third derivative of 1/108*c**5 + 1/1890*c**7 - 180*c**2 + 0*c - 1/270*c**6 - 1/108*c**4 + 0*c**3 + 0. Let v(a) = 0. Calculate a.
0, 1, 2
Suppose -21*u - 10*u = -3*u. Solve 5*q**3 - 33075*q**2 + 33110*q**2 + 0*q**3 + u*q**3 - 5*q**4 + 30 - 23*q - 42*q = 0 for q.
-3, 1, 2
Let x be -5 - ((-914)/96 - 666/(-148)). Let u(o) be the second derivative of -5/4*o**2 - 3/8*o**3 + 0 + 43*o + x*o**4. Factor u(n).
(n - 10)*(n + 1)/4
Let k(a) = -52*a**2 + 8*a. Let z(f) = 4*f**2 - 10*f + 9*f - 2*f**2. Let s(u) = k(u) + 24*z(u). Determine b, given that s(b) = 0.
-4, 0
Let u(w) be the first derivative of -178 - 1/4*w**4 + 1/3*w**3 + 5/2*w**2 + 3*w. Determine r so that u(r) = 0.
-1, 3
Let l(k) be the third derivative of k**5/30 - 10*k**4/3 + 115*k**2. Let s be l(40). Factor 0*f**2 + 3/5*f**5 - 6/5*f**3 + 0*f**4 + 3/5*f + s.
3*f*(f - 1)**2*(f + 1)**2/5
Let i(m) be the second derivative of m**4/18 - 50*m**3/9 - 72*m**2 + 965*m. Determine s, given that i(s) = 0.
-4, 54
Let l be (42/27)/((-112)/(-63)). Let y(q) be the third derivative of 20*q**2 + l*q**6 + 0*q + 5/3*q**3 - 5/24*q**4 - 11/6*q**5 + 0. Find j such that y(j) = 0.
-2/7, 1/3, 1
Let q(i) be the first derivative of -i**5/5 - 45*i**4/4 - 199*i**3/3 + 45*i**2/2 + 200*i + 4880. What is l in q(l) = 0?
-40, -5, -1, 1
Let x(b) be the third derivative of b**6/540 - b**5/30 - 25*b**4/27 - 64*b**3/9 - 3*b**2 + 157*b. Find q, given that x(q) = 0.
-4, -3, 16
Let r(w) be the third derivative of w**5/30 - 155*w**4/72 - 161*w**3/18 - 7*w**2 - 192*w. Solve r(c) = 0 for c.
-1, 161/6
Determine d, given that 42*d**3 + 9*d**3 - 27*d**3 - 41*d - 289*d - 4*d**2 - 22*d**3 - 900 = 0.
-10, -3, 15
Let p be 46*(-5)/20*-22 + 2. Let y = 257 - p. Find m, given that 9/7*m - 3/7*m**3 + 0 + 6/7*m**y = 0.
-1, 0, 3
Let w = 43236 + -43234. Factor 4/11*d + 0 - 14/11*d**3 - 10/11*d**w.
-2*d*(d + 1)*(7*d - 2)/11
Suppose 2*r + 2*t + 10 = 0, -5*r - 293*t + 292*t = 5. Let u(n) be the first derivative of r*n - 1/10*n**4 + 2/15*n**3 + 34 + 0*n**2. Solve u(f) = 0.
0, 1
Let j(n) be the first derivative of n**3/9 - 13*n**2/6 - 14*n/3 + 2247. Factor j(c).
(c - 14)*(c + 1)/3
Let o(m) be the third derivative of -m**5/12 + 125*m**4/12 - 245*m**3/6 + 229*m**2 + 1. Find q, given that o(q) = 0.
1, 49
Let f(n) = 87*n - 64. Let w be f(7). Let p = w + -543. Let 0*k**p + 3/2*k**3 - 3 - 9/2*k = 0. Calculate k.
-1, 2
Let k(s) be the second derivative of 7/36*s**3 - 7/120*s**5 - 5/6*s**2 + 1/180*s**6 + 1/8*s**4 - 18 + 2*s. Determine c, given that k(c) = 0.
-1, 1, 2, 5
Find f such that 7104*f**2 + 14240/9*f + 10584*f**3 + 352/3 - 162*f**4 = 0.
-2/9, 66
Let i(z) be the second derivative of z**4/4 - 17*z**3/2 + 105*z**2 - 76*z + 2. Factor i(w).
3*(w - 10)*(w - 7)
Let n = -16816 - -16816. Let b(x) be the first derivative of 11 - 6*x**5 - 250/3*x**3 - 75/2*x**4 - 1/3*x**6 + n*x + 0*x**2. Factor b(m).
-2*m**2*(m + 5)**3
What is k in -2492/3*k - 220/3*k**2 - 8036/3 - 4/3*k**3 = 0?
-41, -7
Let k = -14223 - -284731/20. Let x = k - 51/4. What is p in 4*p**3 - 4*p - x + 4/5*p**2 = 0?
-1, -1/5, 1
Let r be (19 - 765/36)/(2*(-9)/24). Factor 1/8*t**4 - 1/4*t**2 + 1/8*t**r + 0*t + 0.
t**2*(t - 1)*(t + 2)/8
Let h = 26564/483 - 817/23. Let x = 155/7 - h. Find m, given that 4/9*m**2 - 20/9*m - x = 0.
-1, 6
Let s(g) be the second derivative of 1/270*g**6 + 261*g + 0*g**4 + 0*g**2 + 0 + 1/10*g**5 + 0*g**3. Suppose s(y) = 0. What is y?
-18, 0
Let s(c) be the second derivative of c**4/48 + 49*c**3/24 - 574*c. Factor s(w).
w*(w + 49)/4
Let g(p) be the second derivative of -p**5/95 + 25*p**4/38 + 116*p**3/57 + 39*p**2/19 - 5398*p. Solve g(d) = 0 for d.
-1, -1/2, 39
Determine y so that 18198756/7*y - 8626210344/7 - 12798/7*y**2 + 3/7*y**3 = 0.
1422
Let r(f) be the first derivative of -3*f**4 - 68*f**3/3 - 12*f**2 + 4*f + 41. Let g(v) = 2*v**2 + 1. Let q(a) = 4*g(a) - r(a). Find p, given that q(p) = 0.
-6, -1/3, 0
Let z(w) be the second derivative of -w**6/6 + 27*w**5/4 + 35*w**4/3 - 7*w + 64. Solve z(r) = 0.
-1, 0, 28
Factor 97356*c**2 - 48700*c**2 - 78 - 48730*c**2 + 2*c**3 - 154*c.
2*(c - 39)*(c + 1)**2
Let h(r) = 6*r**4 - 113*r**3 + 403*r**2