/3*u**3 + m*u**2 + 20*u.
4*(u + 1)*(u + 3)**2/3
Let a be 8 - (5 + -2) - -4. Determine z, given that 72*z**3 - a*z + 63*z**2 + 26*z + 17*z**2 + 28*z**4 + 4*z**5 + 15*z = 0.
-2, -1, 0
Let f(l) = -l - 1. Let n(w) = 4*w - 10. Let x(b) = -5*f(b) - n(b). Let d be x(-7). Suppose 0*i + 3*i**2 - 4*i**5 - d*i**4 + 5*i**2 + 3*i + i = 0. What is i?
-1, 0, 1
Let i(n) = -7*n**2 + 4*n - 7. Suppose 2*g = g + 4. Let f(w) = -1 + 6 + 4*w**2 + 3 - 2*w - g. Let p(y) = 10*f(y) + 6*i(y). Factor p(s).
-2*(s - 1)**2
Let d(s) be the first derivative of -3 - 7/4*s**2 + 49/4*s + 1/12*s**3. Solve d(j) = 0.
7
Let h = -283350/7 - -40550. Factor -928/7*x**2 + 0 - 128/7*x + h*x**5 - 2160/7*x**3 - 200*x**4.
4*x*(x - 4)*(5*x + 2)**3/7
Let y(u) be the first derivative of u**8/336 + u**7/42 + 7*u**6/120 + u**5/20 - 15*u**2/2 - 19. Let w(l) be the second derivative of y(l). Solve w(c) = 0.
-3, -1, 0
Let i be (-1269)/(-3572) + (-78)/19 + 4. Factor 0*x - 1/4*x**2 + i.
-(x - 1)*(x + 1)/4
Let n(u) be the second derivative of u**7/56 + 3*u**6/10 - 81*u**5/80 + 7*u**4/8 + 71*u. Factor n(z).
3*z**2*(z - 1)**2*(z + 14)/4
Let q = 221 - 221. Let s(a) be the third derivative of 2/9*a**3 - 1/90*a**6 - 1/60*a**5 + 0*a + 1/18*a**4 + q - 1/630*a**7 + 4*a**2. Factor s(w).
-(w - 1)*(w + 1)*(w + 2)**2/3
Suppose 6*g + 11 = 23. Factor 0 + 3/2*k + 3/2*k**g.
3*k*(k + 1)/2
Factor -u**4 - 8*u**4 + 20 - 3*u**4 - 35*u + 40*u**3 + 2*u**4 - 5*u**5 - 10*u**2.
-5*(u - 1)**3*(u + 1)*(u + 4)
Let m(o) be the first derivative of -o**5/5 - o**3/3 - o**2/2 + 6. Let a(n) = n**4 + 22*n**2 - 20*n + 9. Let i(s) = a(s) + 4*m(s). Let i(p) = 0. Calculate p.
-3, 1
Let j(v) be the third derivative of -3*v**8/2240 + v**7/28 - 5*v**6/12 - 37*v**5/60 - 42*v**2. Let l(f) be the third derivative of j(f). Factor l(p).
-3*(3*p - 10)**2
Suppose -10*r = -0*r - 690. Let o = r - 66. Factor 1/5*b**o + 1/5*b**5 + 0 + 0*b**2 + 0*b + 2/5*b**4.
b**3*(b + 1)**2/5
Let m be -6 - (12/(-35)*10)/(20/42). Factor 0 - m*w - 21/5*w**2 + 12/5*w**3.
3*w*(w - 2)*(4*w + 1)/5
Suppose 5 = 4*q - 11. Suppose q*f + 2 = 5*f. Solve 8*a + 4*a**3 - f + 0 - a**2 - 9*a**2 = 0.
1/2, 1
Let q = 4 - -2. Let f(z) = 3*z**4 - 15*z**3 - 3*z**2 - 9*z. Let b(j) = -2*j**4 + 14*j**3 + 4*j**2 + 8*j. Let h(d) = q*b(d) + 5*f(d). Factor h(w).
3*w*(w + 1)**3
Let g(h) be the second derivative of -h**2 - 34*h + 1/10*h**5 - 1/42*h**7 + 0 + 1/15*h**6 + 7/6*h**3 - 2/3*h**4. Factor g(t).
-(t - 1)**4*(t + 2)
Suppose 25*y - 19*y - 168 = 0. Suppose -27*o + y = -26. What is d in 0*d + 0 + 1/2*d**4 + 1/2*d**o + d**3 = 0?
-1, 0
Let c(n) = -n**3 - 22*n**2 - 19*n + 44. Let x be c(-21). Let a be (7 - 1) + -4 - x. Factor 6/5*m**2 + a + 3/5*m + 3/5*m**3.
3*m*(m + 1)**2/5
Let s(x) be the first derivative of -x**3/7 + 111*x**2/7 - 4107*x/7 - 23. Factor s(a).
-3*(a - 37)**2/7
Let n be (-2)/((-10)/45) + -9. Factor 3/2*t**2 + n + t**3 + 0*t - 1/2*t**4.
-t**2*(t - 3)*(t + 1)/2
Let a(o) = 7*o**2 + 11*o + 27. Let c(k) = -235*k - 10*k**2 - 37 + 218*k - 4. Let x(v) = -7*a(v) - 5*c(v). Factor x(n).
(n + 4)**2
Let u(m) be the second derivative of -m**7/56 - 3*m**6/20 - 21*m**5/40 - m**4 - 9*m**3/8 - 3*m**2/4 - 27*m. Factor u(j).
-3*(j + 1)**4*(j + 2)/4
Let h = 4 + 0. Factor -h*x**4 + 2*x + 3*x + 2*x**2 + 2*x**2 - 6*x + x**3.
-x*(x - 1)*(x + 1)*(4*x - 1)
Find u such that -1 + 1/2*u - 14*u**3 + 29/2*u**2 = 0.
-1/4, 2/7, 1
Let o(x) = -x**2 - 95*x + 112. Let v(g) = -2*g - 2. Let s(u) = -5*o(u) - 20*v(u). Determine y, given that s(y) = 0.
-104, 1
Let f(a) be the second derivative of a**7/11340 + a**4/12 - 12*a. Let k(d) be the third derivative of f(d). Determine p so that k(p) = 0.
0
Solve k**2 - 2*k**2 + k**2 - 5144*k + 5168*k + 4*k**2 = 0 for k.
-6, 0
Suppose 26*m - 349 = 15. Suppose 0 = -z - 3*o + m, -4*z + z - 14 = -5*o. Factor -2/7*g**3 + 0*g + 8/7 - 6/7*g**z.
-2*(g - 1)*(g + 2)**2/7
Let h(r) be the third derivative of r**7/630 - r**6/120 + r**5/60 - r**4/72 - 96*r**2. Determine z so that h(z) = 0.
0, 1
Let m = 2496 - 2493. Factor -1/2*p**m - 1/2*p**2 + 1/2*p + 1/2.
-(p - 1)*(p + 1)**2/2
Let d = -2467/5 + 500. Factor 4/5 - 4*v + v**4 + d*v**2 - 22/5*v**3.
(v - 2)*(v - 1)**2*(5*v - 2)/5
Let d = 571/156 - -7/78. Suppose -5/4 - d*k - 15/4*k**2 - 5/4*k**3 = 0. Calculate k.
-1
Suppose -147 - 197 - 196 = -180*u. Factor 42*i + 2/3*i**u + 98/3 + 10*i**2.
2*(i + 1)*(i + 7)**2/3
Let z(p) be the first derivative of p**9/18144 - p**8/2016 + p**7/630 - p**6/540 - 2*p**3 - 13. Let k(r) be the third derivative of z(r). Factor k(d).
d**2*(d - 2)**2*(d - 1)/6
Factor 1/5*p**3 - 24/5*p - 44/5 + 21/5*p**2.
(p - 2)*(p + 1)*(p + 22)/5
Find g, given that 4/5*g**3 + 16/5*g**2 + 0 - 2/5*g**4 + 0*g = 0.
-2, 0, 4
Let n be ((-15)/10)/(18/(-24)). Let m(t) be the second derivative of 6*t + 1/24*t**3 + 1/4*t**n + 0 - 1/48*t**4. Determine a, given that m(a) = 0.
-1, 2
Factor 39*x**5 + 100*x**3 - 24*x**5 - 11*x**5 - 40*x**4.
4*x**3*(x - 5)**2
Let l(y) be the third derivative of 0*y + 0*y**3 - 6*y**2 + 1/10*y**5 + 1/40*y**6 + 0 + 0*y**4. What is f in l(f) = 0?
-2, 0
Let b(i) = -163*i - 97*i**2 - 16 - 3 - 34 + 20*i**3. Let z(j) = -10*j**3 + 49*j**2 + 81*j + 26. Let s(u) = -4*b(u) - 7*z(u). Factor s(v).
-5*(v - 6)*(v + 1)*(2*v + 1)
Let u(h) be the third derivative of 0*h + 1/60*h**5 - 42*h**2 + 2/3*h**3 - 1/6*h**4 + 0. Factor u(w).
(w - 2)**2
Let p(v) be the third derivative of -1/126*v**4 - 1/21*v**3 + 0 + 1/630*v**5 + 0*v + 11*v**2. Solve p(c) = 0.
-1, 3
Factor -2*l - 7/2*l**2 - l**3 + 2.
-(l + 2)**2*(2*l - 1)/2
Suppose 38*n - 151 = 37*n. Find s such that -154*s**2 + n*s**2 + 6 - 6*s + 3*s = 0.
-2, 1
Let z(v) be the third derivative of v**5/2 - 55*v**4/24 + 25*v**3/6 - 9*v**2. Let w(r) = 5*r**2 - 9*r + 4. Let j(x) = 35*w(x) - 6*z(x). Factor j(n).
-5*(n - 2)*(n - 1)
Let f be 11*(-13)/(-858)*12/10. What is u in f*u**3 + 3/5*u + 1/5 + 3/5*u**2 = 0?
-1
Let o(l) be the first derivative of 3*l**4/7 + 2*l**3/21 - 24*l**2/7 - 8*l/7 - 232. Determine n so that o(n) = 0.
-2, -1/6, 2
Let s(k) = -18*k**2 - 57*k - 32. Let y(z) = -35*z**2 - 115*z - 65. Let w be ((-15)/(-2))/((-6)/(-4)). Let o(q) = w*s(q) - 2*y(q). Factor o(x).
-5*(x + 2)*(4*x + 3)
Let u = -487 - -491. Let c(d) be the second derivative of -7*d + d**2 - 5/12*d**u + 0 + 1/6*d**3 + 1/10*d**6 - 1/20*d**5. Suppose c(y) = 0. What is y?
-1, -2/3, 1
Let 3/5 - 1/5*b - 2/5*b**2 = 0. What is b?
-3/2, 1
Let z(i) be the second derivative of i**4/12 - 29*i**3 - 175*i**2/2 - 90*i + 1. Find t such that z(t) = 0.
-1, 175
Let u(l) be the first derivative of -l**5/15 + 5*l**4/3 + 22*l**3/9 - 10*l**2/3 - 7*l + 115. Factor u(f).
-(f - 21)*(f - 1)*(f + 1)**2/3
Factor -4 + 4*r**2 - 5 + 4*r**2 - 8*r + 3*r**2 - 10*r**2.
(r - 9)*(r + 1)
Find o, given that -62/7*o**4 - 2/7*o**5 - 4096/7*o - 704/7*o**3 + 8192/7 - 3328/7*o**2 = 0.
-8, 1
Let b(m) be the second derivative of m**4/18 - 64*m**3/9 + 1024*m**2/3 - 530*m. Factor b(k).
2*(k - 32)**2/3
Let g be 7 - (-17)/306*-153*(-6)/(-15). Factor -8*k**2 + 7/5*k**3 + 51/5*k + g.
(k - 3)**2*(7*k + 2)/5
Let t(x) = -16*x - 123. Let k be t(-8). Suppose -4*j + y + 12 = 0, 2 + 1 = j + 4*y. Find u, given that 8*u**2 + 0*u + 4*u + k*u**3 - u**j = 0.
-1, 0
Let v(a) be the third derivative of a**8/560 - a**7/70 + a**6/30 + a**3/6 - 9*a**2. Let d(i) be the first derivative of v(i). Factor d(s).
3*s**2*(s - 2)**2
Suppose -5*s = -6 - 9. Let j(t) = -t**3 + 2*t**2 + 5*t - 3. Let g be j(s). Find z, given that z - 10*z**g - 12*z**2 - z - 6*z**2 + 4*z = 0.
-2, 0, 1/5
Suppose -7 = -2*m + 5*t, -5 = -t - 4. Factor 0*u**2 - 91*u**3 - 5 - 6*u**2 + 89*u**3 - m*u + 3.
-2*(u + 1)**3
Factor 42/13*t - 36/13 + 2/13*t**3 - 16/13*t**2.
2*(t - 3)**2*(t - 2)/13
Let u(o) be the second derivative of o**5/30 - o**4/4 + 2*o**3/9 - 228*o. Factor u(g).
g*(g - 4)*(2*g - 1)/3
Solve -32 - 2*t**3 + 74*t - 10*t**2 + 26*t - 56*t = 0 for t.
-8, 1, 2
Let n(d) = d**2. Let z(v) = v**4 - 5*v**3 + 13*v + 10. Let y(b) = 3*n(b) - z(b). Factor y(k).
-(k - 5)*(k - 2)*(k + 1)**2
Suppose 5*y - 6*y + 20 = 0. Let j be (24/(-84))/(-2 + y/14). Factor 0 + 0*h - j*h**2 - h**3 - 1/2*h**4.
-h**2*(h + 1)**2/2
Determine l, given that 11/4*l**3 + 19/4 - 7*l**2 - 1/8*l**5 + 9/4*l**4 - 21/8*l = 0.
-2, -1, 1, 19
Let g(m) be the first derivative of m**6/3 + 6*m**5/5 + m**4/2 - 2*m**3 - 2*m**2 - 76. Find u such that g(u) = 0.
-2, -1, 0, 1
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