 = 3 - 7*l + 7*l + 2*l**2 - l**3 + 2*l**2 - 4*l. Let c be s(3). Determine g so that c + 0*g + 2/13*g**2 = 0.
0
Suppose 0 = -0*j - 6*j + 60. Suppose -2*z = z - 4*i - 6, 5*z = 4*i + j. Find q, given that z*q**4 - 2*q - 2*q**4 - 3*q**2 + q**4 = 0.
-1, 0, 2
Suppose 250 = 8*l + 218. Let b(o) be the third derivative of -4*o**2 - 1/360*o**5 + 1/36*o**3 + 1/720*o**6 - 1/144*o**l + 0 + 0*o. Solve b(k) = 0 for k.
-1, 1
Let k(u) be the first derivative of 4/5*u**2 + u - 3/50*u**5 - 1/6*u**4 + 4/15*u**3 + 5. Let z(v) be the first derivative of k(v). Factor z(l).
-2*(l - 1)*(l + 2)*(3*l + 2)/5
Let u(l) be the third derivative of -l**6/540 - 7*l**5/270 + l**4/108 + 7*l**3/27 + 66*l**2. Solve u(j) = 0 for j.
-7, -1, 1
Let f(y) be the third derivative of y**6/40 + 11*y**5/20 - 3*y**4/2 - 431*y**2. Solve f(i) = 0 for i.
-12, 0, 1
Let p(y) = 4*y**3 - 20*y**2 - 16*y + 16. Let r(m) = m**3 - m**2 - m + 2. Let t(x) = -p(x) + 8*r(x). Let t(s) = 0. Calculate s.
-2, -1, 0
Suppose -2 = -0*p - p. Suppose 1 - 82*a**p + 79*a**2 + a**3 + 0 + 2*a**4 - a = 0. Calculate a.
-1, 1/2, 1
Factor 2/11*d**2 + 82/11*d - 84/11.
2*(d - 1)*(d + 42)/11
Let p(g) be the second derivative of 13*g**4/3 + 58*g**3/3 + 12*g**2 + 24*g. Suppose p(u) = 0. What is u?
-2, -3/13
Let y(p) be the second derivative of -p**5/45 + 40*p**4/27 - 800*p**3/27 - 11*p - 2. Determine g, given that y(g) = 0.
0, 20
Let o be 12/(-5*14/(-35)). Let r(z) be the second derivative of 1/60*z**o + 0 - 27/8*z**2 - 17/80*z**5 - 9/8*z**3 + 15/16*z**4 - 2*z. Factor r(q).
(q - 3)**3*(2*q + 1)/4
Let j(b) be the third derivative of b**7/1260 - b**5/40 + b**4/36 + b**3/3 - 259*b**2. Factor j(d).
(d - 2)**2*(d + 1)*(d + 3)/6
Suppose 5*r + p = 5, 75*p - 76*p - 15 = -5*r. Let j(i) be the second derivative of 1/21*i**3 + 1/21*i**4 + 0 + 0*i**r + 1/70*i**5 + 9*i. Factor j(k).
2*k*(k + 1)**2/7
Let u be ((-3)/4)/(102/(-272)). Let w be 0*2/2*1. Find h, given that -u*h**3 + w*h + 0 + 0*h**2 - 1/2*h**5 + 2*h**4 = 0.
0, 2
Find a, given that -40/7 - 16/7*a + 2/7*a**2 = 0.
-2, 10
Let c(x) be the first derivative of -2*x**5/5 - x**4 - 2*x**3/3 - 81. Factor c(t).
-2*t**2*(t + 1)**2
Suppose 0 = 3*z + 4*o + 6, 4*z + 2*o = -3*o - 7. Suppose c - 1 - 2 = 0. Factor 3 + 3 + c*a**2 + 2*a**2 - z*a**2 + 9*a.
3*(a + 1)*(a + 2)
Suppose 1 = -t - p - 6, -4*p + 20 = 0. Let i = t + 22. Find o such that 3*o**3 - i - 3*o + 3*o**2 + 7 + 0*o = 0.
-1, 1
Let o(w) be the first derivative of 1/6*w**3 - 1/2*w - 17 - 1/16*w**4 + 1/8*w**2. Factor o(k).
-(k - 2)*(k - 1)*(k + 1)/4
Factor 0*j + 0 + 2/11*j**2 + 4/11*j**3 + 2/11*j**4.
2*j**2*(j + 1)**2/11
Suppose -2*q - 2*j - 66 = -6*q, 3*j = 3*q - 51. Let d = -13 + q. Factor -7 - 6*b**3 + 13*b - 5*b - 2*b**d - 1 + 6*b**2 + 2*b**4.
2*(b - 2)**2*(b - 1)*(b + 1)
Let m(o) be the first derivative of 0*o**2 + 0*o + 1/6*o**6 - 2/5*o**5 - o**4 + 8/3*o**3 + 30. Factor m(d).
d**2*(d - 2)**2*(d + 2)
Let w(r) be the second derivative of -r**6/45 + r**5/5 - 2*r**4/3 + 10*r**3/9 - r**2 + 48*r. Factor w(k).
-2*(k - 3)*(k - 1)**3/3
Suppose -32/3 - 2166*m**2 + 304*m = 0. What is m?
4/57
Let a(j) be the first derivative of -j**4/72 + j**3/36 + j**2/6 + 14*j + 21. Let t(f) be the first derivative of a(f). Factor t(s).
-(s - 2)*(s + 1)/6
Let t(r) be the third derivative of r**8/336 - r**7/30 + r**6/12 + 12*r**2. Factor t(y).
y**3*(y - 5)*(y - 2)
Let l be (-1)/4 + (-690)/(-40). Let 10*p - 5*p - 9*p**2 + 3*p**3 - l*p = 0. Calculate p.
-1, 0, 4
Let p(q) be the third derivative of 0 - 1/15*q**3 + 0*q + 2*q**2 - 1/40*q**4 - 1/300*q**5. Let p(l) = 0. Calculate l.
-2, -1
Suppose 3*f + 5 = -4*d + 1, 5*f + 1 = -d. Suppose 14 = -2*m - 4*j, 4*m + 5*j = -0*m - 13. Factor -6*a - 7*a**2 + f*a**2 - 3 + a**2 + m*a**2.
-3*(a + 1)**2
Let -14/19*l**2 + 0 + 2/19*l**3 - 16/19*l = 0. Calculate l.
-1, 0, 8
Factor -9/7*w**2 - 129/7*w - 6.
-3*(w + 14)*(3*w + 1)/7
Let r be 16/232 + 8/(-116). Let k(d) be the second derivative of 4/3*d**3 + 0 + r*d**2 + 3*d + 1/3*d**4 - 2/5*d**6 - 4/5*d**5. Let k(v) = 0. Calculate v.
-1, 0, 2/3
Let f be 10/45 - 129/(-27). Let v(z) = -8*z**3 - 15*z + f*z**4 - 4 - z**4 - 5*z**2 + 18*z. Let c(i) = i**2 + i. Let y(r) = 5*c(r) + v(r). What is h in y(h) = 0?
-1, 1
Find n such that 114*n + 28*n**3 + 38/9*n**4 + 54 + 84*n**2 + 2/9*n**5 = 0.
-9, -3, -1
Let h be 4/(-3) + 1 - (-19)/3. Let g(c) be the third derivative of 1/240*c**5 + 0*c + 1/120*c**h + 0*c**4 + 1/280*c**7 + 0*c**3 + c**2 + 0. Factor g(q).
q**2*(q + 1)*(3*q + 1)/4
Determine t, given that 16/5*t**5 + 1153/5*t**3 + 48/5 + 42/5*t**2 + 792/5*t**4 - 287/5*t = 0.
-48, -1, 1/4
Find c such that 72/5*c + 0 + 2/5*c**2 = 0.
-36, 0
Factor 6/13*t + 56/13 - 2/13*t**2.
-2*(t - 7)*(t + 4)/13
Let a(u) be the second derivative of -7*u**6/65 + 29*u**5/65 - 7*u**4/26 - 28*u**3/39 + 12*u**2/13 + 144*u. Find i such that a(i) = 0.
-2/3, 3/7, 1, 2
Suppose 0*s + 30 = 5*s. Suppose 3*w - 18 + s = 0. Solve 3*k**3 + 0*k**3 - k**5 - w*k**3 - 7*k**4 + 5*k**4 = 0 for k.
-1, 0
Let f(y) = -y**2 + 4*y + 80. Let l be f(11). Let s(d) be the first derivative of -1 - 1/6*d**l - d + 3/4*d**2. Factor s(h).
-(h - 2)*(h - 1)/2
Let c(w) be the third derivative of w**5/180 - w**4/18 + 11*w**2 + 2*w. Suppose c(s) = 0. What is s?
0, 4
Let p(g) be the second derivative of g**3/3 + 3*g**2 + 7*g. Let d be p(-2). Factor -6*u - 8*u - u + 21*u**d - 3 - 3.
3*(u - 1)*(7*u + 2)
Let d(c) be the first derivative of -c**5/20 - 3*c**4/8 - c**3 + 8*c**2 + 20. Let m(n) be the second derivative of d(n). Factor m(o).
-3*(o + 1)*(o + 2)
Let n(u) be the first derivative of u**5/25 + u**4/4 + 3*u**3/5 + 7*u**2/10 + 2*u/5 + 33. Factor n(b).
(b + 1)**3*(b + 2)/5
Let h be (-34)/(-18) + 0 + -1. Suppose 6 = -2*t + 5*t. Suppose -2/9*c**t - 2/3 + h*c = 0. Calculate c.
1, 3
Let c(d) be the first derivative of d**6/6 - 3*d**5/5 - 23*d**4/4 - 11*d**3 - 7*d**2 + 89. Factor c(n).
n*(n - 7)*(n + 1)**2*(n + 2)
Let d(s) be the first derivative of -1/22*s**4 + 2/33*s**3 - 2/55*s**5 + 3 + 0*s + 1/11*s**2. Find o such that d(o) = 0.
-1, 0, 1
Let h(q) be the first derivative of 5*q**4/18 - 28*q**3/27 + 8*q**2/9 + 10. Factor h(x).
2*x*(x - 2)*(5*x - 4)/9
Let b = 14 - 5. Let o(u) = u - 3. Let p be o(b). Determine s so that 9*s + p*s**3 - 3*s - 4*s**3 + 6*s**2 + 2 = 0.
-1
Suppose -10 = 5*c - 5*b, -c - 3*b = -7*b + 17. Solve -12*o**c - 4*o + 22*o**3 - 6*o**3 = 0.
-1, 0, 1
Let h(n) be the first derivative of 0*n**2 + 1/3*n**3 - n + 24. Factor h(l).
(l - 1)*(l + 1)
Let p = 50 - 449/9. Let t(j) be the third derivative of -3*j**2 + 0 + 1/315*j**7 + 0*j**4 + p*j**3 - 1/45*j**5 + 0*j + 0*j**6. Factor t(v).
2*(v - 1)**2*(v + 1)**2/3
Let i(d) be the third derivative of -d**5/12 + 395*d**4/24 - 65*d**3 + d**2 + 58. Factor i(h).
-5*(h - 78)*(h - 1)
Suppose 3*j - 3 - 6 = 2*d, 11 = 5*j - 2*d. Let x be 93/6 - 4/((-4)/j). Find t, given that x*t**3 + 9*t**2 - 15*t**4 - 15/2*t - 3 = 0.
-1/2, -2/5, 1
Let r = -1043/6 + 174. Let b(z) be the second derivative of -r*z**3 + 6*z + 0*z**2 - 1/20*z**5 + 1/6*z**4 + 0. Solve b(i) = 0.
0, 1
Let y = 3048/11 + -277. Solve 0 - 1/11*s**3 + 0*s - y*s**2 = 0 for s.
-1, 0
Let u(l) be the second derivative of l**5/70 - 5*l**4/21 + 32*l**3/21 - 32*l**2/7 - l - 27. Let u(f) = 0. What is f?
2, 4
Let s be ((-18)/(-4) - 1)/((-45)/(-90)). Let m(j) be the second derivative of 0 - s*j + 2*j**3 + 1/3*j**4 - 3/5*j**5 + 2/15*j**6 - 4*j**2. Factor m(d).
4*(d - 2)*(d - 1)**2*(d + 1)
Suppose -5*r - 14 = -7*r. Let f(i) be the first derivative of r - 3/10*i**2 + 6/5*i + 3/20*i**4 - 2/5*i**3. Find d such that f(d) = 0.
-1, 1, 2
Find c such that 36/7*c**2 + 8/7 + 44/7*c = 0.
-1, -2/9
Suppose 5*p + 4 = 2*o, 7*o - 3*p + 8 = 11*o. Factor m**o - 2 + 7/3*m.
(m + 3)*(3*m - 2)/3
Let c = 5/4 + -1. Suppose 19*d - 2 - 36 = 0. Suppose c*z**3 + 0*z**d - 1/4*z + 0 = 0. Calculate z.
-1, 0, 1
Factor -7*d**3 - 72 + 7*d**3 - 28*d - 8*d**3 + 4*d**3 + 40*d**2.
-4*(d - 9)*(d - 2)*(d + 1)
Solve 8/5 - 1/5*q**2 + 2/5*q = 0.
-2, 4
Suppose -4*x = -53*k + 57*k - 28, -5 = 5*x - 5*k. Solve 9/7 + 30/7*r + 4/7*r**x - 23/7*r**2 = 0 for r.
-1/4, 3
Suppose -16 = -4*f + 4, 5*f = i - 493. Let 4*q**2 + 517*q**3 - 4*q - i*q**3 + 2 - q = 0. Calculate q.
1, 2
Suppose -60 + 68 = 2*u. Suppose 20 = 4*c, -u*v - v + 15 = -c. What is i in 1/5*i**v + 0 - 1/5*i + 1/5*i**3 - 1/5*i**2 = 0?
-1, 0, 1
Let f(p) be the seco