3, 2/5
Let k(x) = x**3 - 6*x**2 + 7*x - 8. Let j = 43 - 38. Let q be k(j). Find n such that -3/2*n**q - 3*n + 0 = 0.
-2, 0
Let c(m) = 10*m**5 + 2*m**4 - 39*m**3 - 31*m**2 + 409*m + 9. Let k(j) = -j**5 - j**2 - j - 1. Let a(q) = 2*c(q) + 18*k(q). Suppose a(r) = 0. Calculate r.
-5, 0, 4
Suppose -2*c = 2*g - 9 + 5, 0 = -3*c + 5*g + 30. Factor c*y**3 - 4*y**3 - 5*y**2 + y**3 - 7*y**3 + 10*y.
-5*y*(y - 1)*(y + 2)
Let m(q) be the second derivative of 0 + 1/4*q**3 + 5*q + 1/32*q**4 + 3/4*q**2. Factor m(p).
3*(p + 2)**2/8
Let i(s) be the third derivative of -s**5/300 - 43*s**4/60 - s**2 + 159*s. Determine x, given that i(x) = 0.
-86, 0
Let c(a) be the first derivative of -1/8*a**3 - 3 - 1/32*a**4 - 1/8*a - 3/16*a**2. Let c(q) = 0. Calculate q.
-1
Let r(q) = 11*q - 106. Let l be r(14). Let y be (l/(-20))/(-4)*(-20)/(-14). Find o such that y*o**3 + 0*o**2 + 0 - 9/7*o**4 + 0*o = 0.
0, 2/3
Factor 6*z - 2/3*z**2 - 16/3.
-2*(z - 8)*(z - 1)/3
Let a(f) be the second derivative of -f**5/60 - 7*f**4/36 + 14*f**3/9 - 10*f**2/3 + 79*f. Let a(r) = 0. Calculate r.
-10, 1, 2
Let q(g) be the third derivative of -13*g**2 - 1/60*g**6 - 2/15*g**5 - 1/3*g**4 + 0*g + 0*g**3 + 0. Determine d so that q(d) = 0.
-2, 0
Let s(c) = -2*c**2 - 94*c + 9. Let n be s(-38). Suppose 0 = n*t - 692*t. Find d, given that -3/4*d**3 - 1/2*d**2 + t*d + 0 - 1/4*d**4 = 0.
-2, -1, 0
Let l(x) = 2*x**2 + 1. Let u be l(1). Suppose 3*v - 9 = 3*m, 4*v + 3*m = -m + 4. Factor -3*y**3 - u*y**4 - 4*y**v - y**2 + 5*y**2.
-3*y**3*(y + 1)
Solve 72*p**2 - 16*p**3 - 34 + 10 + 51 - 81*p = 0.
3/4, 3
Let w be (-3)/(-1)*(-250)/(-375). Factor 0 + 0*x**w + 1/3*x**3 - 1/3*x.
x*(x - 1)*(x + 1)/3
Suppose -i + m = -11, 5*m + 45 = 5*i + 2*m. Suppose 4*k - i*k = 0. What is z in 0*z**4 + 0*z - 2/3*z**3 + k*z**2 + 0 + 2/3*z**5 = 0?
-1, 0, 1
Factor 4*a**2 + 0*a + 0 - 2/3*a**4 - 10/3*a**3.
-2*a**2*(a - 1)*(a + 6)/3
Let y = 4684/3 - 1552. Find p such that y*p - 8/3 + 12*p**2 = 0.
-1, 2/9
Let c(w) be the second derivative of -w**5/25 + 22*w**4/15 - 82*w**3/15 + 8*w**2 - 107*w. Determine d, given that c(d) = 0.
1, 20
Let s be 5*24/20 - (-6)/11*-10. Factor -4/11 + s*c - 2/11*c**2.
-2*(c - 2)*(c - 1)/11
Let v(c) be the third derivative of c**5/24 + 15*c**4/8 + 135*c**3/4 - c**2 + 109. Find o, given that v(o) = 0.
-9
Suppose 6*q**2 + 3/4*q**3 + 9*q + 0 = 0. What is q?
-6, -2, 0
Let n(h) be the second derivative of -h**4/54 + h**3/9 - 2*h**2/9 + h + 32. Find i, given that n(i) = 0.
1, 2
Let m(y) = 173*y**3 + 479*y**2 + 397*y + 105. Let b(i) = -115*i**3 - 320*i**2 - 265*i - 70. Let s(d) = -7*b(d) - 5*m(d). Factor s(t).
-5*(t + 1)**2*(12*t + 7)
Let m(q) be the second derivative of 0*q**2 - 25*q + 0 - 1/66*q**4 + 4/33*q**3. Suppose m(k) = 0. What is k?
0, 4
Let b = -16 - -30. Solve -2*k**4 + 2*k**2 + k - 15*k**5 + b*k**5 + 0*k**2 = 0 for k.
-1, 0, 1
Let p be (-6)/15*(-5)/1. Suppose -5*r = p + 18. Let o(z) = -3*z**2 + 2*z - 4. Let u(i) = -3*i**2 + i - 5. Let a(w) = r*u(w) + 5*o(w). What is g in a(g) = 0?
0, 2
Factor 1/3*d + 4/3 - 4/3*d**2 - 1/3*d**3.
-(d - 1)*(d + 1)*(d + 4)/3
Solve 72*k**3 - 2*k**4 + 64*k**2 - 8*k**4 + 20*k + k**5 + 3*k**5 + 31*k**4 + 11*k**4 = 0 for k.
-5, -1, 0
Let g(x) = x**2 - x + 1. Suppose a = 5*v + 124, 2*v = 2*a - a - 49. Let z(r) = 30*r**2 - 30*r + 25. Let n(b) = v*g(b) + z(b). Suppose n(t) = 0. What is t?
0, 1
Let m(w) be the second derivative of -2*w**6/45 - w**5/5 + 2*w**4/3 + 16*w**3/9 - 11*w - 1. Factor m(t).
-4*t*(t - 2)*(t + 1)*(t + 4)/3
Let t(q) be the second derivative of -4*q**7/105 - 2*q**6/75 + q**5/25 + 34*q. Determine x, given that t(x) = 0.
-1, 0, 1/2
Suppose 3*m + 0*o - o - 6 = 0, -4*o + 24 = 4*m. Solve 12*h**2 + m*h**2 - 10*h - 507*h**3 + 517*h**3 = 0 for h.
-2, 0, 1/2
Let i(w) be the second derivative of -w**5/35 - 2*w**4/21 - 2*w**3/21 + 81*w. Factor i(v).
-4*v*(v + 1)**2/7
Let p(j) be the first derivative of -5*j**5 + 65*j**4/4 + 280*j**3/3 + 50*j**2 + 101. Factor p(c).
-5*c*(c - 5)*(c + 2)*(5*c + 2)
Suppose 78 = -y + 4*y - 4*b, -y + 34 = -4*b. Solve y*l + 2*l**2 + 2 - 34*l + 16*l = 0 for l.
-1
Let a(t) be the first derivative of 0*t + 2/27*t**6 - 1/6*t**4 + 2/15*t**5 - 13 + 0*t**2 - 4/27*t**3. Solve a(b) = 0.
-2, -1/2, 0, 1
Suppose t + 20 - 27 = 0. Find p such that t*p**2 - 8*p**2 + 2*p + 2*p**2 = 0.
-2, 0
Suppose 0*b - 4*b = -16. Factor -12*y**4 + 23*y**4 + 3*y**2 + 2*y - 12*y**b.
-y*(y - 2)*(y + 1)**2
Let d(u) be the first derivative of -1/6*u**4 + 0*u**2 - 8/9*u - 3 + 14/27*u**3. Factor d(a).
-2*(a - 2)*(a - 1)*(3*a + 2)/9
Let q(d) be the first derivative of 27*d**5/10 - 21*d**4/8 - d**3 + 253. Factor q(r).
3*r**2*(r - 1)*(9*r + 2)/2
Let g = -21 - -23. Factor -59*a - a**g + 27*a + 34*a.
-a*(a - 2)
Let q = -20 + 22. Suppose o - w = 5, 3*o + w = q*o - 1. Solve -7*u**2 + 15 - 3 + 4*u**o = 0.
-2, 2
Suppose 0*z + 2*z = 4*t + 16, 0 = -4*z + t + 39. Let x(c) = -c + 10. Let j be x(z). Find p such that -2*p**2 + 0 + j - p**2 + 6*p**3 - 3*p**4 = 0.
0, 1
Let r(k) be the first derivative of -2*k**3 - 4*k + 7*k**2 - 8 - 7/2*k**4 + 2*k**5. Factor r(j).
2*(j - 1)**2*(j + 1)*(5*j - 2)
Let y(j) = -2*j - 22. Let g be y(-12). Factor 43*t**2 + 0*t**3 + 2*t**3 - 43*t**g - 8*t.
2*t*(t - 2)*(t + 2)
Suppose 0 = 10*m - 147 + 97. Let r(w) be the second derivative of -1/15*w**5 + m*w + 0*w**4 + 1/45*w**6 + 0 - 1/3*w**2 + 2/9*w**3. Factor r(b).
2*(b - 1)**3*(b + 1)/3
Let p = -8 + 2. Let x(n) = 70*n**2 - 280. Let c(a) = 5*a**2 - 20. Let q(o) = p*x(o) + 85*c(o). Factor q(b).
5*(b - 2)*(b + 2)
Let q(j) be the third derivative of -j**6/300 - j**5/75 + j**4/60 + 2*j**3/15 + 4*j**2 - 9. Factor q(c).
-2*(c - 1)*(c + 1)*(c + 2)/5
Let r be (4/8)/(93/(-87)). Let s = 1/31 - r. Solve 1/4*p**2 + 0 - s*p = 0.
0, 2
Suppose 0 = -3*i + 41 - 221. Let l be -5*3/(i/8). Let 16*f**2 + f**2 + 4 - 12*f - 5*f**l - 4*f**3 = 0. What is f?
1
Factor 68 + 39*z**2 + 96 - 23*z**2 - 160*z - 20*z**2.
-4*(z - 1)*(z + 41)
Let s(c) = c**2 + 18*c - 22. Let q be s(-20). Let k be (-17 + q)/((-1)/(-2)). Solve -1/2*b**k + b + 3/2 = 0 for b.
-1, 3
Let c(d) = -d**2 - 10*d - 5. Let s be c(-12). Let q = s - -32. Determine o so that 4*o**q + 8/3*o - 20/3*o**5 + 0 + 28/3*o**2 - 28/3*o**4 = 0.
-1, -2/5, 0, 1
Let z be (-30)/(-25)*(-9*(-14)/24 + -4). What is d in 0 + 0*d**2 - z*d**3 + 0*d = 0?
0
Find v, given that 0 - 3/7*v**2 - 3/7*v**4 + 6/7*v**3 + 0*v = 0.
0, 1
Suppose 3*t - 4*t = 4*a + 5, 3*a = -5*t - 25. Let n(g) be the second derivative of 8*g + a*g**3 - 1/3*g**4 + 3/10*g**5 - 1/15*g**6 + 0 + 0*g**2. Factor n(x).
-2*x**2*(x - 2)*(x - 1)
Let c(p) = p**3 - 3*p**2 - 12. Let w be c(4). Let u be (-75)/(-90) - 2/w. Factor u + 2/3*n**2 + n.
(n + 1)*(2*n + 1)/3
Let p(k) be the first derivative of k**3/3 + 8*k**2 + 15*k - 82. Solve p(c) = 0 for c.
-15, -1
Let h = 1715 + -1715. Let s(d) be the second derivative of -1/48*d**4 + 1/160*d**5 + h - 1/48*d**3 - 14*d + 1/8*d**2. Find g such that s(g) = 0.
-1, 1, 2
Let h(s) = -170*s**2 + 165*s**2 + 2 + 5*s - 1. Suppose 2*o + o = -6. Let w(t) = t**2 - t. Let a(x) = o*h(x) - 9*w(x). Factor a(i).
(i - 2)*(i + 1)
Let s = -322 - -326. Find x such that -2/3*x**s - 2/3*x**2 - 4/3*x**3 + 0*x + 0 = 0.
-1, 0
Let s = 3094/2063 + 1/4126. Determine t so that 1/4 + 1/4*t**4 + 3/4*t**5 + 3/4*t - s*t**3 - 1/2*t**2 = 0.
-1, -1/3, 1
Let y(v) be the first derivative of -1/6*v**6 + v**4 + 0*v**5 + 8 + 0*v**3 + 0*v**2 + 0*v. Factor y(m).
-m**3*(m - 2)*(m + 2)
Let q be ((-5)/10 - (-181)/(-6))*3. Let w = -459/5 - q. What is o in -w*o**4 + 0 - 1/5*o - 3/5*o**3 - 3/5*o**2 = 0?
-1, 0
Let o(f) = 2*f + 12. Let q be o(-6). Suppose q = 3*k - 10 - 2. Factor -k*m**2 + 2*m**3 - 2*m**5 + 2*m**4 + 3*m**2 - m**2 + 0*m**2.
-2*m**2*(m - 1)**2*(m + 1)
Let g(j) = -2*j**3 - 7*j**2 + 98*j - 9. Let c be g(-9). Determine p so that 2/3 + c*p**2 - 2/3*p**4 - 4/3*p**3 + 4/3*p = 0.
-1, 1
Let y(b) be the second derivative of -5/6*b**3 + 0*b**2 + 6*b + 0*b**6 + 0 - 5/42*b**7 + 1/2*b**5 + 0*b**4. Factor y(i).
-5*i*(i - 1)**2*(i + 1)**2
Let n(b) = -12*b - 55. Let z be n(-5). Let j(q) be the third derivative of 0 - 1/180*q**z + 0*q - 1/72*q**4 + 0*q**3 - 5*q**2. What is p in j(p) = 0?
-1, 0
Let n(b) = -b**3 - 9*b**2 + 9*b - 10. Let x be n(-10). Suppose -7*d + 149 - 128 = 0. Solve 3/4*r**5 + 0 + 7/4*r**d - 1/2*r**2 + x*r - 2*r**4 = 0.
0, 2/3, 1
Let q(t) be the second deri