 1)*(k + 1)**3/6
Let i = 5197 - 140338/27. Let a = -1/27 - i. Determine z, given that 0 - a*z**2 + 4/3*z - 2/3*z**3 = 0.
-2, 0, 1
Let m be (-2)/4 - 5/(-10) - -95. Let z = 99 - m. Determine u, given that 2*u**3 - 3*u**z + 8/3*u**2 - 2*u + 1/3 = 0.
-1, 1/3, 1
Let o(m) be the first derivative of 0*m**4 + 0*m + 0*m**3 - 1/18*m**6 + 1/15*m**5 + 5 + 0*m**2. What is s in o(s) = 0?
0, 1
Suppose -m = 2*v - 7, 74*m + 14 = 3*v + 72*m. Find d, given that 3*d + 1/2*d**2 + v = 0.
-4, -2
Determine o so that -3*o**3 + 8*o**2 - 7*o**2 - 3*o**4 + 4*o**2 - 9*o + 5*o**2 + 5*o**2 = 0.
-3, 0, 1
Let i(h) be the first derivative of 9*h**4/4 + 58*h**3 - 309*h**2/2 + 126*h + 59. Suppose i(d) = 0. What is d?
-21, 2/3, 1
Let s(v) be the third derivative of v**7/630 - v**6/60 - 2*v**5/15 + 2*v**4/3 + 19*v**2. Let l(w) be the second derivative of s(w). Let l(c) = 0. Calculate c.
-1, 4
Let p(o) be the second derivative of -o**4/6 + 58*o**3/3 - 841*o**2 + 55*o. Factor p(k).
-2*(k - 29)**2
Let k be 6/18 + 417/(-1260). Let p(b) be the third derivative of -k*b**6 + 0*b**3 + 0 + 1/210*b**5 + 5*b**2 + 1/42*b**4 + 0*b. Suppose p(l) = 0. What is l?
-1, 0, 2
Suppose i**3 + 13*i + 3*i**2 - 27*i + 11*i + 5*i = 0. Calculate i.
-2, -1, 0
Let j = 38 + -110/3. Suppose w = -4*y + 20, -5*w - 2*y + 0 = -28. Factor 2/9*u**w + 20/9*u + 2/3 + 8/3*u**2 + j*u**3.
2*(u + 1)**3*(u + 3)/9
Let i = 7 - 0. Suppose -3*k = -10 + 4. Factor 2*q - 2*q - 28*q**3 - 9*q**4 - 6*q**k + i*q**3.
-3*q**2*(q + 2)*(3*q + 1)
Let n(u) be the third derivative of 1/18*u**4 + 0*u**3 - 7/180*u**6 + 0 + 1/18*u**5 + 0*u + 6*u**2. Factor n(w).
-2*w*(w - 1)*(7*w + 2)/3
Let z be 8 + (-3 - 2) + 2 + -3. Let m(a) be the third derivative of 0 + 0*a + 0*a**7 + 1/840*a**8 + 4*a**z + 0*a**5 - 1/300*a**6 + 0*a**3 + 0*a**4. Factor m(h).
2*h**3*(h - 1)*(h + 1)/5
Let m(p) be the first derivative of -p**4/4 + 3*p**3/2 - 3*p**2 + 15*p + 13. Let d(x) be the first derivative of m(x). Determine z, given that d(z) = 0.
1, 2
Suppose -d = 83 - 95. Let z be (5 + -3 - 2) + d/9. Solve -1/3*c**2 + z*c - 1 = 0.
1, 3
Factor 93/4*z + 15/4*z**2 + 9/2.
3*(z + 6)*(5*z + 1)/4
Let l = -573 + 576. Let w(b) be the second derivative of 9*b + 1/9*b**4 + 7/9*b**l - 1/30*b**5 + 0 + 4/3*b**2. Factor w(s).
-2*(s - 4)*(s + 1)**2/3
Let 149/4*p + 1/4*p**2 + 37 = 0. What is p?
-148, -1
Determine b, given that -21*b**3 + 8 - 3*b**2 - 11*b**3 + 2*b - 2*b**2 + 33*b**3 = 0.
-1, 2, 4
Suppose -19*q = -14 - 43. Let l(v) be the second derivative of -2*v + 1/6*v**4 + 0 + 1/3*v**q + 0*v**2. Factor l(k).
2*k*(k + 1)
Let j(a) be the second derivative of -a**5/20 - a**4/4 - a**2 + 9*a. Let d(x) = -x**4 - 6*x**3 - 14*x**2 - x - 11. Let q(v) = -4*d(v) + 22*j(v). Factor q(w).
2*w*(w - 1)*(w + 2)*(2*w - 1)
Let a(z) = -z**4 - 116*z**3 + 301*z**2 + 436*z. Let p(s) = -2*s**4 - 116*s**3 + 302*s**2 + 440*s. Let d(m) = -6*a(m) + 5*p(m). Factor d(o).
-4*o*(o - 26)*(o - 4)*(o + 1)
Suppose 4*n - 2*a = -2, -4*a + 0 = -4. Let o(u) be the third derivative of -1/15*u**5 + 0*u**4 + 11*u**2 + 2/3*u**3 + n*u + 0. Determine w so that o(w) = 0.
-1, 1
Suppose -7 - 2*k**3 + 8*k + 3/4*k**2 + 1/4*k**4 = 0. What is k?
-2, 1, 2, 7
Suppose 92*y - 17*y = 225. Let a(l) be the second derivative of l**y - 2*l**2 + 0 + 6*l - 1/6*l**4. Suppose a(m) = 0. What is m?
1, 2
Let c(b) be the first derivative of -b**6/36 - 8*b**5/15 - 29*b**4/24 - 7*b**3/9 + 73. Solve c(y) = 0 for y.
-14, -1, 0
Let t = -68/3 - -23. Suppose -3 = 36*v - 35*v - 5. Factor -2/3*i**3 - 1/3 + t*i + 2/3*i**v + 1/3*i**5 - 1/3*i**4.
(i - 1)**3*(i + 1)**2/3
Let z(n) = -10*n**2 + 20*n - 5. Let l(w) = 9*w**2 - 20*w + 7. Let i(v) = -5*l(v) - 4*z(v). What is d in i(d) = 0?
1, 3
Let n = -23891/18 - -2655/2. Factor 0 + n*x**4 + 2/9*x**5 + 0*x**3 + 0*x + 0*x**2.
2*x**4*(x + 1)/9
Let q(h) = 12*h + 61. Let s be q(-5). Let f be ((-2)/(-8) + 51/68)*s. Factor -1/3*v**3 + f - v**2 + 1/3*v.
-(v - 1)*(v + 1)*(v + 3)/3
Let w = 11 - 11. Let v = 63/2 + -31. Suppose w - v*c**2 - 1/2*c = 0. Calculate c.
-1, 0
Let m(d) be the first derivative of -d**6/24 + d**5/6 + 5*d**4/8 - 2*d**2 - 34. Let q(s) be the second derivative of m(s). Factor q(j).
-5*j*(j - 3)*(j + 1)
Let q(v) be the second derivative of -1/5*v**3 + 0*v**2 - 46*v - 1/50*v**5 + 0 + 2/15*v**4. Let q(g) = 0. What is g?
0, 1, 3
Factor 0*u**3 - 15*u**2 + 5*u**3 + 171 - 171.
5*u**2*(u - 3)
Let a(l) be the first derivative of 3*l**4/28 + 22*l**3/7 - 141*l**2/14 + 72*l/7 - 45. Solve a(d) = 0 for d.
-24, 1
Let a(b) be the second derivative of b**7/2310 - b**6/1320 - b**5/660 + b**4/264 - 5*b**2/2 + 7*b. Let y(x) be the first derivative of a(x). Factor y(z).
z*(z - 1)**2*(z + 1)/11
Let g = 248980/19803 + -4/2829. Let w be ((-8)/(-6))/((-21)/(-216)). Factor -36/7*n**4 + w*n**3 - 4/7 - g*n**2 + 32/7*n.
-4*(n - 1)**2*(3*n - 1)**2/7
Let c(p) be the third derivative of p**8/672 - p**7/20 + 33*p**6/80 + 121*p**5/120 - 72*p**2. Find f such that c(f) = 0.
-1, 0, 11
Let r(g) be the second derivative of -g**5/80 + 41*g**4/48 - 44*g**3/3 - 363*g**2/2 + g + 89. Factor r(b).
-(b - 22)**2*(b + 3)/4
Let n(h) be the second derivative of -h**4/15 + 2*h**3/5 + 4*h**2 + 60*h. Determine r, given that n(r) = 0.
-2, 5
Determine q so that -3/2*q**2 + 0*q + 27/2 = 0.
-3, 3
Let n = -8 - 2. Let s(h) = -h**2 - 10*h + 3. Let a be s(n). Solve 4*r**2 - 5*r**2 - 4*r**2 + a*r**3 - r**2 = 0.
0, 2
Let p = -7207/5 + 1442. Let l = 2/501 - -1493/2505. Factor -l*w + p*w**2 + 0.
3*w*(w - 1)/5
Factor 463 - 5*n**3 - 58 + 4214*n**2 - 475*n - 4129*n**2 + 470.
-5*(n - 7)*(n - 5)**2
Let n be (-14)/(-3)*(-12)/(-14). Suppose -2*z = v - 15, -60 = n*v - 7*v - z. Factor 8*t - 3*t**3 - 5*t - 18*t**2 + v*t**2 - 3*t**4.
-3*t*(t - 1)*(t + 1)**2
Let 4*n**3 - 20*n**2 + 2 - 4*n - 10 - 12*n**2 + 40*n**2 = 0. Calculate n.
-2, -1, 1
Factor -8/7*a**3 + 8/7 - 4/7*a - 20/7*a**2.
-4*(a + 1)*(a + 2)*(2*a - 1)/7
Let l(f) be the first derivative of -2/9*f**3 + 4 - 8/3*f**2 - 32/3*f. Solve l(q) = 0.
-4
Let l(y) = -92*y**3 + 20*y**2 - 9*y + 8. Let z(b) = b**3 - b + 1. Suppose -4*g = -5*a - 3*g + 123, 0 = a + 3*g - 15. Let r(w) = a*z(w) - 3*l(w). Factor r(h).
3*h*(10*h - 1)**2
Let t(h) = -h + 9. Let u(v) = v - 9. Let z(l) = 5*t(l) + 4*u(l). Let q be z(8). Determine r, given that 3*r**3 - q - 5 - 1 - 3*r + 4 + 3*r**2 = 0.
-1, 1
Let o be (8/(-16))/(1311/(-654) + 2). Let r = -109 + o. Find p, given that 0*p + 7/3*p**3 + 2/3*p**2 + r = 0.
-2/7, 0
Let o(x) = 30*x**2 + 15*x - 20. Let f(y) = -y**2 - 3*y. Let j(u) = u**2 + 2*u. Let i(g) = 2*f(g) + 3*j(g). Let t(h) = -25*i(h) + o(h). Let t(d) = 0. What is d?
-4, 1
Let t be ((-6)/10)/(2/10). Let v be (t*12/(-9))/2. Suppose 0*p - 1/4 + 1/2*p**v + 0*p**3 - 1/4*p**4 = 0. Calculate p.
-1, 1
Let n = 8 + -6. Factor -i**4 - 50*i + 50*i - 2*i**n + 3*i**3.
-i**2*(i - 2)*(i - 1)
Let m(w) = 7*w**2 - 17*w + 66. Let c(v) = -19*v**2 + 55*v - 199. Let j(y) = -4*c(y) - 11*m(y). Factor j(p).
-(p - 2)*(p + 35)
Let s(a) be the second derivative of -a**5/20 + a**4/12 + 329*a. Factor s(p).
-p**2*(p - 1)
Determine f, given that 4/5*f**2 + 0 - 8/5*f = 0.
0, 2
Let f(p) = -p**2 - 148*p - 151. Let o(w) = w**2 + 295*w + 304. Let c(d) = 5*f(d) + 2*o(d). Determine t, given that c(t) = 0.
-49, -1
Let y(a) = -2*a**2 - a + 1. Let b(h) = 3*h**2 - 117*h - 1203. Let d(w) = b(w) + 3*y(w). Determine o so that d(o) = 0.
-20
Let j(w) = 21*w**4 + 191*w**3 + 959*w**2 + 1451*w + 640. Let l(c) = -4*c**4 - 38*c**3 - 192*c**2 - 290*c - 128. Let m(s) = -2*j(s) - 11*l(s). Solve m(r) = 0.
-8, -1
Let v(a) be the third derivative of 5*a**8/336 - a**7/14 - 34*a**2 - 1. Suppose v(l) = 0. What is l?
0, 3
Let y(q) be the second derivative of 2*q**7/147 - 34*q**6/105 - 38*q**5/35 + 282*q**4/7 + 2574*q**3/7 + 9126*q**2/7 + q - 140. Factor y(n).
4*(n - 13)**2*(n + 3)**3/7
Factor 13*w**2 + 21*w - 12*w - 145*w**3 + 148*w**3 + 3 - 4*w**2.
3*(w + 1)**3
Factor 40/7*z**2 + 2/7*z**3 + 102/7*z + 0.
2*z*(z + 3)*(z + 17)/7
Let g(f) be the third derivative of -13*f**2 + f**3 + 1/40*f**5 - 1/4*f**4 + 0*f + 0. Factor g(v).
3*(v - 2)**2/2
Let o(m) = m + 17. Let c be o(-17). Suppose t**4 + t**5 + c*t**5 - 4*t**4 + 2*t**4 = 0. What is t?
0, 1
Let v(f) be the first derivative of -5*f**3/6 + 25*f**2/4 - 10*f + 17. Determine i, given that v(i) = 0.
1, 4
Suppose 0 = 2*a - 2 - 4. Let m be a/(2 - (-20)/(-16)). Let -60*q*