2/21*g**3 - 4/7*g. Let p(k) = 0. What is k?
1, 2
Suppose 4*c + l + 27 = 0, -c - c - l = 15. Let x be (-875)/(-532) + c/(-57). Find i such that 3/4*i**3 + 1/2*i + 0 + x*i**2 = 0.
-2, -1/3, 0
Let q(o) be the third derivative of 2*o**7/15 + 2*o**6/3 + 6*o**5/5 + 2*o**4/3 - 2*o**3/3 + 2*o**2 + 7*o. Find j, given that q(j) = 0.
-1, 1/7
Let f(h) be the first derivative of -h**7/840 + h**5/40 - h**4/12 - 11*h**3/3 + 3. Let z(b) be the third derivative of f(b). Determine p so that z(p) = 0.
-2, 1
Let c(m) = -m**3 + 59*m**2 + 120*m + 124. Let h be c(61). Factor -2/13*o**5 + 4/13*o**h - 2/13*o - 2/13*o**4 + 4/13*o**3 - 2/13.
-2*(o - 1)**2*(o + 1)**3/13
Let w(u) = 70*u**2 - 950*u - 910. Let b(k) = -5*k**2 + 68*k + 65. Let s(n) = -55*b(n) - 4*w(n). Find j, given that s(j) = 0.
-1, 13
Let x = 2029 - 2024. Let 0*z**4 - 8/3*z**3 + 0*z**2 + 4/3*z + 4/3*z**x + 0 = 0. Calculate z.
-1, 0, 1
Let o be ((-6)/(-16))/((-1)/(-12)). Let f = -1/23697 - -23699/47394. Factor 3*l + f*l**2 + o.
(l + 3)**2/2
Find a, given that 88/9*a + 0 - 40/9*a**2 - 2/9*a**3 = 0.
-22, 0, 2
Let j(q) = -3*q**2. Suppose -3*w - 4 = w. Suppose -11*n = -8*n + 9. Let u(b) = -b. Let o(k) = n*u(k) + w*j(k). Factor o(y).
3*y*(y + 1)
Let o = 32/33 - 1283/1221. Let l = 89/185 + o. Solve 2/5*x**3 - l - 2/5*x + 2/5*x**2 = 0 for x.
-1, 1
Suppose -q + 16 = 22. Let s be (2/(-6))/(q*(-5)/(-135)). Find u, given that -1/2*u - 3/2*u**2 + u**5 + 0 + s*u**4 - 1/2*u**3 = 0.
-1, -1/2, 0, 1
Factor 1/2*g**3 + 155/2*g**2 - 3042 + 2964*g.
(g - 1)*(g + 78)**2/2
Let j be (-3 - 35/(-10))*6. Let s be (-584)/(-48) + -7 - (-2)/(-3). Let j*v + 3/2*v**3 + s*v**2 + 0 = 0. Calculate v.
-2, -1, 0
Determine g, given that 16*g**4 - 8*g**3 + 0 + 0 + 12*g**2 - 20*g**4 = 0.
-3, 0, 1
Let f(x) be the third derivative of -x**7/1512 + x**6/108 - x**5/18 + 13*x**4/24 + x**2. Let t(q) be the second derivative of f(q). Factor t(h).
-5*(h - 2)**2/3
Let a(j) = j**3 + 12*j**2 - 21*j + 16. Let r(h) = -4*h**3 - 36*h**2 + 62*h - 48. Suppose -n - 7 - 3 = 0. Let v(y) = n*a(y) - 3*r(y). Factor v(p).
2*(p - 2)**3
Let h(l) be the second derivative of 13/5*l**5 + 5/3*l**4 + 13*l + 6/5*l**6 - 2*l**3 + 0 + 4/21*l**7 - 4*l**2. Let h(u) = 0. Calculate u.
-2, -1, 1/2
Let n(v) be the third derivative of v**8/1680 + v**7/1050 - v**6/300 + v**2 + 15. Factor n(w).
w**3*(w - 1)*(w + 2)/5
Let r(k) = 5*k - 12. Let j be r(3). Solve -37*t + 6*t**4 + 5*t - 10*t**3 - 16*t**2 + 34*t**j + 4*t**5 + 14*t**4 = 0 for t.
-2, 0, 1
Let j(n) = n**4 + 88*n**3 + 81*n**2 - 93*n - 87. Let q(u) = 4*u**4 + 440*u**3 + 408*u**2 - 464*u - 436. Let z(h) = -24*j(h) + 5*q(h). Factor z(p).
-4*(p - 23)*(p - 1)*(p + 1)**2
Let r(c) = 9*c**2 + 3*c. Let q(a) = -8*a**2 - 5*a. Let y(o) = 6*q(o) + 5*r(o). Find z such that y(z) = 0.
-5, 0
Let c(w) be the third derivative of 0*w - 13*w**2 + 0 + 3/2*w**4 + 18*w**3 + 1/20*w**5. Factor c(o).
3*(o + 6)**2
Suppose u + 34 = m, m + 133 = -4*u + 2*m. Let d = -33 - u. Determine f so that -2/11*f + d - 8/11*f**2 - 12/11*f**3 - 2/11*f**5 - 8/11*f**4 = 0.
-1, 0
Factor -94*s**2 - 43 + 41 + 7*s - 103*s.
-2*(s + 1)*(47*s + 1)
Let p(d) be the second derivative of -d**6/120 - 9*d**5/80 - d**4/8 + 2*d**3/3 + 529*d. Find s such that p(s) = 0.
-8, -2, 0, 1
Let a be -1 - -3 - 0 - -7. Let j = a - 7. Factor 3*b**5 + 0*b**5 + 2*b**2 - 3*b**3 - 8*b**4 + 11*b**4 - 5*b**j.
3*b**2*(b - 1)*(b + 1)**2
Let y(n) = -n**2 - n - 36. Let v(h) = h**2 + h + 72. Let j(w) = -4*v(w) - 7*y(w). Determine o, given that j(o) = 0.
-4, 3
Let t(s) = -3*s**3 + 4*s**2 - 52*s + 60. Let c(l) = -7*l**3 + 7*l**2 - 106*l + 123. Let p(w) = 4*c(w) - 9*t(w). Find q such that p(q) = 0.
-12, 2
Find t such that 2/9*t**3 + 0 + 50/9*t - 20/9*t**2 = 0.
0, 5
Let v = -334 - -338. Let a(p) be the first derivative of -64*p - 4/5*p**5 + 1 - 8*p**v - 32*p**3 - 64*p**2. Let a(k) = 0. What is k?
-2
Let a be 1183/130 + 21/15. Let -6 + a*d - 9/4*d**2 = 0. Calculate d.
2/3, 4
What is s in 76/9 + 8*s**3 - 80/9*s**2 - 8*s + 4/9*s**4 = 0?
-19, -1, 1
Let o(c) = -6*c**4 + 19*c**3 + 199*c**2 - 1279*c + 17. Let q(z) = -2*z**4 + 6*z**3 + 66*z**2 - 426*z + 6. Let x(l) = 6*o(l) - 17*q(l). Solve x(w) = 0 for w.
-6, 0, 6
Factor 10/3*s - 8 + 4*s**2 + 2/3*s**3.
2*(s - 1)*(s + 3)*(s + 4)/3
Let a = 25/101 - -2099/1313. Find u such that -a*u**3 - 12/13*u**4 - 2/13*u**5 + 0 - 20/13*u**2 - 6/13*u = 0.
-3, -1, 0
Let j(z) = 664*z. Let u be j(0). Factor -1/3*c**4 - 1/3*c**5 + 0*c**3 + 0 + u*c + 0*c**2.
-c**4*(c + 1)/3
Let c(o) be the second derivative of -o**6/40 + 9*o**5/80 + 5*o**4/8 - 3*o - 4. Solve c(x) = 0.
-2, 0, 5
Let x(t) be the second derivative of t**4/16 - 3*t**3/2 + 767*t. Factor x(r).
3*r*(r - 12)/4
Let o(h) be the third derivative of h**7/1512 - 5*h**6/432 - 7*h**4/8 - 10*h**2. Let t(u) be the second derivative of o(u). Factor t(x).
5*x*(x - 5)/3
Determine v, given that -8*v**2 + 23*v**4 - 28/3*v**5 + 0 - 4/3*v - 13/3*v**3 = 0.
-2/7, -1/4, 0, 1, 2
Let p be ((-7)/(-84))/(21/7). Let g(k) be the third derivative of p*k**4 + 0 - 1/315*k**7 + 4*k**2 - 1/30*k**5 + 0*k + 1/60*k**6 + 0*k**3. Factor g(i).
-2*i*(i - 1)**3/3
Let f(h) = 8*h + 11. Let o be f(0). Factor -o*x**4 + 4*x**5 - x**5 + 300*x**3 + 71*x**4.
3*x**3*(x + 10)**2
Let d(p) be the first derivative of -p**5/10 - 11*p**4/8 - 20*p**3/3 - 12*p**2 + 89. Determine q, given that d(q) = 0.
-4, -3, 0
Find b, given that 50*b**2 - 92*b**2 + 5*b**3 + 2*b - 3*b**3 + 38*b**2 = 0.
0, 1
Let b = 9 - 6. What is y in 20*y**2 + 16*y + 107*y**3 - 209*y**b + 106*y**3 = 0?
-4, -1, 0
Suppose 0 = 4*c - 34*c. Solve -4/7*i + 4/7*i**3 + c*i**2 + 0 = 0.
-1, 0, 1
Suppose 101*o - 106*o + 45 = -3*g, -14 = o + 4*g. Factor -33*j**2 + 12*j - 51/2*j**4 - 3/2 + 42*j**3 + o*j**5.
3*(j - 1)**4*(4*j - 1)/2
Let x(f) = 90*f**4 - 365*f**3 + 325*f**2 - 120*f. Let i(b) = 15*b**4 - 61*b**3 + 54*b**2 - 20*b. Let d(c) = -35*i(c) + 6*x(c). Factor d(h).
5*h*(h - 2)*(h - 1)*(3*h - 2)
Let g be 2 + (-14)/(-10) - 612/(-1020). Factor 3/4*a**2 - 1 - a + a**3 + 1/4*a**g.
(a - 1)*(a + 1)*(a + 2)**2/4
Let b(l) be the second derivative of 0 + 0*l**2 - 1/4*l**4 + 5/2*l**3 + 9*l. Determine m, given that b(m) = 0.
0, 5
Let o be (20/(-12))/(-5) - (-4 - -2). Factor -4/3 - 13/3*f - 1/3*f**4 - 5*f**2 - o*f**3.
-(f + 1)**3*(f + 4)/3
Let k be 4/(-6)*33/(-22). Let w(x) = -x**3 + x. Let z(b) = -b**3 + 16*b**2 + 25*b + 8. Let r(u) = k*z(u) - 5*w(u). Factor r(g).
4*(g + 1)**2*(g + 2)
Let b be 1/((-1)/(-10)*5). Factor -12*g + 211*g**3 + g**2 + 1 - 4 - 223*g**3 - 19*g**b - 3*g**4.
-3*(g + 1)**4
Suppose -8/11*t**5 + 194/11*t**2 - 10*t + 24/11 - 162/11*t**3 + 62/11*t**4 = 0. What is t?
3/4, 1, 4
Let q(s) be the first derivative of -s**4/120 - 3*s**3/20 - 2*s**2/5 + 9*s - 27. Let z(c) be the first derivative of q(c). Let z(n) = 0. Calculate n.
-8, -1
Suppose 169*y**2 - 282*y**2 + 189*y**2 - 8*y = 0. What is y?
0, 2/19
Suppose -180 - 209 - 189 = -289*l. Let f = 13/34 - -2/17. Factor 1/2*v**l - f*v - 1.
(v - 2)*(v + 1)/2
Let q(r) be the third derivative of 0 + 0*r + 5/2*r**3 + 1/4*r**4 - 11*r**2 + 1/100*r**5. Suppose q(w) = 0. What is w?
-5
Suppose 22*a - 30 = 14. Let z(q) be the third derivative of 0 + 0*q + 0*q**3 + 1/120*q**5 + 0*q**4 + 1/420*q**7 + 1/120*q**6 - 2*q**a. Factor z(n).
n**2*(n + 1)**2/2
Suppose -43*r = 15*r + 12*r - 8*r. Factor 0*f + r - 2/5*f**2 - 1/10*f**4 + 2/5*f**3.
-f**2*(f - 2)**2/10
Let x(r) = -2*r + 5. Let m be x(3). Let c = m + 4. Solve -w**c - w + w - w**4 = 0 for w.
-1, 0
Let o(q) be the first derivative of q**5/5 - 4*q**3/3 - 34. Determine l, given that o(l) = 0.
-2, 0, 2
Let u(r) be the first derivative of 2*r**3/3 + 95*r**2 + 188*r - 124. Determine b so that u(b) = 0.
-94, -1
Suppose 0 = -94*a + 295 - 13. Determine l so that 2/13*l**a + 0 + 12/13*l**2 - 14/13*l = 0.
-7, 0, 1
Determine z so that z**4 + 88*z**3 - 138*z**3 - 6*z**4 - 107*z**2 - 18*z**2 = 0.
-5, 0
Factor 0*w + 0 - 6*w**3 + 18*w**2 + 1/2*w**4.
w**2*(w - 6)**2/2
Let p be (1/(-2))/((-16)/64). Determine y, given that 120*y**4 - 284*y + 236*y + 96*y**2 + 216*y**3 + 19*y**5 + p*y**5 = 0.
-2, 0, 2/7
Let i(f) be the first derivative of 0*f - 24 - 8/9*f**2 - 2/27*f**3. Determine c, given that i(c) = 0.
-8, 0
Let c = -196 + 196. Let b(p) be the second derivative of c*p**3 - 4*p + 0 + 0*p**2 + 1/10*p**5 + 1/6*p**4. Determine t so that b(t) = 0.
-1, 0
Find w, given tha