200*r**3 + 407*r**2. Let w(j) = 0. Calculate j.
1, 60
Let l be (-4 - 4)/(-8)*8/2. Factor -7*a + 6*a**4 + 9*a**3 - 5*a - 13*a**4 + 4*a**l.
-3*a*(a - 2)**2*(a + 1)
Let j be 46/14 - -9*18/(-567). Suppose 4*q + 0*q + 2*k = 0, -j*q + 2*k = -14. Suppose -1/3*t**4 + 4/3*t - 1/3 - q*t**2 + 4/3*t**3 = 0. What is t?
1
Let n = 1302 + -1299. Let d(t) be the first derivative of -2/15*t**n + 2/5*t + 1/10*t**4 - 1 - 1/5*t**2. Factor d(g).
2*(g - 1)**2*(g + 1)/5
Let i be 157/(-36) + (-26)/39. Let b = i + 52/9. Suppose 0 + 3/4*h**2 + b*h**3 + 0*h = 0. Calculate h.
-1, 0
Suppose -2*c + 45 = 5*j - 7*c, -2*j = 5*c + 17. Factor -2/5*y**3 + 0*y + 2/5*y**5 + 2/5*y**j - 2/5*y**2 + 0.
2*y**2*(y - 1)*(y + 1)**2/5
Let j(p) be the first derivative of p**3/12 + 15*p**2/8 + 9*p + 91. Solve j(a) = 0.
-12, -3
Let x(h) be the second derivative of 4*h**7/7 - h**6 - 9*h**5/4 + 5*h**4/4 + h**3 - 230*h + 2. Find l, given that x(l) = 0.
-1, -1/4, 0, 1/2, 2
Let k = -14344/7 + 2050. Factor k*c + 0*c**2 - 2/7*c**3 - 4/7.
-2*(c - 1)**2*(c + 2)/7
Let d = 384637/12 + -32005. Let r = -275/6 + d. Find m such that -6*m + 4*m**2 + r = 0.
3/4
Let -28*x**4 + 3*x**3 + 217 + 28*x**2 + x**5 - 4*x**3 - 119 - 98 = 0. What is x?
-1, 0, 1, 28
Let a = 517/945 + 10/189. Let f(j) be the first derivative of -1/5*j**3 + a*j**2 + 4 + 0*j. Find c such that f(c) = 0.
0, 2
Let b(t) be the third derivative of -t**6/165 + t**5/66 + 7*t**4/132 - 2*t**3/33 - 243*t**2. Suppose b(o) = 0. What is o?
-1, 1/4, 2
Factor 16/3*m**2 - 65/3*m + 4/3.
(m - 4)*(16*m - 1)/3
Let f = 1333 + -1333. Factor 2*v + f + 2/3*v**2.
2*v*(v + 3)/3
Suppose -3*y = -17*r - 89 + 86, -3 = r - 3*y. Solve -4/9*v**3 - 1/9*v**4 - 2/9*v - 5/9*v**2 + r = 0 for v.
-2, -1, 0
Let g = 537 - 535. Let k(x) be the first derivative of 3/10*x**4 + 0*x + 3/10*x**g + 3/5*x**3 + 7. Factor k(w).
3*w*(w + 1)*(2*w + 1)/5
Solve -20/7*u**3 - 50/7*u**2 + 0*u - 2/7*u**4 + 0 = 0.
-5, 0
Let q(l) = -l**3 - l**2 + 2*l + 2. Let j be q(3). Let d be 15 - 7/(j/(-8)). Factor 6*w**2 + w**3 + d*w + 3*w**3 - 3*w**3 - 4*w.
w*(w + 3)**2
Suppose 0 = 395*c - 407*c + 36. Find l such that -4768/5*l**2 - 2662/5*l**5 - 992/5*l - 5104/5*l**c - 64/5 + 9196/5*l**4 = 0.
-2/11, 2
Suppose 5*i - 22 = -3*v + 2*v, 3*i - 2 = 5*v. Suppose 3*k + 8*k + 25*k**3 - k - 40*k**2 - 5*k**i + 10*k = 0. What is k?
0, 1, 2
Factor 0*r + 0 - 43/7*r**3 - 9/7*r**4 + 10/7*r**2.
-r**2*(r + 5)*(9*r - 2)/7
Let q(f) be the second derivative of -f**8/3360 - f**7/630 + f**6/120 - 13*f**4/4 + 6*f. Let p(b) be the third derivative of q(b). Determine j so that p(j) = 0.
-3, 0, 1
Factor -65/8*o**2 + 9/8*o**3 + 17/2*o - 3/2.
(o - 6)*(o - 1)*(9*o - 2)/8
Let n(g) be the first derivative of g**4/40 + 19*g**3/15 - 39*g**2/20 + 297. Find y, given that n(y) = 0.
-39, 0, 1
Let p(v) be the third derivative of -22*v**7/735 - v**6/105 + 56*v**2 + 2. What is s in p(s) = 0?
-2/11, 0
Let d(a) = -a - 16. Let n be d(-30). Suppose -4*b + n = -2*s, 2 = -2*b + 4*s + 18. Let -3/2*z**b + 0 + 0*z - 15/4*z**4 + 21/4*z**3 = 0. Calculate z.
0, 2/5, 1
Let r = 2016 - 22168/11. Factor 0 - r*y**4 - 4/11*y**2 + 0*y + 10/11*y**3 + 2/11*y**5.
2*y**2*(y - 2)*(y - 1)**2/11
Let y(g) be the second derivative of g**9/336 - g**8/140 + g**7/210 - 13*g**3/6 - 9*g. Let q(m) be the second derivative of y(m). Let q(w) = 0. Calculate w.
0, 2/3
Let w(i) = 2*i**4 + 4*i**3 - 8*i**2 + 2*i. Let u(p) = -3*p**4 - 4*p**3 + 9*p**2 - 2*p. Let y(k) = 3*u(k) + 4*w(k). Factor y(q).
-q*(q - 2)*(q - 1)**2
Factor -360*k**3 - 166*k**2 + 12*k**2 - 32*k**5 - 188*k**4 - 44*k**2 - 10*k**2 + 32*k.
-4*k*(k + 2)**3*(8*k - 1)
Let d = 50 - 46. Factor -8 - v - 23*v - d*v**3 + 4*v - 16*v**2.
-4*(v + 1)**2*(v + 2)
Let u(j) = 672*j - 1329. Let c be u(2). Let -33/2 + 3/2*t**2 + c*t = 0. Calculate t.
-11, 1
Let x(u) be the third derivative of -u**7/210 - 3*u**6/20 - 73*u**5/60 - 9*u**4/2 - 26*u**3/3 - 224*u**2. Factor x(b).
-(b + 1)*(b + 2)**2*(b + 13)
Suppose -10*g + 6*g = -2*i - 20, g = 4*i + 5. Let x(p) be the third derivative of i*p + 0 + 1/270*p**5 + 0*p**3 - 6*p**2 + 1/108*p**4. Factor x(t).
2*t*(t + 1)/9
Let d(p) = -12*p**4 - 8*p**3 + 40*p**2. Let r(h) = -2*h**4 - h**3 + 6*h**2. Let u(b) = 3*d(b) - 20*r(b). Factor u(x).
4*x**3*(x - 1)
Suppose 5*g + 2*u + 0*u - 4 = 0, 2*g = 4*u - 8. Suppose g*q + 5*q - 65 = 0. Suppose 16*l**3 - 12*l**4 + 7*l**3 + 6*l + q*l**3 - 27*l**2 = 0. What is l?
0, 1/2, 2
Let a = 2171 - 19537/9. Factor 4/9*v + 2/3 - a*v**2.
-2*(v - 3)*(v + 1)/9
Let i(o) be the first derivative of -36992*o**3/45 - 272*o**2/15 - 2*o/15 + 68. Determine u, given that i(u) = 0.
-1/136
Let t be (1/3)/((-1)/15). Let x be (6/12)/(-2 - t). Factor 0*c**3 - 1/6*c**4 + 0 + x*c**2 + 0*c.
-c**2*(c - 1)*(c + 1)/6
Let z(r) be the third derivative of 2*r**7/315 - r**6/3 + 53*r**5/45 + 14*r**4/3 + 860*r**2. Let z(i) = 0. Calculate i.
-1, 0, 3, 28
Let d(x) be the first derivative of -5 - 5/3*x**3 - 5*x + 5*x**2. What is j in d(j) = 0?
1
Let g = 26136 - 26134. Determine k so that -1/2 + 1/3*k + 1/6*k**g = 0.
-3, 1
Let -2/3*w + 1/6*w**3 + 0 + 1/6*w**4 - 2/3*w**2 = 0. Calculate w.
-2, -1, 0, 2
Let o(w) be the first derivative of -w**6/2 - 41*w**5/5 - 499*w**4/12 - 95*w**3/3 + 200*w**2 - 500*w/3 - 58. Factor o(z).
-(z + 5)**3*(3*z - 2)**2/3
Let h = -1 - -3. Factor -36*f**3 + 13*f + 8*f**h - 8 + 0*f**2 + 14*f + 9*f.
-4*(f - 1)*(f + 1)*(9*f - 2)
Factor -6*f - 2/5*f**2 + 32/5.
-2*(f - 1)*(f + 16)/5
Let u be (-3 - 3 - -1)/(-1). Suppose 4*o = l - 4, 0 = 2*l + u*o - 0*o + 5. Factor -3*a + 0*a**3 + l*a + 3*a**3.
3*a*(a - 1)*(a + 1)
Factor -120/13*j**2 - 24/13*j**4 + 50/13*j + 2/13*j**5 + 92/13*j**3 + 0.
2*j*(j - 5)**2*(j - 1)**2/13
Suppose 10*q - 6 = 7*q. Let 9 + 5*g**3 - 8 - 1 - 15*g**q = 0. What is g?
0, 3
Let r(b) = -2*b + 3. Let v be r(-1). Let t(h) be the third derivative of 1/6*h**4 - v*h**2 + 1/3*h**3 + 1/30*h**5 + 0*h + 0. Factor t(x).
2*(x + 1)**2
Determine c, given that 155*c + 0*c**3 + 4880*c**2 - c**3 - 5340*c**2 - 6*c**3 - 8*c**3 = 0.
-31, 0, 1/3
Suppose -v - 3*v = 12. Let i = 3 - v. Let h(k) = -k**3 - k - 1. Let p(a) = a**4 - 5*a**3 - a**2 - 7*a - 6. Let w(d) = i*h(d) - p(d). Factor w(z).
-z*(z - 1)*(z + 1)**2
Let r(s) = -27*s**2 + s + 4. Let v(n) be the third derivative of 7*n**5/30 - n**3/3 - 44*n**2. Let y(o) = 6*r(o) + 11*v(o). Factor y(p).
-2*(p - 1)*(4*p + 1)
Let -1/2*a**2 + 0 + 0*a - 1/4*a**4 - 3/4*a**3 = 0. Calculate a.
-2, -1, 0
Let p(q) = -4*q**5 + 4*q**4 + 29*q**3 - 46*q**2 + 44*q - 12. Let r(d) = d**3 + 2*d**2. Let w(v) = -p(v) + 5*r(v). Factor w(i).
4*(i - 1)**4*(i + 3)
Let r = 206 + -87. Suppose 692*v = 698*v - 36. Find s such that -114*s**3 + 8*s + 6*s + 9*s + r*s**3 - 22*s**2 - v = 0.
2/5, 1, 3
Suppose -4*q = -2*x + 37 + 19, -4*q - 5*x = 70. Let b be 23/(-21) - q/9. Factor -2/7*p**2 - b - 6/7*p.
-2*(p + 1)*(p + 2)/7
Suppose -4*a + 28 = 5*v, 5*v + 49 + 7 = 3*a. Let i = a + -10. Factor -5*n + 5*n**i + 5*n - 2*n**2.
3*n**2
Let k(o) = -o**2 - 12*o + 5. Let n be k(-12). Let l = -74 - -130. Let -l*i**3 + 20*i**4 - 4*i**2 + 0*i**2 + 60*i**3 + 12*i**n = 0. What is i?
-1, 0, 1/3
Determine u so that 4/3*u + 0 - u**2 - 23/6*u**4 + 2*u**5 - 33/2*u**3 = 0.
-2, -1/3, 0, 1/4, 4
Let b = -70 - -73. Find i, given that 54 - 6*i**3 + b*i + 53 + 6*i**4 - 12*i**2 - 101 + 3*i**5 = 0.
-2, -1, 1
Let v(w) be the first derivative of w**7/378 - w**6/135 - w**5/60 - 19*w - 11. Let n(g) be the first derivative of v(g). Let n(i) = 0. Calculate i.
-1, 0, 3
Find n, given that 2592 + 72*n + 1/2*n**2 = 0.
-72
Factor -n**2 - 15*n - 19*n**2 - 360*n**3 + 355*n**3 - 10*n**2 + 50.
-5*(n - 1)*(n + 2)*(n + 5)
Let b be (210/(-75))/(2/(-10)). Let i = 44/3 - b. Factor 4/3*m**3 - 2/3*m + 0 + i*m**2.
2*m*(m + 1)*(2*m - 1)/3
Suppose 5*k - 25 = 0, -321*f + 320*f + 4*k - 15 = 0. Solve -1/4*y**f - y**2 - 3/2*y**3 - 1/4*y - y**4 + 0 = 0.
-1, 0
Let p(v) be the first derivative of -1/50*v**5 + 0*v**4 + 0*v**3 + 8 + 0*v + v**2 + 1/200*v**6. Let a(b) be the second derivative of p(b). Factor a(q).
3*q**2*(q - 2)/5
Let o be -2 - (4/(-34) + (-1539)/646). Factor o*r**4 - r - 1/2 + 0*r**2 + r**3.
(r - 1)*(r + 1)**3/2
Factor -1/7 + 1/7*m - 1/7*m**3 + 1/7*m**2.
-(m - 1)**2*(m + 1)/7
Let k be 5/15*21 + 0 + -1. Find w such that -4*w + 2*w**3 + 7*w**5 - 43*w**4 + 49*w**4 - 5*w**5 - k*w**2 = 0.
-2, -1, 0, 1
Suppose 0 = -5*t, l - 4*t + 9 = 4*l. Let