e i*l - 5*k + 5 = 153*l, 5*l = -3*k + 3. Factor l - 4/3*s**2 - 2*s + 2/3*s**3.
2*s*(s - 3)*(s + 1)/3
Let x be (2 - 11)*(-40)/15. Suppose 3*o + o = 16. Factor 78 + x*f - o*f**2 + 7*f**2 - 30.
3*(f + 4)**2
Let y be 7/((-196)/8) + 1518/(-77). Let m be (-12)/y*10/4. Factor 1/2*p**3 + 3/2*p**2 + 1/2 + m*p.
(p + 1)**3/2
Let n(s) = s + 1. Let p be n(3). Suppose -29 = -2*c + 5*g, -2*c = 5*g + 26 - 5. Solve -19199*r**3 - p - 120*r - 2686*r**c + 3199*r**3 + 286*r**2 + 2 = 0 for r.
-1/20
Let i(w) be the third derivative of -w**6/120 - 11*w**5/10 + 349*w**4/24 - 71*w**3 - 2792*w**2 + w. Factor i(z).
-(z - 3)*(z - 2)*(z + 71)
Let a(x) be the third derivative of -x**6/10 + 26*x**5/15 - 21*x**4/2 + 80*x**3/3 + 3*x**2 + 4*x. Find c such that a(c) = 0.
1, 8/3, 5
Let h(z) be the first derivative of -2*z**3/9 + 1304*z**2/3 - 850208*z/3 - 1137. Find v such that h(v) = 0.
652
Let p(d) be the second derivative of -d**4/16 - 805*d**3/8 - 603*d**2/2 + 867*d. Find z such that p(z) = 0.
-804, -1
Find b, given that -25*b**5 + 3850644*b**3 - 340*b**4 + 72*b**2 + 220*b - 3851379*b**3 - 272*b**2 = 0.
-11, -2, -1, 0, 2/5
Let h(a) be the second derivative of -1/60*a**6 - 27*a**3 + 90 + 0*a**2 - 12*a**4 + a + 7/8*a**5. Factor h(q).
-q*(q - 18)**2*(q + 1)/2
Suppose -3*b = 6, 5*r = -2*b + 6*b + 88. Let j be ((-4)/(-3))/((-62)/(-93)). What is y in -y**j - 16*y - 16*y - 11*y - r + 35*y = 0?
-4
Let g(w) be the first derivative of -16/19*w**2 + 0*w + 111 - 2/57*w**3. Find a, given that g(a) = 0.
-16, 0
Let l be 2/(20/130) - 3. Let u(f) be the second derivative of 0 + 35/3*f**3 + l*f**2 + 5/8*f**5 - 12*f + 55/12*f**4. Factor u(a).
5*(a + 2)**2*(5*a + 2)/2
Suppose -3*g - 20 = -2*c, -4*c + 3*g + 20 = 2*g. Let h be 1/(c/2)*(5 + -1). Determine d, given that 2*d**3 - 404*d**h + 403*d**2 - d**3 = 0.
0, 1
Let w = -9553/1448 + 1262/181. Find i such that 7/4*i**3 + 5/8*i**2 + w*i**4 - 7/4*i - 1 = 0.
-4, -1, -2/3, 1
Let u(w) be the third derivative of -2*w**7/105 - 2*w**6/5 + w**5/15 + 2*w**4 - 2*w**2 + 51. Factor u(p).
-4*p*(p - 1)*(p + 1)*(p + 12)
Let m(o) be the third derivative of 157216*o**6/45 - 4624*o**5/5 + 102*o**4 - 6*o**3 + 135*o**2 - 20*o - 2. What is f in m(f) = 0?
3/68
Let q(g) be the first derivative of g**4/42 - 8*g**3/21 - 20*g**2/7 - 62*g + 61. Let x(l) be the first derivative of q(l). Factor x(o).
2*(o - 10)*(o + 2)/7
Let r(h) = h**3 - 18*h**2 + 9*h - 37. Let b be r(18). Suppose -26*d - b = -51*d. Find q such that 16/7*q + 0 - 64/7*q**2 - 4*q**d + 64/7*q**4 + 12/7*q**3 = 0.
-1, 0, 2/7, 1, 2
Suppose -w - 111 = -3*u + 2*w, 0 = -3*u - 3*w + 99. Determine m so that 108*m**2 + 5*m**4 - 12*m - u*m**3 + 12*m - 58*m**2 = 0.
0, 2, 5
Let a(n) = -4*n**2 + 157*n + 197. Let l(c) = -c**2 - 14*c - 1. Let h(b) = 4*a(b) - 12*l(b). Let h(z) = 0. What is z?
-1, 200
Determine z so that 6/5*z**3 + 0 - 740*z**2 - 1234/5*z = 0.
-1/3, 0, 617
Determine k, given that -3/4*k**5 - 42*k**2 - 72*k + 33/2*k**3 + 96 + 9/4*k**4 = 0.
-4, -2, 1, 4
Let w(v) = 49*v**3 - 443*v**2 + 1068*v - 700. Let a(j) = -540*j**3 + 4870*j**2 - 11745*j + 7700. Let m(l) = -4*a(l) - 45*w(l). Solve m(i) = 0.
10/9, 2, 7
Factor -20 - 27/2*g - 1/2*g**3 + 6*g**2.
-(g - 8)*(g - 5)*(g + 1)/2
Let y(i) be the third derivative of -i**6/30 - 103*i**5/30 + 13*i**4/3 + 77*i**2. Solve y(c) = 0 for c.
-52, 0, 1/2
Let x = -40297 - -40297. Factor x + 40/9*s**4 + 0*s**2 - 64/9*s**3 + 0*s - 4/9*s**5.
-4*s**3*(s - 8)*(s - 2)/9
Let o(j) = -j**3 - j**2 + j + 1. Let p(v) = v**3 + 16*v**2 - v - 16. Suppose 2*k = -2, 4*b + 4*k = b - 1. Let g(s) = b*p(s) + 6*o(s). Factor g(r).
-5*(r - 2)*(r - 1)*(r + 1)
Let r(l) be the second derivative of 0*l**2 - 1 + 30*l + 0*l**3 - 1/15*l**6 + 1/10*l**5 + 0*l**4. Factor r(z).
-2*z**3*(z - 1)
Let t(z) = -2*z**4 - 23*z**3 + 153*z**2 - 106*z - 994. Let h(p) = p**4 - p**2 + 2*p - 2. Let u(c) = 3*h(c) + t(c). Factor u(r).
(r - 10)**2*(r - 5)*(r + 2)
Let k(j) be the second derivative of j**5/90 + 58*j**4/27 + 1085*j**3/27 + 2650*j**2/9 - 3*j + 88. Factor k(b).
2*(b + 5)**2*(b + 106)/9
Factor 0*p - 26/5*p**3 + 0 + 24/5*p**2 + 2/5*p**4.
2*p**2*(p - 12)*(p - 1)/5
Let y(t) = -8*t**2 + 244*t - 3840. Let p(v) = 7*v**2 - 255*v + 3846. Let q(l) = -2*l + 1. Let j(c) = p(c) - 5*q(c). Let d(f) = -4*j(f) - 3*y(f). Factor d(r).
-4*(r - 31)**2
Let r be (999/(-1188))/(7/244). Let g = -291/11 - r. Factor 0 + 32/7*w**2 + 12/7*w**3 + g*w.
4*w*(w + 1)*(3*w + 5)/7
Find s such that -1/2*s**3 - 1800*s + 0 - 60*s**2 = 0.
-60, 0
Suppose 163*y + 252*y + 272*y + 1219*y - 57*y = 0. Determine d, given that 0 + y*d + 8*d**2 - 14/3*d**5 - 12*d**4 + 26/3*d**3 = 0.
-3, -4/7, 0, 1
Let a(i) be the second derivative of 3*i**5/5 - 71*i**4/3 + 704*i**3/3 - 408*i**2 + i - 1271. Factor a(g).
4*(g - 17)*(g - 6)*(3*g - 2)
Let t(n) = n - 6. Let v be t(13). Determine b so that 18*b**5 - 6*b**2 + 25*b**2 + v*b**3 + 51*b**4 + 3*b + 2*b**2 + 44*b**3 = 0.
-1, -1/2, -1/3, 0
Let x(t) be the first derivative of 2*t**3/9 + 7*t**2/3 - 12*t + 2180. Factor x(r).
2*(r - 2)*(r + 9)/3
Let l be 99*((-10)/6 - (5 + -7)). Suppose 19*x - 208 = -l*x. Determine b so that 2/3*b**3 - 4/3 - 4/3*b - 1/3*b**x + b**2 = 0.
-1, 2
Let v(z) = z**2 - 39*z - 520. Let p(o) = -2*o**2 + 30*o + 520. Let g(l) = -3*p(l) - 2*v(l). Factor g(w).
4*(w - 13)*(w + 10)
Determine u, given that 106/7*u + 40/7*u**2 + 68/7 + 2/7*u**3 = 0.
-17, -2, -1
Let b(p) be the third derivative of 0*p**5 + 1/70*p**7 + 0*p + 0*p**3 - 32*p**2 - 3/160*p**6 - 2 + 0*p**4. Let b(x) = 0. What is x?
0, 3/4
Factor -825*n**2 + 1420029/5*n + 3/5*n**3 - 1415907/5.
3*(n - 687)**2*(n - 1)/5
Suppose 133*n - 5*o = 134*n - 27, 2*n = 3*o - 11. Let j(q) be the second derivative of 10/3*q**4 + 0*q**n - 3/4*q**5 - 10/3*q**3 + 0 + 11*q. Factor j(k).
-5*k*(k - 2)*(3*k - 2)
Let i(m) be the third derivative of 0*m**7 - 2/15*m**6 + 1/84*m**8 + 1 + 0*m + 4/3*m**3 + 1/2*m**4 - 2*m**2 - 2/15*m**5. Factor i(y).
4*(y - 2)*(y - 1)*(y + 1)**3
Let o(k) be the third derivative of k**5/330 + 65*k**4/132 + 62*k**3/11 + 1660*k**2. Find t, given that o(t) = 0.
-62, -3
Let f(d) be the third derivative of d**5/10 + d**4 + 3*d**3 + d**2. Let o(v) = -v**2 - v. Let u be (4 - 54)/5 - -18. Let k(y) = u*o(y) + f(y). Factor k(i).
-2*(i - 9)*(i + 1)
Let l be 12*(-84)/(-80)*((-49)/42 + 2). Let 10*u**3 - l*u**2 + 0*u + 1/2*u**4 + 0 = 0. What is u?
-21, 0, 1
Suppose 0 = 9*l - 51 + 33. Solve -130*a**4 + 18*a**5 + 480*a**l + 20 - 832*a + 55 + 43*a**3 + 85 + 93*a**3 = 0 for a.
-2, 2/9, 2, 5
Suppose 0*i = -5*s - 3*i + 57, 2*i - 8 = 0. Let x be (s/2)/3 - -2. Suppose -q**2 + 0 + 0*q - x*q**3 = 0. Calculate q.
-2/7, 0
Suppose v = 3*b + 39, -2*v = -10*b + 9*b - 88. Let y be (-141)/(-27) - (415/v + -9). Factor 368/5*n**3 + 10*n**y + 192/5*n**2 + 32/5*n + 48*n**4 + 0.
2*n*(n + 2)**2*(5*n + 2)**2/5
Let y = 1193 - 1153. Let m(k) be the second derivative of -5/12*k**4 - y*k**2 + 0 - 9*k - 20/3*k**3. Solve m(c) = 0 for c.
-4
Factor -17*z**2 + 7 - 112*z - 8*z**2 - 10*z**2 + 137 + z**3 + 2*z**2.
(z - 36)*(z - 1)*(z + 4)
Suppose -b = -2*n - 8, 0*b + 22 = 5*b - 4*n. Suppose 2*y = -2*c, 2*y - 3*c = -b*y + 35. Factor 0*u**5 + 2*u**5 + y*u - 3*u - 4*u**3.
2*u*(u - 1)**2*(u + 1)**2
Let n(x) be the first derivative of 5/12*x**4 + 33 + 0*x**2 - 9*x + 10/3*x**3. Let j(c) be the first derivative of n(c). Suppose j(t) = 0. Calculate t.
-4, 0
What is j in 192/11*j + 0 - 58/11*j**2 + 2/11*j**5 - 194/11*j**3 + 58/11*j**4 = 0?
-32, -1, 0, 1, 3
Let i(w) be the first derivative of w**4 - 148*w**3/3 + 720*w**2 - 1296*w + 1549. Let i(f) = 0. What is f?
1, 18
Let a(k) be the first derivative of -2*k**3/45 + 524*k**2/15 + 70*k - 4724. Determine x so that a(x) = 0.
-1, 525
Suppose 7825*d - 7826*d = 5*w, 4*w - 3*d = 0. Suppose 0 - 3/7*i**2 + 4/7*i**3 - 1/7*i**4 + w*i = 0. Calculate i.
0, 1, 3
Suppose 5*v + 18 = -k, k = 3*k + 5*v + 21. Let z(p) = -11*p**2 + 38*p - 3. Let b(m) = -25*m**2 + 76*m - 7. Let y(r) = k*b(r) + 7*z(r). What is n in y(n) = 0?
0, 19
Let i be (-14)/(-28)*(1 + -2 - (-9)/7). Find m, given that -i*m**3 - 24/7*m - 11/7*m**2 + 36/7 = 0.
-6, 1
Determine v, given that 199*v**3 + 6 - 355*v**3 + 4*v**5 + 16*v**4 + 216*v**2 - 6 = 0.
-9, 0, 2, 3
Let g(u) be the third derivative of -u**5/24 + 7355*u**4/48 - 1225*u**3/2 + u**2 + 4081. Factor g(i).
-5*(i - 1470)*(i - 1)/2
Suppose 3*b + 63 = -5*l + 78, 6 