**2/2
Suppose 13*g - 76*g + 126 = 0. Factor 6*z**g - 1150*z**4 - 2*z**2 + 1151*z**4 + 5*z**3.
z**2*(z + 1)*(z + 4)
Let q be ((-66)/18 - (-6)/9) + 59. Suppose 70*i - 170*i + q*i - 2*i**2 = 0. What is i?
-22, 0
Let u be (-2)/5 + (-12)/(-5). Let a(m) = -3*m + 10. Let g be a(-7). Factor -u*b**2 - g*b + 0*b**2 - b**2 + 25*b.
-3*b*(b + 2)
Let v be (4 - (-1066)/(-273)) + 4/(-42). Let g(r) be the first derivative of v*r - 28 + 4/15*r**3 + 1/20*r**4 + 3/10*r**2. Determine a, given that g(a) = 0.
-3, -1, 0
Suppose -528 = -11*a + 55. Factor 31*b - a*b + 12*b - 5*b**3 - 15*b**2.
-5*b*(b + 1)*(b + 2)
Let f(c) = -3*c + 70. Let t be f(31). Let b be (-20)/(-80) - t/36. Let 10/3*u - 8/9*u**2 + b = 0. Calculate u.
-1/4, 4
Let b(r) be the first derivative of -4*r**3/3 - 348*r**2 - 1376*r - 1845. Determine t, given that b(t) = 0.
-172, -2
Let h(z) be the second derivative of 1/10*z**5 - 118*z - 3*z**3 + 9/2*z**2 + 0 + 1/10*z**6 - 7/3*z**4. Determine m, given that h(m) = 0.
-3, -1, 1/3, 3
Let o = -22 - -27. Suppose n + 215 = o*p + 5*n, -20 = 4*n. What is v in -47 + 4*v**2 + p = 0?
0
Let o(u) be the first derivative of u**6/16 - u**5/8 - 11*u**4/32 - u**3/8 - 632. Let o(l) = 0. What is l?
-1, -1/3, 0, 3
Let h(w) = -7*w - 52. Let b be h(-8). What is t in -236*t**4 + 6*t + 115*t**4 + 107*t**b - 6*t**3 + 14*t**2 = 0?
-1, -3/7, 0, 1
Let s = 1582500 + -1582498. What is w in 52*w - 1/2*w**5 - 31/2*w**3 - 40 - 11/2*w**4 + 19/2*w**s = 0?
-5, -4, 1
Let r(q) = -27*q**3 - q**2 - 7*q - 9. Suppose 3*y + 5*w = -29, w + 1 = -5*y - 18. Let i be r(y). Factor 5*o**2 - 5*o**4 + o + 5*o**3 - i*o**5 + 727*o**5 - o.
-5*o**2*(o - 1)*(o + 1)**2
Let w(u) = 9*u**3 + 62*u**2 - 79*u - 172. Let z(n) = -8*n**3 - 64*n**2 + 80*n + 168. Let j(d) = -4*w(d) - 5*z(d). Determine l, given that j(l) = 0.
-19, -1, 2
Solve 2/5*u**4 + 3754/5*u**2 + 4788/5 + 7998/5*u + 546/5*u**3 = 0.
-266, -3, -1
Let u(w) be the second derivative of -w**6/15 + 7*w**5/4 + 49*w**4/6 + 20*w**3/3 + w + 78. Find s such that u(s) = 0.
-2, -1/2, 0, 20
Let o(d) be the second derivative of d**5 + 156*d**4 + 554*d**3/3 - 372*d**2 + 2559*d. Solve o(v) = 0 for v.
-93, -1, 2/5
Let y(g) be the first derivative of 42*g**5 - 7251*g**4/4 - 8073*g**3/7 - 636*g**2/7 + 60*g + 2044. What is c in y(c) = 0?
-2/7, 1/10, 35
Let c be ((0 - -9) + (-3354)/312)/(1/(-2)). Let z be -3 + 1 + 1 - -3. Factor c*t**2 - z - 6*t.
(t - 2)*(7*t + 2)/2
Suppose 5*r = -r + 102. Suppose 11 = -3*i + r. Solve q**i - q**3 + q + 6*q - 3*q - q**4 - 3*q = 0 for q.
-1, 0, 1
Find y, given that -760*y - 801*y**2 - 906*y**3 - 711*y**2 - 10*y**4 + 1872*y**3 = 0.
-2/5, 0, 2, 95
Suppose -722 + 734 = -4*z. Let c be 7 - ((-44)/(-6) - (-1)/z). Solve 12/11*p**2 - 2/11*p + c = 0 for p.
0, 1/6
Let w(j) = j**3 + 1145*j**2 - 1121*j - 2265. Let c(d) = d**3 + 573*d**2 - 561*d - 1133. Let k(s) = -9*c(s) + 5*w(s). Suppose k(l) = 0. What is l?
-1, 2, 141
Let u be 6/18*1*12. Suppose -g + 14 = 4*p, -2*g - 12 = -u*p + 2*p. What is z in p*z + 21*z**2 - 111*z**2 + 10 + 30 + 25*z**3 + 56*z = 0?
-2/5, 2
Suppose -103 = -9*p + 7*s - 2*s, -70 = -p + 4*s. Solve -5/2*f**3 + p*f - 5/2*f**2 + 1/2*f**5 + 1/2*f**4 + 2 = 0 for f.
-2, -1, 1, 2
Let q(o) be the first derivative of o**6/3 - 4*o**5/5 - 5*o**4/2 + 4*o**3 - 240. Let q(t) = 0. Calculate t.
-2, 0, 1, 3
Suppose -8*y = -2933 - 235. Factor -444*g - 52 - y*g + 1375*g**2 + 3 - 131 - 385*g**3 + 30*g**4.
5*(g - 6)**2*(g - 1)*(6*g + 1)
Let v(w) be the first derivative of 3*w**4/4 - 374*w**3 - 3*w**2/2 + 1122*w - 1549. Factor v(q).
3*(q - 374)*(q - 1)*(q + 1)
Let t(o) be the second derivative of o**4/3 - 332*o**3/3 + 13778*o**2 + 1020*o. Suppose t(a) = 0. Calculate a.
83
Let o(s) = -4*s**2 + 69*s - 37. Let v be o(17). Let r(i) = -3*i**3 - 61*i**2 - 19*i + 25. Let d be r(v). Factor 0*j**2 + 0*j**3 + 0*j + 0 + 2/3*j**d - 2/3*j**4.
2*j**4*(j - 1)/3
Factor 585/2 + 5/6*j**2 + 100*j.
5*(j + 3)*(j + 117)/6
Let o(f) = -4*f**2 - 1147*f + 163610. Let u(g) = -22*g**2 - 6881*g + 981654. Let v(n) = -34*o(n) + 6*u(n). Factor v(a).
4*(a - 286)**2
Let j(v) = 20*v + 401. Let u be j(-20). Let i be (4 - (3 + u))*(-3)/(-6). Factor 1/3*y**4 - 16/3*y + i + 7/3*y**3 + 8/3*y**2.
y*(y - 1)*(y + 4)**2/3
Suppose -2*a = p - 10, 5*a - 22549 = 5*p - 22569. Find m, given that 10/9*m**a - 2/9*m**3 - 16/9*m + 8/9 = 0.
1, 2
Determine i, given that 1/2*i**3 + 0*i + 305/2*i**2 + 0 = 0.
-305, 0
Suppose 128 = 3*r - 2*z - 3*z, -r + 3*z = -40. Let j = r - 46. Solve -194*o**3 - 9*o**2 - 6*o + 191*o**3 + j*o = 0 for o.
-2, -1, 0
Let 523*j**2 + 807*j**2 - 1135*j - 250 - 426*j**3 + 481*j**3 = 0. What is j?
-25, -2/11, 1
Let x(o) be the first derivative of -o**6/780 - o**5/390 + o**4/39 + 4*o**3/39 + 19*o**2/2 - 24. Let t(l) be the second derivative of x(l). Factor t(r).
-2*(r - 2)*(r + 1)*(r + 2)/13
Let a(k) be the second derivative of -k**6/192 + 23*k**5/480 - 5*k**4/48 - k**3/4 + 97*k**2/2 + 200*k. Let p(y) be the first derivative of a(y). Factor p(h).
-(h - 3)*(h - 2)*(5*h + 2)/8
Suppose 0 = -4*d - 4*o - 44, 1276*d = 1277*d - 5*o - 67. Factor 26/7*c**3 + d*c - 8/7*c**4 - 30/7*c**2 - 2/7.
-2*(c - 1)**3*(4*c - 1)/7
Let f = -331 + 241. Let k be (-190)/f - (-2)/(-18). Suppose -1/2*i**k + 0*i + 1/2 = 0. Calculate i.
-1, 1
Let v(g) = -g + 2. Let c be v(-1). Factor -828*t**c - 2*t**2 + 831*t**3 + t**5 - 2*t**5.
-t**2*(t - 1)**2*(t + 2)
Let g(v) be the first derivative of -4*v**3/3 - 130*v**2 + 609. Factor g(o).
-4*o*(o + 65)
Let n(i) = -2*i**3 + 17*i**2 + 143*i - 1142. Let s be n(7). Let -3/2*z**3 - 12 + s*z + 3*z**2 = 0. Calculate z.
-2, 2
Let y = 40135 - 40135. Let z(c) be the first derivative of -1/10*c**2 + 1/15*c**3 - 34 + y*c. Factor z(b).
b*(b - 1)/5
Let n(w) be the first derivative of w**5/40 + 5*w**4/8 - 11*w**3/8 - 63*w**2/4 - 8900. Factor n(f).
f*(f - 4)*(f + 3)*(f + 21)/8
Let u(m) = -6*m**4 - 106*m**3 - 322*m**2 - 310*m - 118. Let a(c) = -c**4 - c**3 - c**2 + c - 1. Let g = 134 - 124. Let r(q) = g*a(q) - u(q). Factor r(x).
-4*(x - 27)*(x + 1)**3
Let u be 1/(-2)*(-152)/19. Factor -20*f**2 + 0*f - u*f**3 - 16*f + 5*f**3 + 5*f**3 + 22*f.
2*f*(f - 3)*(3*f - 1)
Let g(r) be the second derivative of r**9/9072 - r**8/1680 + 7*r**3/3 + 11*r. Let p(j) be the second derivative of g(j). Let p(i) = 0. Calculate i.
0, 3
Let j(k) = -k**3 + 10*k**2 - 11*k + 22. Let p be j(6). Suppose -7*x**2 + 15*x + p*x**5 + x + 8*x**2 - 120*x**4 - 44*x**3 + 47*x**2 = 0. Calculate x.
-2/5, 0, 1
Let j(v) = 11*v**3 - 3072*v**2 + 181516*v - 27844. Let t(o) = 65*o**3 - 18433*o**2 + 1089112*o - 167062. Let l(p) = -13*j(p) + 2*t(p). Factor l(a).
-(a - 118)**2*(13*a - 2)
Let p(r) be the third derivative of r**4/8 - 17*r**3/6 - 2*r**2. Let o be p(6). Factor -o - 43*n - 5*n**2 + 33*n - 4.
-5*(n + 1)**2
Let s(k) be the third derivative of -k**6/30 + 2*k**5/3 + 24*k**4 + k**2 - 18. Factor s(g).
-4*g*(g - 18)*(g + 8)
Suppose 3*f + 4*n = 26 - 25, 4*f - n = 14. Factor -f + 1/6*x**2 - 7/6*x.
(x - 9)*(x + 2)/6
Suppose -f = -2*w + 2 + 2, w = 5*f + 11. Factor 13*s + 0 - 14*s + s**3 + s**2 - w.
(s - 1)*(s + 1)**2
Let l(y) be the second derivative of 2*y**7/7 + 76*y**6/15 + 30*y**5 + 80*y**4 + 334*y**3/3 + 84*y**2 + 129*y - 2. What is i in l(i) = 0?
-7, -3, -1, -2/3
Let x(t) = 2*t**2 + t - 3. Let k(q) = q**2 + q + 1. Suppose -3*j + 14 = 56. Let m be (-18)/(-28)*-2 - 4/j. Let v(h) = m*x(h) + k(h). Factor v(l).
-(l - 2)*(l + 2)
Let r(x) = -16*x - 2. Let y be r(-4). Let m = y + -58. Factor 4*h + 3*h**2 - m*h**2 - 3*h**2 + 3*h**2 - 4.
-(h - 2)**2
Suppose -6*o + 19 = 7. Suppose o*t - 4*t = -10, 2*t = 3*c - 35. Factor -3*a + c*a + 4*a**3 + 36*a + 24*a**2 + 32.
4*(a + 2)**3
Suppose -486/7*a + 3/7*a**4 - 240/7*a**2 - 243/7 + 6/7*a**3 = 0. Calculate a.
-9, -1, 9
Find z such that -2280*z**2 + 5253*z - 4*z**5 + 1475*z - 620*z**2 - 608*z**3 - 2980*z**3 - 236*z**4 = 0.
-29, -2, 0, 1
Suppose -5*a + n + 1400 + 724 = 0, 0 = 4*a - 5*n - 1695. Let j = -425 + a. Factor -6/5*k + j + 1/5*k**2.
k*(k - 6)/5
Suppose 17 = 6*p - 577. Factor 4*x**2 + p + 593 + 464 - 49*x - 87*x.
4*(x - 17)**2
Let d(o) be the first derivative of -10*o**2 - 7/3*o**4 + 18*o - 22/3*o**3 - 1/5*o**5 - 24. Let p(l) be the first derivative of d(l). Factor p(n).
-4*(n + 1)**2*(n + 5)
Let w = 53789/45 + -10756/9. Suppose w*d + 4/5 - d**2 = 0. Calculate d.
-4/5, 1
Suppose -1/7*q**4 - 471/7*q**2