
3*m*(m - 2)*(m - 1)
Let s(m) = -70*m + 1192. Let h be s(17). Determine p, given that -3/7*p**h + 0 + 15/7*p = 0.
0, 5
Let u be (-55)/(-15) - 1/(-3). Suppose 3*x = -u*p + 11, 4*x = x + 3. Let v**2 - v**2 + v**p - 9*v + 8*v = 0. Calculate v.
0, 1
Factor 5/4*l**2 + 720 - 60*l.
5*(l - 24)**2/4
Determine c, given that 2*c**2 - 2 + 1/2*c**3 - 1/2*c = 0.
-4, -1, 1
Factor 8*c**2 + 5 - 8 - 3*c**2 - 3*c - 5*c**2 + 3*c**3 + 3*c**2.
3*(c - 1)*(c + 1)**2
Let y(g) be the third derivative of g**9/60480 - g**7/10080 - 19*g**4/24 + 12*g**2. Let k(x) be the second derivative of y(x). Factor k(b).
b**2*(b - 1)*(b + 1)/4
Let v(j) be the first derivative of 3*j**4/4 - 4*j**3 + 3*j**2/2 + 18*j + 50. Factor v(b).
3*(b - 3)*(b - 2)*(b + 1)
Let j be (1993/(-4010) + 2/4)*132. Let b = j + 2/401. Factor 2*n - 4/5 - 8/5*n**2 + b*n**3.
2*(n - 2)*(n - 1)**2/5
Factor -3 - 1/2*g**3 + 1/2*g + 3*g**2.
-(g - 6)*(g - 1)*(g + 1)/2
Let s(a) = -2*a + 2. Let d be s(0). Suppose -2*y + 4 = -d. Factor 1 + 15*i**y + 10 + 3*i**4 + 0*i**4 - 5 + 21*i + 27*i**2.
3*(i + 1)**3*(i + 2)
Find z, given that -1/2 + 0*z + 1/2*z**2 = 0.
-1, 1
Let i(d) be the second derivative of d**4/48 - 11*d**3/4 + 1089*d**2/8 - 3*d - 70. Suppose i(z) = 0. Calculate z.
33
Let j(b) be the third derivative of b**11/79200 - 19*b**10/252000 - b**9/16800 - 7*b**5/20 - 26*b**2. Let z(h) be the third derivative of j(h). Factor z(t).
3*t**3*(t - 3)*(7*t + 2)/5
What is w in -1/5*w**3 - 4/5 + 0*w + 3/5*w**2 = 0?
-1, 2
Let t(m) be the third derivative of 7*m**5/150 - 11*m**4/60 - 2*m**3/5 - m**2 - 10*m. Factor t(s).
2*(s - 2)*(7*s + 3)/5
Let d(h) be the first derivative of h**4/8 - h**3/6 + 49. Let d(q) = 0. Calculate q.
0, 1
Let w be 12/(-8 + 22 - 11). Find g, given that 1/3*g**2 - 1/3*g**w + 0 - 1/3*g + g**3 - 2/3*g**5 = 0.
-1, 0, 1/2, 1
Determine o, given that -1/7*o**3 + 0*o - 4/7*o**2 + 0 = 0.
-4, 0
Let s(b) be the first derivative of -4*b**5/5 - 8*b**4 - 28*b**3 - 36*b**2 + 17. Suppose s(q) = 0. Calculate q.
-3, -2, 0
Let v(t) be the third derivative of -t**6/240 + t**5/240 + t**4/96 - 31*t**2 + t. Find r, given that v(r) = 0.
-1/2, 0, 1
Let l(i) = -2*i**2 - 10*i - 4. Let j be l(-4). Solve -8*h**4 - 7*h**5 - 8*h**3 + j*h**2 + 6*h**5 - h**5 + 4 + 10*h = 0.
-2, -1, 1
Let l be (1/16*4)/(6/96). Let 5/6*r**3 - 5/6*r**l + 0*r + 0*r**2 + 0 = 0. What is r?
0, 1
Let t = 851/3436 - -2/859. Factor -1/4*z**3 + 5/4*z - t*z**2 - 3/4.
-(z - 1)**2*(z + 3)/4
Let j(g) = -g - 11. Let p be j(9). Let m be (-8)/p + 24/15. What is i in -5*i**2 + 5*i - i + 2*i**m - 5*i**2 = 0?
0, 1/2
Let b be 58/(-29) + (0/(-2) - -3). Suppose 3/2*d + b + 0*d**2 - 1/2*d**3 = 0. Calculate d.
-1, 2
Let t(c) be the first derivative of -3*c**3 - 3*c**2 + 81/4*c**4 - 11 + 0*c. Factor t(w).
3*w*(3*w - 1)*(9*w + 2)
Let r(u) be the second derivative of u**7/21 - 8*u**6/15 + 12*u**5/5 - 17*u**4/3 + 23*u**3/3 - 6*u**2 + 2*u + 133. What is f in r(f) = 0?
1, 2, 3
Suppose -2*g - 4*t = t - 17, -g + 2*t - 14 = 0. Let x be 3/(-12) - 13/g. What is y in -2 + 4*y**3 - 2*y - 4*y**3 + y**x - 6*y**2 - 5*y + 2*y**4 = 0?
-1, -1/2, 2
Suppose 123*w = 98*w + 50. Let n(u) be the third derivative of 1/720*u**6 + 1/360*u**5 + 0*u**3 + 0 - 1/144*u**4 - 1/1260*u**7 + 0*u - 9*u**w. Factor n(a).
-a*(a - 1)**2*(a + 1)/6
Let o(r) = -r**5 + r**4 + r**3 - r**2 + r. Let f(y) = 7*y**5 - 9*y**4 - 5*y**3 + 9*y**2 - 8*y. Let d(v) = f(v) + 6*o(v). Factor d(j).
j*(j - 2)*(j - 1)**2*(j + 1)
Suppose 0 = 8*r - 0*r - 40. Factor 799 - 799 - r*w - 5*w**2.
-5*w*(w + 1)
Let f be -3 + (-13)/(-4) - (-398)/(-900). Let c = 3/100 - f. What is n in -2/9*n**3 + 0 + 2/9*n + 2/9*n**4 - c*n**2 = 0?
-1, 0, 1
Suppose 2*x + 0 = -5*h + 26, -19 = -x - 4*h. Factor 3*l**x - 17*l**2 + l**3 + 15*l**2 - 3*l**3.
l**2*(l - 2)
Let l = 3281/5 + -656. Solve -4/5*z**4 + 0 + 0*z - z**3 - 2/5*z**2 - l*z**5 = 0 for z.
-2, -1, 0
Factor 5*m**3 - 751*m**2 - 30*m + 796*m**2 - 20*m.
5*m*(m - 1)*(m + 10)
Factor -1139*a**2 + 11*a**3 - 23*a**3 + 1734*a**2 + 125 - 13*a**3 + 745*a.
-5*(a - 25)*(a + 1)*(5*a + 1)
Let b = 1310 + -1310. Solve 6/5*s**4 + 6/5*s**3 + b + 2/5*s**2 + 0*s + 2/5*s**5 = 0 for s.
-1, 0
Let v(c) be the second derivative of -c**6/288 - c**5/12 - 5*c**4/6 - c**3/2 - 6*c. Let y(n) be the second derivative of v(n). Factor y(l).
-5*(l + 4)**2/4
Let t(l) = -l**5 + 2*l**4 - 4*l**2 + 5*l**3 + 2*l + 2 - 3*l**4 + 0*l**3. Let k(i) = i**4 - i**3 - i. Let a(x) = -3*k(x) - t(x). Factor a(n).
(n - 2)*(n - 1)**2*(n + 1)**2
Factor 38*m**2 + 2/21*m**4 + 82/21*m**3 + 0 - 42*m.
2*m*(m - 1)*(m + 21)**2/21
Suppose 3*r + 5*h = 2*h + 48, -4*r + 5*h + 82 = 0. Factor -20*n - r*n**2 + 2*n**4 - n**4 - 7*n**3 - 2*n**4 - 8.
-(n + 1)*(n + 2)**3
Let z(x) be the first derivative of -3*x**5/80 - x**4/8 - 2*x + 18. Let b(y) be the first derivative of z(y). Factor b(n).
-3*n**2*(n + 2)/4
Let s(k) be the third derivative of k**5/240 - 7*k**4/96 + 5*k**3/12 - 287*k**2. Factor s(q).
(q - 5)*(q - 2)/4
Let w be 7/12*3 - 2/(-8). Suppose -5*u**2 + 3*u**5 - 7*u**2 + 3*u - 4*u**w + 18*u**3 + 4*u**2 - 12*u**4 = 0. Calculate u.
0, 1
Let z be -2 + 2 - (8 + -11). Let r(k) be the second derivative of k**z + 0 - 3/2*k**2 + 2*k - 1/4*k**4. Factor r(t).
-3*(t - 1)**2
Let z(w) be the first derivative of -2*w**5/5 - 88*w**4 - 7744*w**3 - 340736*w**2 - 7496192*w + 594. Factor z(l).
-2*(l + 44)**4
Let r(x) = -4*x**2 + 54*x - 579. Let q(p) = 7*p**2 - 106*p + 1157. Let a(l) = -6*q(l) - 10*r(l). Solve a(j) = 0 for j.
24
Find o, given that -22/15*o**3 - 8/15 + 26/15*o**2 + 8/3*o = 0.
-1, 2/11, 2
Suppose 120 = 4*d + 3*o, -3*o - 2*o = -d + 30. Let p be (-24)/d*10/(-4). Factor 0*q**4 - 4*q**2 + 0*q**3 - p*q**4 + 8*q**2 - 2*q**3.
-2*q**2*(q - 1)*(q + 2)
Suppose -a**5 + 0*a**5 + 3*a**5 - 9*a**4 + 2*a**5 - a**5 + 12*a**2 = 0. What is a?
-1, 0, 2
Suppose -4*j - 12 = 0, 16*s - j + 21 = 17*s. Let w be -8*3/(6/(-4)). Factor 12*o**3 + 2*o**4 - 9 + w*o + s*o**2 + 14 - 5.
2*o*(o + 2)**3
Suppose 4*t = 3*g + 83, -60*t + 62*t - 3*g - 43 = 0. Solve -t*w**3 - 25/3*w**4 - 46/3*w**2 - 1/3 - 4*w = 0 for w.
-1, -1/5
Let l = 8115/56903 + 2/8129. Suppose 3/7*j + 9/7 + l*j**3 - 5/7*j**2 = 0. Calculate j.
-1, 3
Suppose 7*v - 2*p = 4*v + 16, 5*p = -4*v + 29. Suppose -4*w**2 - v*w + 19 - 19 = 0. Calculate w.
-3/2, 0
Let h = 140 - 136. Suppose -3*c - 17 = -4*b + 5, 0 = -b - 4*c - h. Let 1/3*o**5 - 2/3*o**2 + 5/3*o**3 + 0*o - 4/3*o**b + 0 = 0. Calculate o.
0, 1, 2
Let m = 25 + -19. Let u(d) = -10*d**2 - 25*d - 15. Let x(i) = i**4 + i**3 + 9*i**2 + 25*i + 16. Let c = 4 + 1. Let z(o) = c*x(o) + m*u(o). Factor z(r).
5*(r - 2)*(r + 1)**3
Let z(d) be the third derivative of -15*d**2 + 0*d**3 + 0*d**4 - 1/42*d**7 - 1/48*d**6 + 0*d**5 + 0 + 0*d. Factor z(j).
-5*j**3*(2*j + 1)/2
Let i(f) be the third derivative of -f**7/1155 + f**5/110 - f**4/66 + 12*f**2 + 9*f. Solve i(z) = 0 for z.
-2, 0, 1
Suppose 14 - 16 = 2*y, 3*t = 2*y + 2. Let z(p) be the second derivative of -1/6*p**4 - 4*p + t - 2*p**3 - 9*p**2. Factor z(g).
-2*(g + 3)**2
Let n(c) = 23*c - 322. Let j be n(14). Determine t so that j + 0*t - 6/5*t**2 + 2/5*t**3 = 0.
0, 3
Determine d so that -1/6 + 1/6*d**5 + 1/6*d + 1/3*d**2 - 1/3*d**3 - 1/6*d**4 = 0.
-1, 1
Let o(z) = -z. Let k(r) = -72*r**2 + 1 - 5 + 68*r**2. Let q(h) = k(h) + 2*o(h). Let d(c) = 5*c**2 + 2*c + 5. Let n(m) = -3*d(m) - 4*q(m). Factor n(t).
(t + 1)**2
Factor 0 + 8/3*s**2 + 2/3*s**4 + 0*s - 8/3*s**3.
2*s**2*(s - 2)**2/3
Let n = 133 - 133. Let p(l) be the second derivative of n + 4*l + 0*l**3 + 1/21*l**7 - 2/9*l**5 - 4/27*l**4 - 2/45*l**6 + 0*l**2. Factor p(d).
2*d**2*(d - 2)*(3*d + 2)**2/9
Factor 1/5*v**4 + 6/5*v**2 - 8/5 + v**3 - 4/5*v.
(v - 1)*(v + 2)**3/5
Let u(p) be the second derivative of -1/20*p**5 - 1/12*p**4 + 0*p**2 - 1/90*p**6 + 0 - 1/18*p**3 + 10*p. Factor u(q).
-q*(q + 1)**3/3
Let h be 2/6 + (-141)/(-9). Suppose -f + 10 = f + 2*n, -2*f + h = -n. Factor 11 - 2*w + 3*w**2 - f - 5*w**2 + 0*w**2.
-2*(w - 1)*(w + 2)
Let p be (-712)/(-70) + 14/35 - -2. Let u = p - 331/28. Solve 0 + u*a - 51/4*a**4 + 15/4*a**2 - 3/4*a**3 + 9*a**5 = 0 for a.
-1/3, -1/4, 0, 1
Solve -115*n**2 + 51*n**2 - 24 + 4*n - 8*n**3 + 84*n**2 = 0.
-1, 3/2, 2
Factor -5/2*r**2 - 35/2 - 20*r.
-5*(r + 1)*(r + 7)/2
Let k(n) be the second derivative of 3*n**5/20 - 45*n**4 + 5400*n**3 - 324000*n**2 - 3*n - 70. Determine h so that k(h