**2*(s + 8)/2
Let p(r) be the third derivative of r**6/360 - 43*r**5/180 + 65*r**4/9 - 200*r**3/3 + 9*r**2 - 45. Factor p(i).
(i - 20)**2*(i - 3)/3
Let i = 19304 + -19298. Let g(m) be the second derivative of 0*m**2 + 0*m**6 - i*m + 0 + 0*m**4 + 2/63*m**7 + 2/9*m**3 - 2/15*m**5. Let g(h) = 0. Calculate h.
-1, 0, 1
Suppose 2*c = 10*c - 30*c - 20*c + 168. Factor -4/3*d + 4/3*d**c + 0 - 4/3*d**2 + 4/3*d**3.
4*d*(d - 1)*(d + 1)**2/3
Let b(d) be the third derivative of -7/12*d**5 + 0*d + 4*d**2 - 4 - 10/3*d**3 + 11/42*d**7 - 5*d**4 + d**6. Find x such that b(x) = 0.
-2, -1, -2/11, 1
Let u(r) = 5*r**5 - 6*r**4 - 31*r**3 + 32*r**2 + 92*r + 68. Let p(g) = g**5 - g**4 - 2*g**3 + g**2 - 5*g + 1. Let t(a) = -4*p(a) + u(a). Solve t(l) = 0 for l.
-4, -1, 4
Find l such that -21*l**4 - 36*l**2 - 45*l + 18 - 13 + 15*l**2 + 3*l**5 + 15*l**2 + 22 + 42*l**3 = 0.
-1, 1, 3
Let n(a) = 12*a**4 + 9*a**3 - 87*a**2 + 201. Suppose 4*v - 27 = v. Let g(w) = 3*w**4 + 2*w**3 - 22*w**2 + 50. Let l(f) = v*g(f) - 2*n(f). Factor l(x).
3*(x - 2)**2*(x + 2)**2
Let w(k) = -9*k - 498. Let x be w(-46). Let d = x + 86. Determine z, given that -3/4*z**5 - 3/4*z**d + 3/4*z**4 + 0*z + 3/4*z**3 + 0 = 0.
-1, 0, 1
Solve 10112688/5*f + 41310*f**2 + 3/5*f**4 - 32234193/5 + 1368/5*f**3 = 0.
-153, 3
Let h(t) be the third derivative of 0 - 79*t**2 + 1/6*t**4 + 0*t - 1/210*t**7 - 1/120*t**6 + 0*t**3 + 1/15*t**5. Suppose h(p) = 0. Calculate p.
-2, -1, 0, 2
Let u = 476 - 471. Suppose -4*d + u - 3 = -3*m, -5*d + 18 = 4*m. Let -6/11*j**4 + 0 - 2/11*j**d - 6/11*j**3 + 0*j - 2/11*j**5 = 0. What is j?
-1, 0
Suppose 101 + 319 = a. Solve -422*k**5 - 12*k - 2 - 20*k**2 - 20*k**3 - 10*k**4 + a*k**5 + 2*k = 0.
-1
Suppose 488/9*i + 238/9*i**3 - 20/9*i**4 - 2/3*i**5 - 556/9*i**2 - 16 = 0. Calculate i.
-9, 2/3, 1, 2
Let h(m) be the second derivative of m**7/45 + 4*m**6/75 - 16*m**5/75 - 8*m**4/15 + 16*m**3/45 + 585*m - 2. Let h(k) = 0. Calculate k.
-2, 0, 2/7, 2
Let m(u) be the third derivative of -u**5/30 + 31*u**4/2 + 376*u**3/3 + 782*u**2 + 1. Factor m(c).
-2*(c - 188)*(c + 2)
Let j be 3/((-63)/(-48)) - 22/77. Let y be 19/7 + 2 - j/(-7). Factor -19*p**y + 14*p**5 + 5*p**3 + 5*p**2 - 5*p**4 + 0*p**2.
-5*p**2*(p - 1)*(p + 1)**2
Let x be (-945)/(-105) + 140/(-20). Factor 72/7*n + 3/7*n**4 + 66/7*n**x + 24/7*n**3 + 27/7.
3*(n + 1)**2*(n + 3)**2/7
Let f(b) = 2*b**3 + 731*b**2 + 313*b - 18977. Let x be f(-365). Let x - 3/4*d**3 - 3/4*d**2 + 3*d = 0. What is d?
-2, -1, 2
Let r(t) = -4*t**4 + 32*t**3 - 28*t**2 + 12*t - 18. Let c(w) = -w**4 - w**3 + w**2 - w + 3. Let h(b) = -6*c(b) - r(b). Factor h(k).
2*k*(k - 1)**2*(5*k - 3)
Let y(u) = 5*u + 294. Let n be y(-56). What is j in 9*j**3 - n*j**3 - 5*j**2 + 30*j**2 - 37*j**4 - 52*j + 7 + 5 + 7*j**5 + 50*j**3 = 0?
-1, 2/7, 1, 2, 3
Let a(o) be the third derivative of 0*o - 1/20*o**4 - 1/45*o**5 + 0*o**3 + 0 - 16*o**2 - 1/900*o**6. Factor a(t).
-2*t*(t + 1)*(t + 9)/15
Suppose -2*x + 152 = 2*i, -2*i + 17 + 132 = -x. Factor 52*d**3 - 106*d**3 + 375*d - 625 + 59*d**3 - i*d**2.
5*(d - 5)**3
Let j(u) be the first derivative of 4 - 4/3*u**2 + 26/27*u**3 + 8/9*u + 2/45*u**5 - 1/3*u**4. Factor j(a).
2*(a - 2)**2*(a - 1)**2/9
Let o(l) be the first derivative of -l**6/600 + l**5/100 + l**4/30 - 11*l**2/2 + 7*l - 139. Let q(w) be the second derivative of o(w). Factor q(c).
-c*(c - 4)*(c + 1)/5
Let g(u) be the first derivative of u**4/4 + 61*u**3/3 + 759*u**2/2 - 5445*u + 1286. Find t, given that g(t) = 0.
-33, 5
Suppose 0 = 4*u - 4*q - 16, 9*u + 2*q = 10*u - 1. Let j be (210/u)/5 - 4. Factor 21/2*v**j - 21/2*v - 3*v**3 + 3.
-3*(v - 2)*(v - 1)*(2*v - 1)/2
Let m(z) be the first derivative of -4*z**6/9 + 86*z**5/5 - 230*z**4/3 - 302*z**3/3 + 140*z**2/3 - 2447. Let m(p) = 0. What is p?
-1, 0, 1/4, 5, 28
Suppose 5*j - 37 = -7. Let b = 9 - j. Let -s**b + 12*s**4 - 16*s**4 + 0*s**3 - 3*s**3 = 0. Calculate s.
-1, 0
Let f(p) be the first derivative of -p**3/18 + 67*p**2/3 + 432. Factor f(y).
-y*(y - 268)/6
Let m(d) be the first derivative of 0*d**2 - 2/85*d**5 + 20/51*d**3 + 88 + 0*d + 3/34*d**4. Suppose m(f) = 0. Calculate f.
-2, 0, 5
Let t(o) = -o**3 - 9*o**2 - 6*o - 28. Let a be t(-9). Suppose -22*b + 32*b - 14*b - 2*b**4 + 16 - 4*b**5 - 36*b + a*b**3 + 4*b**2 = 0. What is b?
-2, 1/2, 1, 2
Suppose -4*p + j + 6 = 0, 2*p + 73*j - 76*j = -12. Solve 35/4*a**2 - 1225/8*a + 0 - 1/8*a**p = 0 for a.
0, 35
Factor 4/9*w + 2*w**3 - 14/9*w**2 + 0 + 2/9*w**5 - 10/9*w**4.
2*w*(w - 2)*(w - 1)**3/9
Let q(o) be the third derivative of 1/144*o**4 - o + 1/6*o**3 + 0 - 19*o**2 - 1/360*o**5. Factor q(y).
-(y - 3)*(y + 2)/6
Suppose 5*k - w - 159 = 0, 25*k - 23*k - 65 = -w. Let h be (-24)/k*(9 - 13). Factor 3/5*t**2 - 3/5*t**4 + 3/5*t - 3/5*t**h + 0.
-3*t*(t - 1)*(t + 1)**2/5
Let z(w) be the first derivative of -4*w**3/15 - 558*w**2/5 + 2248*w/5 - 5080. Factor z(m).
-4*(m - 2)*(m + 281)/5
Suppose -1059*q + 1060*q = -7. Let y(k) = 6*k**4 - 26*k**3 - 20*k**2. Let o(l) = -8*l**4 + 26*l**3 + 19*l**2 - l. Let a(x) = q*y(x) - 6*o(x). Factor a(w).
2*w*(w + 1)*(w + 3)*(3*w + 1)
Let s(x) be the first derivative of -1/21*x**3 + 0*x - 1/28*x**4 + 0*x**2 - 47. Factor s(g).
-g**2*(g + 1)/7
Let m(d) be the first derivative of -d**6/14 - 27*d**5/35 - 9*d**4/14 + 16*d**3/7 - 1665. Find w, given that m(w) = 0.
-8, -2, 0, 1
Let p(y) be the second derivative of 0 + 12*y + 9/4*y**3 - 7*y**2 + 3/8*y**4 + 1/40*y**5. Let s(g) be the first derivative of p(g). Let s(m) = 0. What is m?
-3
Let f(c) be the first derivative of -5/9*c**3 + 1/3*c**2 - 5/24*c**4 + 1/15*c**5 + 1/36*c**6 + 134 + 4/3*c. Determine n so that f(n) = 0.
-2, -1, 1, 2
Find o, given that -1/3*o**2 - 530/3*o + 177 = 0.
-531, 1
Factor 17*w - 37*w + 2*w**2 + 0*w**3 - w**2 + 8*w + w**3.
w*(w - 3)*(w + 4)
Find j such that 23 + 44*j**3 - 303*j + 129*j**2 + 3*j**4 + 63*j + 19 + 22 = 0.
-8, 1/3, 1
What is w in 47*w**2 - 161*w**3 + 17*w**3 + 13*w**2 + 76*w**4 + 8*w = 0?
-2/19, 0, 1
Let g(i) = -i**3 + i**2 + 2*i. Let q(s) = -3*s**3 + 207*s - 4 - 204*s + 4. Let b(a) = -4*g(a) + 2*q(a). Determine o, given that b(o) = 0.
-1, 0
Factor -15*w - 32*w**2 + w**5 - 152*w**3 - 76*w**3 + 210*w**3.
w*(w - 5)*(w + 1)**2*(w + 3)
Let r(o) be the third derivative of o**7/42 + o**6/2 - 229*o**5/6 - 1235*o**4/2 + 305045*o**3/6 + 1384*o**2. Factor r(g).
5*(g - 13)**2*(g + 19)**2
Let n(m) be the first derivative of -m**6/360 + 13*m**5/120 - 16*m**3/3 - 8. Let v(u) be the third derivative of n(u). What is d in v(d) = 0?
0, 13
Suppose -2*k = -4*k - 2*g, 0 = 8*k - 4*k - 6*g - 20. Factor -8/5 + 2/5*h**3 - 4/5*h**k - 14/5*h.
2*(h - 4)*(h + 1)**2/5
Let k(o) be the second derivative of 1/21*o**3 - 1/84*o**4 + 0*o**2 + 0 + 47*o. Solve k(s) = 0 for s.
0, 2
Let v be (-155 + 154)*6/(-10). Let c(l) be the second derivative of v*l**5 - 23*l - l**4 + 0 + 2/3*l**3 - 2/15*l**6 + 0*l**2. Let c(g) = 0. What is g?
0, 1
Factor -32 - 34/3*x - 2/9*x**2.
-2*(x + 3)*(x + 48)/9
Suppose -22 = t - 74. Factor -2*m**2 + t - m**2 + m**3 - 6*m - 44 + 0*m**3.
(m - 4)*(m - 1)*(m + 2)
Let v(m) = -48 - 18 + 5*m**3 - 4*m**3 - 37*m - 14 + 2*m**2 + 8. Let u be v(-2). Factor -10/11*o**u + 2/11*o**3 - 16/11*o + 24/11.
2*(o - 6)*(o - 1)*(o + 2)/11
Let c(y) be the second derivative of y**4/20 + 691*y**3/10 + 681*y. Factor c(g).
3*g*(g + 691)/5
Let x(j) = j - 3. Let o be x(14). Factor -4*z + 5*z - 8*z - o*z**2 + 10*z**2.
-z*(z + 7)
Factor 27*l - 3/2*l**4 - 15*l**3 - 21/2*l**2 + 0.
-3*l*(l - 1)*(l + 2)*(l + 9)/2
Suppose -85 + 35 = -z + 4*c, 0 = -c + 1. Let u(p) be the first derivative of -1/4*p**4 - 6*p**3 + 4 - z*p**2 - 216*p. Find k such that u(k) = 0.
-6
Let i be -9 + (-203)/(-21) - (-1 - 0). Let d(u) be the first derivative of i*u**3 + 3*u + 13 + 1/4*u**4 + 7/2*u**2. Factor d(a).
(a + 1)**2*(a + 3)
Factor -330/7 + 328/7*o + 2/7*o**2.
2*(o - 1)*(o + 165)/7
Let h(d) be the second derivative of 40*d - 3*d**2 - 1/6*d**4 + 0 - 4/3*d**3. Factor h(x).
-2*(x + 1)*(x + 3)
Suppose 5/6*h**2 + 2305/3*h + 1062605/6 = 0. What is h?
-461
Factor 590*x + 7*x**5 - 264252*x**3 - 240 + 264117*x**3 - 335*x**2 - 2*x**5 + 115*x**4.
5*(x - 1)**3*(x + 2)*(x + 24)
Let q = 50847/14 - 25392/7. What is d in -27/2*d - q*d**2 - 15/2 + 3/2*d**3 = 0?
-1, 5
Let j be (2/5)/((-1200)/(-1250)). Let u(o) be the third derivative of 0*o - 2/15*o**5 - j*o**4 - 5*o**2 + 0 - 1