39 + 4*s**3/39 - 219*s**2. Factor c(g).
2*(g - 2)**2*(g + 1)**2/13
Let x(c) be the third derivative of c**5/330 - 9*c**4/11 - 109*c**3/33 - 2*c**2 - 102*c. Suppose x(p) = 0. What is p?
-1, 109
Let x(j) = -j**3 + 3*j**2 + 9*j + 7. Let f be 5 - (7 + -2) - -5. Let m be x(f). Factor 1/3*y**3 - 4/3*y**m + 5/3*y - 2/3.
(y - 2)*(y - 1)**2/3
Let f(x) be the second derivative of -x**6/150 - 3*x**5/50 - x**4/60 + 4*x**3/5 - 8*x**2/5 + 5740*x. Factor f(y).
-(y - 1)**2*(y + 4)**2/5
Let p(h) be the third derivative of h**8/264 + 296*h**7/1155 - 217*h**6/660 - 43*h**5/165 - 52*h**2. Let p(j) = 0. What is j?
-43, -2/7, 0, 1
Let s = 172397/4 + -43099. Factor -1/8*l**2 - s*l + 0.
-l*(l + 2)/8
Let j(t) be the first derivative of t**5/40 + t**4/2 - 5*t**3 - 33*t**2 + 65. Let a(p) be the second derivative of j(p). Factor a(q).
3*(q - 2)*(q + 10)/2
Let j(i) = 3*i**4 - 4*i**3 - 43*i**2 + 58*i - 1. Let b(n) = -2*n**4 + n**3 - 3*n**2 - 2*n - 1. Let l(w) = b(w) - j(w). Factor l(m).
-5*m*(m - 2)**2*(m + 3)
Let a(u) = -17*u - 246. Let n be a(-15). Let c be -2*n/(-12)*8/6. Factor -2/17*s**c + 0*s + 0 - 2/17*s**4 - 4/17*s**3.
-2*s**2*(s + 1)**2/17
Let a be (1796/(-15715))/((-1084)/(-364) + -3). Let 0 + 2/5*g**4 - a*g**2 + 4*g + 4/5*g**3 = 0. Calculate g.
-5, 0, 1, 2
Let g = -250437 + 1252187/5. Let f(c) = c**2 - 5*c. Let w be f(5). Let 0*i + 0*i**2 - g*i**3 + 2/5*i**5 + w*i**4 + 0 = 0. What is i?
-1, 0, 1
Let a be 15 + 966/(-63) - 7/(-8 - -1). Suppose 2 - 8/3*r + a*r**2 = 0. Calculate r.
1, 3
Suppose a + 6 = 2*f + 2*a, 2*f - 5*a + 18 = 0. Let m be (2/f)/(13/13). Find c, given that 10*c + 67*c**2 + 11*c - 6 - 63*c**2 + m*c = 0.
-6, 1/4
Factor -50*z + 1/4*z**2 + 2500.
(z - 100)**2/4
Let f = -80532 - -644277/8. Solve 5/2*y - 1/8*y**2 + f = 0 for y.
-1, 21
Suppose 10 = 10*o - 20. Let 19*s**2 - 3*s - 4*s**o + 36 + s - 55*s**2 + 6*s = 0. What is s?
-9, -1, 1
Let t(o) be the third derivative of o**5/20 + 663*o**4/2 + 879138*o**3 - 4860*o**2. Let t(m) = 0. What is m?
-1326
Let w = 1302 - 1166. Suppose 4*l + w - 141 = 3*g, -2*g + 15 = l. Factor -36/5*t**2 - 3/5*t**l + 0 - 12/5*t - 18/5*t**4 - 39/5*t**3.
-3*t*(t + 1)**2*(t + 2)**2/5
Let t(p) = -5*p**4 - 70*p**3 - 125*p**2 - 60*p + 2. Let k(v) = -8. Let q(s) = -3. Let y(c) = k(c) - 3*q(c). Let z(r) = -t(r) + 2*y(r). Factor z(b).
5*b*(b + 1)**2*(b + 12)
Let i = 31502 + -218828/7. Let h = -240 + i. Suppose 4/7 + 2/7*t**2 + h*t = 0. What is t?
-2, -1
Let t = 8426 - 8422. Let k(a) be the third derivative of 0 - 8*a**2 + 0*a - 1/90*a**5 - 1/6*a**t - 5/9*a**3. Factor k(r).
-2*(r + 1)*(r + 5)/3
Let v(p) be the second derivative of -10*p + 0 + 1/20*p**6 - 13/8*p**4 + 9/40*p**5 - 51/4*p**3 - 27*p**2. Solve v(w) = 0.
-3, -1, 4
Let h(j) = -j**3 - 3*j**2 + 11*j + 8. Let f be h(-5). Factor -c + 60*c**2 - 35*c**3 + 9*c + 1 - 1 + 3*c**f.
-4*c*(c - 2)*(8*c + 1)
Let w(k) = -2*k**2 - 10 - 9*k**2 + 10*k**2 + 7*k. Let v be w(3). Factor -25*n**2 + 3*n**v - 11*n**2 + 80*n - 2*n**2 - 20.
-5*(n - 2)*(7*n - 2)
Suppose -3*w + 16 = w. Let m(h) = -h**2 + 6*h - 4. Let n be m(w). Factor -3*o**3 + 3*o**3 - 5*o**4 + 10*o**n - 5*o**3.
5*o**3*(o - 1)
Let v(s) = s**2 + 29*s + 62. Let w be v(-27). Suppose 244*d**2 - 246*d**2 - 12*d - w + 4*d = 0. Calculate d.
-2
Let a(g) = g**2 - 8*g + 10. Let o be a(7). Factor -15*y**2 - 119 + y**o + 14*y - 2*y**2 + 17*y + 104.
(y - 15)*(y - 1)**2
Let v(x) be the second derivative of -x**7/168 - x**6/20 + 37*x**5/80 + 15*x**4/8 - 7798*x. Find r such that v(r) = 0.
-9, -2, 0, 5
Suppose 91*c - 90*c = 3. Suppose 4*x - 5 = 3*u, x = 4*u - x. Factor y**4 + 108*y + u + c*y**3 - 112*y - 1.
y*(y - 1)*(y + 2)**2
Let v(g) be the first derivative of g**3 - 2277*g**2/2 - 2280*g - 11151. Suppose v(h) = 0. Calculate h.
-1, 760
Suppose -62*t - 192 + 2*t**2 + 57*t + 195*t = 0. What is t?
-96, 1
Suppose -31 = 14*j + 11. Let h be ((-3)/(-36))/(8/j - -3). Solve 3/4*r**3 + 1/4*r**4 + h*r + 3/4*r**2 + 0 = 0.
-1, 0
Suppose 0*q = 2*u + 3*q + 1, -q = -u + 12. Suppose u*z = -0*z + 56. Let -20*s**2 + 3*s**3 + 21 - 12*s**5 + 20*s**4 - z*s - 21 + 17*s**3 = 0. Calculate s.
-1, -1/3, 0, 1, 2
Suppose -5*b = 2*s + 13, s - 3*s - 2*b - 4 = 0. Let f(t) = -8 + 10 - s. Let d(l) = l**2 - 11*l + 1. Let g(p) = 3*d(p) - 3*f(p). Let g(n) = 0. What is n?
0, 11
Let t(y) = y**4 + y**3 - y**2 - y + 2. Let q(v) = 3*v**4 - 385*v**3 + 249*v**2 + 385*v - 258. Let r(p) = q(p) + 3*t(p). Determine j so that r(j) = 0.
-1, 2/3, 1, 63
Factor -158*i**2 - 33*i + 89*i + 162*i**2.
4*i*(i + 14)
Let t be -9 + 0 + 1309/77. Suppose -4*w = 4*y - 0*y, -4*w = t. Let 0 + 2/13*f**y - 4/13*f + 2/13*f**3 = 0. What is f?
-2, 0, 1
Let j(x) be the second derivative of x**7/42 + 47*x**6/30 + 41*x**5/2 - 923*x**4/3 - 676*x**3 - 2*x + 3033. Factor j(i).
i*(i - 6)*(i + 1)*(i + 26)**2
Let g(w) be the first derivative of -w**3/5 + 7653*w**2/10 - 2532. Factor g(z).
-3*z*(z - 2551)/5
Let b be (-1 - 20)*(4 - (-20)/(-12)). Let n = 69 + b. Find d, given that 45*d - 5*d**2 - 16*d - n - 9*d = 0.
2
Let j be ((-4)/14)/(-3 + 143/91). Let r(h) be the first derivative of j*h**3 - 22 + 9/5*h**2 + 0*h. Determine z, given that r(z) = 0.
-6, 0
Let b(n) be the third derivative of n**6/12 - 215*n**5/12 + 265*n**4/12 + 535*n**3/6 - 2636*n**2 - 3. Factor b(o).
5*(o - 107)*(o - 1)*(2*o + 1)
Let n(b) = -b**2 + b - 1. Let w(a) = -3 - 22*a**2 - 5 + 0 + 14*a + 9*a**3. Let p = -1225 + 1197. Let m(g) = p*n(g) + 4*w(g). Factor m(u).
4*(u - 1)*(3*u - 1)**2
Let r(u) = 84*u**2 + 166*u + 91. Let b be r(-1). Let -33/2*d - b*d**3 + 54*d**4 - 40*d**2 - 2 + 27/2*d**5 = 0. What is d?
-4, -1/3, 1
Let k(b) be the third derivative of 2*b**7/105 - 8*b**6/3 + 559*b**5/5 - 507*b**4 + 4*b**2 + 7. Suppose k(o) = 0. What is o?
0, 2, 39
Suppose -4*s + 2*z - 3*z - 1000 = 0, -3*s = 4*z + 737. Let o = s - -1507/6. What is w in 1/2 - 1/3*w - o*w**2 = 0?
-3, 1
Let g be (-9)/(-6)*(-2)/6*-6. Factor -21*k**2 - 81*k**g - 91*k + 165*k**2 + 3*k + 24*k.
-k*(9*k - 8)**2
Suppose -2 = -3*a + 4. Let y = -513 + 517. Factor 6*u - u**5 - 4*u - u + a*u**2 - 2*u**y.
-u*(u - 1)*(u + 1)**3
Solve 1/5*g**2 + 336/5 + 10*g = 0.
-42, -8
Let p(t) be the second derivative of -5*t**4/36 + 3263*t**3/18 + 653*t**2/3 + 3956*t. Factor p(g).
-(g - 653)*(5*g + 2)/3
Let b(i) be the second derivative of -2*i**7/21 + 26*i**6/15 - 63*i**5/5 + 143*i**4/3 - 304*i**3/3 + 120*i**2 - 9913*i. Let b(w) = 0. Calculate w.
1, 2, 3, 5
Let w(r) be the third derivative of -r**5/300 + 4*r**4/15 - 32*r**3/5 + 276*r**2. Factor w(v).
-(v - 24)*(v - 8)/5
Let o(x) be the first derivative of 42*x**5/5 - 41*x**4 + 152*x**3/3 + 8*x**2 - 5546. Factor o(r).
2*r*(r - 2)**2*(21*r + 2)
Suppose -5500 = 84*c - 104*c. Suppose -303*w**2 - 165*w + 0*w - c*w + 24*w - 184*w + 12 = 0. What is w?
-2, 2/101
Determine i, given that 12 + 1/2*i**4 - 3/2*i**2 + 17*i - 6*i**3 = 0.
-1, 2, 12
Let o(d) be the third derivative of -d**9/332640 - d**8/6930 - 8*d**7/3465 + 4*d**5 + 154*d**2. Let v(u) be the third derivative of o(u). Factor v(p).
-2*p*(p + 8)**2/11
Let z(j) = -10*j**2 - 49*j - 60. Let u(r) = 7*r**2 + 50*r + 57. Let b(v) = 3*u(v) + 2*z(v). Solve b(i) = 0 for i.
-51, -1
Let w(r) be the first derivative of 2*r**2 - 1/3*r**3 + 5*r + 66. Factor w(m).
-(m - 5)*(m + 1)
Find f such that 8/3*f - 2/3*f**3 + f**2 - 4 = 0.
-2, 3/2, 2
Factor -4667729171 - 952200*p**2 + 22*p**4 + 146004000*p + 1705*p**3 - 2151589692 - 25*p**4 - 1575911137 + 1055*p**3.
-3*(p - 230)**4
Factor 3464/3 - 5200/3*p + 2*p**2.
2*(p - 866)*(3*p - 2)/3
Let u(v) be the first derivative of v**7/21 + v**6/5 + v**5/5 - v**4/3 - v**3 - v**2 - 99*v + 46. Let f(g) be the first derivative of u(g). Solve f(l) = 0.
-1, 1
Let r(s) = -26*s**3 + 187*s**2 + 396*s - 10136. Let d(c) = 8*c**3 - 62*c**2 - 132*c + 3380. Let x(v) = 7*d(v) + 2*r(v). Determine b, given that x(b) = 0.
-7, 11
Let f(m) be the third derivative of 0*m + 0 + 1/21*m**4 + 1/3*m**3 - 1/84*m**5 + 1/1260*m**6 - 21*m**2. Let c(j) be the first derivative of f(j). Factor c(y).
2*(y - 4)*(y - 1)/7
Let h be 2*((-6)/9)/(-2). Let l = 300971 + -300969. Factor -4/9*a**l + h*a + 4/9.
-2*(a - 2)*(2*a + 1)/9
Let n(g) = -2*g**2 - 1248*g - 8635. Let m be n(-7). Factor 8/3*x - 32/3 - 1/6*x**m + 2/3*x**2.
-(x - 4)**2*(x + 4)/6
Let a be -32 - ((-256)/56 + -28). Solve -a + 1/7*z**3 - z - 2/7*z**2 = 0 for z.
-1, 4
Suppose -3*b = -5*o +