) = 0. Calculate i.
-1, 1, 2
Factor 29*s**2 - 24*s**2 + 25*s - 8 + 16 + 12.
5*(s + 1)*(s + 4)
Solve 4/3*z**3 + 0 + 28/9*z**2 + 8/9*z = 0.
-2, -1/3, 0
Let g(o) be the first derivative of 5*o**3/3 + 145*o**2/2 - 221. Solve g(t) = 0.
-29, 0
Let g be (2*-1)/(150/(-25)). Let x(n) be the first derivative of 8/3*n + 2/15*n**5 + g*n**4 - 4/3*n**2 - 2/3*n**3 + 3. What is u in x(u) = 0?
-2, 1
Let k(m) = 15*m + 7. Let o be k(-6). Let d be (-5)/((-15)/(-6))*o. Find u, given that d*u - 6*u**2 + 3*u**4 - 154*u + 9 - 6*u**4 - 12*u**3 = 0.
-3, -1, 1
Let o be 56/4 - 2 - 1. Let x = o + -10. Let f(j) = -j**3 + j**2 - 1. Let i(y) = 3*y**4 - 17*y**3 + 17*y**2 - 5. Let z(w) = x*i(w) - 5*f(w). Factor z(a).
3*a**2*(a - 2)**2
Let f = 409 - 281. Factor 4*i + 123*i**3 - f*i**3 - 25*i**2 + 26*i.
-5*i*(i - 1)*(i + 6)
Suppose 473*d**3 - 238*d**3 - 48*d + 50*d**2 - 237*d**3 = 0. What is d?
0, 1, 24
Let t be (-1961)/(-1378) + 12/156. Factor t*b + 1/2*b**3 - 2*b**2 + 0.
b*(b - 3)*(b - 1)/2
Let w(t) = 6*t**5 - 25*t**3 + 15*t**2 - 8. Let a(h) = -5*h**5 + 24*h**3 - 14*h**2 + h + 10. Let b(m) = 3*a(m) + 4*w(m). What is z in b(z) = 0?
-2, -1/3, 1/3, 1
Factor 7/5*o**2 - 17/5*o + 9/5 + 1/5*o**3.
(o - 1)**2*(o + 9)/5
Let h(l) be the second derivative of 0 - 35/12*l**4 - 1/2*l**6 + 5/2*l**5 + 15*l + 10*l**2 - 10/3*l**3. Determine s so that h(s) = 0.
-2/3, 1, 2
Let q = -11557 - -127129/11. Factor 6/11*f + 4/11*f**2 + q.
2*(f + 1)*(2*f + 1)/11
Let i(u) = -u**3 - 11*u**2 - 11*u - 7. Let d be i(-10). Let p be (8/(-10))/(-4 - -2). Factor -8/5 + 8/5*z - 2/5*z**d + p*z**2.
-2*(z - 2)*(z - 1)*(z + 2)/5
Suppose -3*h + 3*m = -12, 4*m = -2 - 2. Suppose 0 = -5*k + 18 - h. Let -7*d**2 + d**k + 3*d**3 + 4*d**5 + 12*d**4 + 0*d**3 - 5*d**2 - 8*d = 0. Calculate d.
-2, -1, 0, 1
Let y(u) be the third derivative of 23*u**5/60 - 3*u**4/8 - 3*u**3/2 - 18*u**2. Let n(k) = 24*k**2 - 8*k - 10. Let t(b) = 5*n(b) - 6*y(b). Factor t(j).
-2*(j - 1)*(9*j + 2)
Let c(d) be the first derivative of d**5/10 - 5*d**4/4 + 8*d**3/3 + 53. Factor c(u).
u**2*(u - 8)*(u - 2)/2
Suppose 23/4*o - 15/2*o**3 - 83/4*o**2 + 3/2 = 0. What is o?
-3, -1/6, 2/5
Let z(g) be the second derivative of -1/2*g**4 - 1/28*g**7 + 0*g**2 + 1/4*g**6 + 7*g + 0 + 2*g**3 - 9/20*g**5. Factor z(j).
-3*j*(j - 2)**3*(j + 1)/2
Let n(w) be the third derivative of -w**6/120 - 9*w**5/20 - 81*w**4/8 + w**3/6 + w**2. Let i(j) be the first derivative of n(j). Factor i(u).
-3*(u + 9)**2
Let n(l) be the second derivative of -l**4/120 - 4*l**3/15 - 3*l**2/4 + 283*l. Let n(a) = 0. What is a?
-15, -1
Let o = 2261/2 - 1130. Find c, given that o*c**2 - 1/2 - 1/2*c**3 + 1/2*c = 0.
-1, 1
Let u be 8/(-68) - 159/51*-1. Let g = 210 + -623/3. Solve g*k**5 - 4*k**4 - 4/3*k**u + 0*k**2 + 0 + 0*k = 0 for k.
-2/7, 0, 2
Let y be (18/60)/(2 - 2/4). Let k(z) be the first derivative of y*z**2 + 3/10*z**4 + 0*z - 4 - 2/5*z**3 - 2/25*z**5. Factor k(f).
-2*f*(f - 1)**3/5
Let g(k) be the first derivative of -4*k + 45 - 6*k**2 - 16/5*k**5 + 20/3*k**3 + 3*k**4. Find y such that g(y) = 0.
-1, -1/4, 1
Let l(s) be the first derivative of 0*s**2 + 0*s**5 + 1/22*s**4 - 1/33*s**6 + 46 + 0*s**3 + 0*s. Factor l(a).
-2*a**3*(a - 1)*(a + 1)/11
Suppose -9*q + 3*q = -2532. Let j = -3794/9 + q. Suppose -2/9*t - 2/9*t**2 + j = 0. Calculate t.
-2, 1
Let n(z) = 3*z**4 + 28*z**3 + 23*z**2 - 50*z + 2. Let x(h) = 15*h**4 + 139*h**3 + 116*h**2 - 248*h + 11. Let a(b) = 11*n(b) - 2*x(b). Factor a(j).
3*j*(j - 1)*(j + 2)*(j + 9)
Let d(p) be the second derivative of -5*p**8/84 + p**7/105 + p**6/30 + p**2 - 17*p. Let l(w) be the first derivative of d(w). Let l(b) = 0. Calculate b.
-2/5, 0, 1/2
Let m be (-6)/(-39) + 4624/26. Determine u so that -u**2 - m + 178 + 3*u = 0.
0, 3
Let t(b) be the third derivative of -2*b**5/105 + 31*b**4/84 + 8*b**3/21 - 5*b**2 + 32*b. Factor t(s).
-2*(s - 8)*(4*s + 1)/7
Suppose 0 = 5*i - 4*p - 37, -3*i + 23 - 2 = -2*p. Suppose 2*o - u = 5, u = -o + 4*u + i. Factor -4/3*y**4 + 8/3*y**o + 0*y + 0*y**3 - 4/3.
-4*(y - 1)**2*(y + 1)**2/3
Let y = 1795 + -1792. Let f(c) be the first derivative of -4/3*c**y + c**4 + 4/5*c**5 - 2/3*c**6 + 0*c + 0*c**2 + 5. Determine j, given that f(j) = 0.
-1, 0, 1
Solve 0 - 34/13*x + 2/13*x**2 = 0.
0, 17
Let b(w) be the first derivative of -2*w**6/21 - 8*w**5/35 + 4*w**4/7 + 32*w**3/21 - 9. Factor b(t).
-4*t**2*(t - 2)*(t + 2)**2/7
Let v(r) = 9*r**2 - 64*r - 63. Let w(p) = -2*p**2 + p + 1. Let m(d) = v(d) + 5*w(d). Suppose m(n) = 0. What is n?
-58, -1
Determine u so that -41*u + 3*u**3 - 498*u**2 + 516*u**2 - 2*u**4 - 13*u + 3*u**3 = 0.
-3, 0, 3
Let f be 312*18/27*(-6)/(-8). Suppose 162 = 3*l + f. Find s, given that -6/7*s - 2/7*s**3 + 2/7 + 6/7*s**l = 0.
1
Let v(p) = 2*p**3 + 5*p**2 + 1 + p**2 - 12. Let d(n) be the second derivative of n**2/2 + 7*n + 6. Let c(a) = 3*d(a) + v(a). Find w, given that c(w) = 0.
-2, 1
Let z(i) be the first derivative of 2*i**5/5 + i**4/7 - 2*i**3/3 - 2*i**2/7 - 412. Find u, given that z(u) = 0.
-1, -2/7, 0, 1
Let j(g) be the second derivative of -g**7/3780 + g**6/810 - 37*g**3/6 - 38*g. Let r(b) be the second derivative of j(b). Solve r(i) = 0 for i.
0, 2
Let f(x) be the second derivative of x**8/3360 - x**7/315 + x**6/120 + 2*x**4/3 - 2*x. Let n(g) be the third derivative of f(g). Factor n(r).
2*r*(r - 3)*(r - 1)
Let h(q) be the first derivative of 1/10*q**4 + 0*q**2 - 1/45*q**6 - 20 + 0*q + 0*q**5 - 4/45*q**3. Factor h(s).
-2*s**2*(s - 1)**2*(s + 2)/15
Let q(o) be the first derivative of -1/36*o**4 + 0*o**3 - 1/45*o**5 + 0*o**2 + 0*o - 1. Suppose q(a) = 0. What is a?
-1, 0
Let a(n) be the third derivative of n**7/420 + 7*n**6/240 - 3*n**5/20 - 250*n**2. Factor a(z).
z**2*(z - 2)*(z + 9)/2
Suppose -7*u + 953 = 239. Let k = u - 407/4. Suppose -3/4*a + 0*a**2 + k*a**3 + 1/2 = 0. What is a?
-2, 1
Let c = 29 + 50. Let x be (-2 - (-3)/2)*-4. Let 36*j**3 - 364*j**x - 7 - 330*j**3 - 9 - 57*j - c*j = 0. What is j?
-2/3, -2/7
Let h(d) be the first derivative of -d**3/3 + 24*d**2 - 576*d - 88. Factor h(z).
-(z - 24)**2
Let u(z) = -2*z - 3. Let c be u(-3). Solve -3*w**3 + 11*w + w + 9 + c - 3*w**2 = 0.
-2, -1, 2
Let r = 72/43 - 461/301. Determine h, given that 0 - 2/7*h**2 + r*h**3 + 0*h = 0.
0, 2
Let l(m) = m**2 + 2*m + 3. Let w be l(-2). Factor -11*v - 18 + 36 - 26 - v + 4*v**w.
4*(v - 2)*(v + 1)**2
Let s(y) be the second derivative of -y**7/280 - y**6/120 + 25*y**3/6 + 4*y. Let c(z) be the second derivative of s(z). Suppose c(b) = 0. Calculate b.
-1, 0
Suppose -3*s + 5 = 2. Let v(o) = o**2 + 2. Let h be v(0). Factor -18*m**h - 9*m**4 + 36*m**3 - 1 + 3*m + s + 9*m**5 - 21*m**4.
3*m*(m - 1)**3*(3*m - 1)
Let 14*n**2 + 5*n**2 + 183184 - 26*n - 1686*n - 15*n**2 = 0. Calculate n.
214
Let w = -7748 + 7748. Factor 2/13 + w*z - 2/13*z**2.
-2*(z - 1)*(z + 1)/13
Let n(t) be the second derivative of 0 + 0*t**2 + 1/18*t**3 + 1/36*t**4 + 11*t. Factor n(z).
z*(z + 1)/3
Let y(k) = k**3 - 220*k**2 - 827*k - 811. Let v(d) = -110*d**2 - 414*d - 406. Let m(r) = -5*v(r) + 2*y(r). What is g in m(g) = 0?
-51, -2
Let b(r) = -17*r**3 - 20*r**2 - 25*r - 16. Let t(g) = -14*g**3 - 19*g**2 - 26*g - 16. Let f(k) = -5*b(k) + 6*t(k). Factor f(v).
(v - 16)*(v + 1)**2
Let g(h) be the second derivative of h**4/24 + h**3/12 - 3*h**2/2 + 126*h. Factor g(w).
(w - 2)*(w + 3)/2
Suppose 23*w - 88 = 27. Let q(x) be the third derivative of 1/40*x**w + 0 + 0*x - 1/24*x**4 + x**2 + 0*x**3. Solve q(i) = 0 for i.
0, 2/3
Let v(k) be the second derivative of 0 + k**2 - 1/270*k**5 - 5*k + 0*k**3 + 1/54*k**4. Let y(b) be the first derivative of v(b). Suppose y(r) = 0. Calculate r.
0, 2
Let d be (-1)/(1/(-10)*2). Let n be 8/d - 4/(-10). What is r in 1/2*r**3 + 1/6*r - 1/2*r**n - 1/6*r**4 + 0 = 0?
0, 1
Let h be ((-3)/2)/(-2*(-9)/(-36)). Suppose -5*c - p + h = 2*p, 2*c + 4*p + 10 = 0. Factor 4/5*v**c + 0*v + 0 + 2/5*v**2.
2*v**2*(2*v + 1)/5
Suppose 0 - 12*v**3 + 0*v - 45/2*v**2 - 3/2*v**4 = 0. Calculate v.
-5, -3, 0
Let n(j) be the first derivative of -j**5/10 + 23*j**4/8 + 225. Factor n(d).
-d**3*(d - 23)/2
Let w(f) = f + 10. Let g be w(-7). Factor -1 + 114*t**3 - 9*t - 6*t**2 - 3 - 115*t**g.
-(t + 1)**2*(t + 4)
Suppose 4*y = 3*y. Suppose 68*t = 189 + 83. Factor 0*o**2 + 4/3*o**3 + 0*o - 2*o**t + y.
-2*o**3*(3*o - 2)/3
Let u(i) be the third derivative of -i**7/7560 + i**6/1080 - i**