. Let k(y) = 0. Calculate y.
-26, -1
Factor -26/3*h**2 + 2/3*h**3 - 10 - 58/3*h.
2*(h - 15)*(h + 1)**2/3
Let w(d) be the third derivative of d**5/80 - 41*d**4/96 + 13*d**3/12 - 92*d**2. Suppose w(l) = 0. Calculate l.
2/3, 13
Let m = 17 - 5. Suppose 3*z = -0*z + m. Solve -6*t**3 + 12*t**2 - 6*t**3 - 3*t**z + 6*t**4 = 0 for t.
0, 2
Let q be 3248/210 + -16 - 6/(-5). Factor -8/3*l - 8/3*l**2 + 0 - q*l**3.
-2*l*(l + 2)**2/3
Let t = 14 + -8. Suppose u + 4*r = -0*r - t, 4*r = -4*u. Determine q so that -q**3 + 2*q**2 + q**2 - u*q**2 + 2*q**2 - 2*q = 0.
0, 1, 2
Let v(b) = b**2 + 1. Let y(w) = 2*w**3 - 34*w**2 + 98*w - 30. Let j(f) = 36*v(f) - 2*y(f). Factor j(q).
-4*(q - 24)*(q - 1)**2
Let q(c) = c**2 - 2*c + 2. Let x be q(5). Let i = x - 15. Factor -2*l**2 - 12*l + 11*l + i + 2*l**2 - l**2.
-(l - 1)*(l + 2)
Factor 35*q**3 + 43*q**2 - 31*q**3 - 23*q**2.
4*q**2*(q + 5)
Let s(z) = z**2 + 282*z + 2641. Let p(n) = 3*n**2 + 990*n + 9243. Let c(g) = 5*p(g) - 18*s(g). Factor c(v).
-3*(v + 21)**2
Let g(j) = j**4 - j. Let i(r) = 26*r**4 + 135*r**3 + 250*r**2 + 179*r + 40. Let c = 89 + -88. Let s(o) = c*g(o) - i(o). Suppose s(p) = 0. Calculate p.
-2, -1, -2/5
Let s(o) = o**2 - 9*o + 9. Let i be s(9). Factor 3*l**3 - 4 - 5*l**3 - 3*l + 8 + i*l.
-2*(l - 2)*(l + 1)**2
Let b be (-128)/(-20)*90/12. Suppose -b*o + 78*o**2 + 98*o - 54*o = 0. What is o?
0, 2/39
Factor -10/3*p - 2/9*p**2 - 28/9.
-2*(p + 1)*(p + 14)/9
Let l(p) be the third derivative of p**8/42 - 11*p**7/105 - 19*p**6/60 + 22*p**5/15 + p**4 + 2*p**2 - 119. Let l(n) = 0. Calculate n.
-2, -1/4, 0, 2, 3
Let b(i) be the third derivative of -3/16*i**4 - 1/240*i**6 + 0*i**3 - 1/20*i**5 - i**2 + 0*i + 0. Find g, given that b(g) = 0.
-3, 0
Let 64/3*g + 13/3*g**2 - 1/3*g**3 + 68/3 = 0. What is g?
-2, 17
Suppose 33*g = 22*g. Let t(m) be the third derivative of 1/150*m**5 - m**2 + 0*m + 1/60*m**4 + 0*m**3 + g. Determine u so that t(u) = 0.
-1, 0
Let f be 96/54 + (-2)/(-9). Factor 5*d**3 + 25*d + 6*d**f + d**2 + 13*d**2 + 10.
5*(d + 1)**2*(d + 2)
Let c(w) be the first derivative of 0*w**5 + 0*w**2 + 0*w - 1/4*w**6 + 0*w**3 + 5 + 3/8*w**4. Factor c(r).
-3*r**3*(r - 1)*(r + 1)/2
Let y = -410 + 412. Let o(x) be the third derivative of 0*x**3 - 4*x**y - 1/120*x**5 - 1/48*x**4 + 0 + 0*x. Let o(b) = 0. Calculate b.
-1, 0
Let y(n) be the first derivative of -n**5/270 + 7*n**4/108 - 2*n**3/9 - 5*n**2 - 10. Let v(p) be the second derivative of y(p). Let v(w) = 0. Calculate w.
1, 6
Let m be 3/(18/4)*(-1602)/(-1869). Factor 0 - m*n - 2/7*n**2 + 2/7*n**3.
2*n*(n - 2)*(n + 1)/7
Find v such that 48*v**3 - 513/2*v**2 - 5/2*v**4 + 0 + 243*v = 0.
0, 6/5, 9
Let q(b) be the first derivative of -1/16*b**4 + 2 - 5/12*b**3 + 9/4*b - 3/8*b**2. Let q(l) = 0. What is l?
-3, 1
Let c(q) be the second derivative of 0 + 1/4*q**2 + 1/4*q**3 + 19*q - 1/6*q**4. Let c(y) = 0. What is y?
-1/4, 1
Let q(h) = -h**3 - 13*h**2 - 13*h - 9. Let b be q(-12). Solve 24/5*c**2 + 3/5*c**5 + 36/5*c**b + 18/5*c**4 + 0 + 0*c = 0 for c.
-2, 0
Suppose 2*r = 3*r - 3. Suppose -r*i = -5*i + 68. Find u, given that 9*u**5 - 3 + 24*u**2 - 2*u + 3*u + 46*u**3 + i*u**4 + 0*u**5 + 1 = 0.
-1, 2/9
Find n, given that 38/7*n - 2/7*n**3 - 16/7*n**2 - 20/7 = 0.
-10, 1
Let f(b) be the first derivative of 2/5*b**2 + 6 + 2/15*b**3 + 0*b - 1/5*b**4 - 2/25*b**5. Let f(j) = 0. What is j?
-2, -1, 0, 1
Let d(c) be the second derivative of c**7/105 - c**6/25 - 13*c**5/25 - 3*c**4/5 + 5*c**3/3 + 21*c**2/5 - c - 342. Suppose d(t) = 0. Calculate t.
-3, -1, 1, 7
Suppose -15 = -3*t, -5*g = -2*t - 3*t + 50. Let h be (-10)/25*g - (2 - 4). Let 0*j**3 - 1/2 + 0*j + j**2 - 1/2*j**h = 0. Calculate j.
-1, 1
Suppose 14*w = 17*w - 6. Factor -2/5*l**3 + 1/5*l**w + 0*l + 1/5*l**4 + 0.
l**2*(l - 1)**2/5
Let s be ((-4)/(-5))/4 + (-28)/(-10). What is l in -9*l - 5*l**3 - 5*l**2 + 12 - 7*l**2 - s - 11 = 0?
-1, -2/5
Let i(x) be the first derivative of 0*x - 1/9*x**6 + 0*x**2 - 8/9*x**3 + 0*x**4 + 2/5*x**5 + 3. Factor i(k).
-2*k**2*(k - 2)**2*(k + 1)/3
Let z(q) = 3*q + 23. Let k be z(-8). Let v be (-54)/(-10) - (k - -4). Suppose -4/5 - x**2 - v*x = 0. What is x?
-2, -2/5
Suppose 6*y - 2681 - 1111 = 0. Suppose y*n - 11 + 1 - 688*n + 14*n**3 - 20*n**2 - 6 + 6*n**4 = 0. Calculate n.
-2, -1/3, 2
Let c(j) = -3*j**2 + 22*j + 20. Let z be c(8). Factor 0 + 0*m**3 + 0*m + 1/6*m**z - 1/6*m**2.
m**2*(m - 1)*(m + 1)/6
Let d(b) be the second derivative of b**7/4620 + b**6/792 - b**5/330 - b**4 + 10*b. Let f(z) be the third derivative of d(z). Factor f(k).
2*(k + 2)*(3*k - 1)/11
Let p = 86 + -90. Let w be (-2)/p*(-1 + 5). Solve 0 - 1/4*d**3 + 7/4*d**4 + 3/4*d**5 - 7/4*d**w - 1/2*d = 0.
-2, -1, -1/3, 0, 1
Suppose 31*i - 29*i - 66 = 0. Let n = i - 30. Factor -2/3*u**2 + 2/3 - 5/3*u**n + 5/3*u.
-(u - 1)*(u + 1)*(5*u + 2)/3
Let c = -18039 - -18042. Factor 0*a**2 - 3/7*a**c + 0 + 3/7*a**4 + 0*a.
3*a**3*(a - 1)/7
Suppose 5*j + 33 = 5*c - 3*c, -3*j = 2*c + 7. Factor -4*g**2 - 351 + 351 - c*g.
-4*g*(g + 1)
Let c(o) = 7*o - 189. Let j be c(27). Let x(r) be the second derivative of j*r**2 + 0 + 2/3*r**3 + 2*r + 1/2*r**5 - 7/6*r**4. What is b in x(b) = 0?
0, 2/5, 1
Let c(q) = -72*q + 80. Let z(h) = h**2 + 73*h - 80. Let y(l) = 3*c(l) + 4*z(l). Factor y(n).
4*(n - 1)*(n + 20)
Let t(g) = 3*g**3 - 13*g**2 - 7*g + 42. Let f(d) = 4*d**3 - 12*d**2 - 6*d + 44. Let a(p) = -5*f(p) + 6*t(p). Factor a(l).
-2*(l - 1)*(l + 2)*(l + 8)
Let x be (-1560)/96*(-1 - -8). Let w = x + 114. Solve -w - 7/8*r + 7/8*r**3 + 3/4*r**2 - 1/2*r**4 = 0.
-1, -1/4, 1, 2
Suppose -2*x = -x - 2*a - 19, 12 = -3*a. Factor -5*y**2 - 12*y - x*y + 30 + 28*y.
-5*(y - 3)*(y + 2)
Let u = 44 - 41. Factor 0*w - 5*w**3 + w + 2*w**2 + 6*w**u.
w*(w + 1)**2
Let w(i) be the second derivative of 1/3*i**3 + 2*i - 1/5*i**7 + 1 + 3/5*i**4 - 32/25*i**5 + 64/75*i**6 - 2/5*i**2. Suppose w(j) = 0. Calculate j.
-2/7, 1/3, 1
Factor 0*n + 0 - 1/6*n**5 - 1/3*n**3 - 1/2*n**4 + 0*n**2.
-n**3*(n + 1)*(n + 2)/6
Let x be ((-27)/6 - 3) + 3. Let k = -3 - x. Let -k*f - 9*f**5 + 129/4*f**4 + 0 + 51/4*f**2 - 69/2*f**3 = 0. Calculate f.
0, 1/4, 1/3, 1, 2
Let v(q) be the second derivative of -q**5/8 - 35*q**4/12 - 10*q**3 - 2*q + 57. Factor v(w).
-5*w*(w + 2)*(w + 12)/2
Suppose j - 5 - 6 = 0. Find k such that 15*k - 2 - j - 5*k**2 + 3 = 0.
1, 2
Let t = -214 + 208. Let u be 4 + t/(-21)*-13. Factor u*w**2 + 6/7 - 8/7*w.
2*(w - 3)*(w - 1)/7
Let p be ((-427)/(-210) - 8) + 4 + 2. Let l(g) be the third derivative of 0*g + 1/300*g**6 + 2*g**2 + 0 - p*g**4 + 0*g**3 - 1/150*g**5. Factor l(c).
2*c*(c - 2)*(c + 1)/5
Suppose 3*a - 15 = -5*o, 4*a + 0*o - 3 = -o. Let f = -934 + 936. Factor 2/3 - 2/3*s**f + a*s.
-2*(s - 1)*(s + 1)/3
Let h(n) be the second derivative of 0*n**2 - n + 0*n**6 + 0 - 1/14*n**7 + 0*n**3 + 3/20*n**5 + 0*n**4. Let h(g) = 0. Calculate g.
-1, 0, 1
Let a(l) = 4*l**2 + 18*l - 10. Let m(o) = 3*o**2 + 17*o - 11. Let w(d) = -5*a(d) + 4*m(d). Factor w(j).
-2*(j + 3)*(4*j - 1)
Let i(s) = -s**2 - 62*s + 267. Let p be i(-65). Determine u, given that -192 - 192*u - p*u**2 - 12*u**3 - 3/4*u**4 = 0.
-4
Suppose -1288 + 1282 = -3*h. Let k(d) be the third derivative of 0 - 1/360*d**6 + 0*d**5 + 0*d - 4*d**h - 1/9*d**3 + 1/24*d**4. Factor k(f).
-(f - 1)**2*(f + 2)/3
Let u(p) = p + 1. Let k be u(2). Suppose -5*g - k = -13. Solve r**5 - 4*r + 3*r**3 + 4*r + r**g + 3*r**4 = 0 for r.
-1, 0
Let a be 134/8 + -4 + 2. Let f = -161/12 + a. Factor 0 - 2/3*i**3 - 2/3*i**5 + f*i**4 + 0*i + 0*i**2.
-2*i**3*(i - 1)**2/3
Let d(c) = -2*c**2 + 22*c - 39. Let k(l) = -3*l**2 + 23*l - 36. Let t(b) = -2*d(b) + 3*k(b). Factor t(z).
-5*(z - 3)*(z - 2)
Factor 0 + 40/3*c + 6*c**2 + 2/3*c**3.
2*c*(c + 4)*(c + 5)/3
Let h(v) = -3*v**2 - 84*v - 210. Let n(o) = -o**2 - 5. Let z(d) = -h(d) + 6*n(d). Suppose z(s) = 0. What is s?
-2, 30
Let a(r) be the first derivative of -1/3*r**4 + 12 + 4/25*r**5 - 2/75*r**6 + 4/15*r**3 + 8*r + 0*r**2. Let l(s) be the first derivative of a(s). Factor l(i).
-4*i*(i - 2)*(i - 1)**2/5
Let t(q) = -2*q**3 + 154*q**2 + 155*q + 81. Let f be t(78). Factor -3/2*s**2 + 3*s + 3/2*s**4 - f*s**3 + 0.
3*s*(s - 2)*(s - 1)*(s + 1)/2
Let h(u) be the third derivative of -10*u**2 + 0*u**4 + 0*u - 1/8*u**6 + 2/21*u**7 - 1/12*u**5 + 0 + 0*u**3. Determine q, given that h(q) = 0.
-1/4, 0, 1
Let r(g) be the first derivative of -16 - 1