
Let f(c) = -c**3 - 2*c**2 + 5*c - 3. Let q be f(-4). Suppose q = 4*g + 5. Factor 0*t + 2*t**2 + 2*t**3 + g + 4*t**2 + 4*t + 2*t**3 + t**4.
(t + 1)**4
Suppose -130 - 38 = -21*j. Let v(a) be the first derivative of 1/10*a**2 - j - 1/25*a**5 + 1/30*a**6 - 1/10*a**4 + 2/15*a**3 - 1/5*a. Let v(n) = 0. Calculate n.
-1, 1
Let x(p) = -p - 2. Let v be x(-5). Solve 8*o - 6 + 14*o**2 - 4 - 20*o**v + 6*o**4 + 2 = 0.
-2/3, 1, 2
Let n(m) = m**2 - 4*m - 2. Let g be n(6). Factor 20*v + 5*v**5 - 15*v**3 + g*v**4 - 13*v**2 - 6*v**2 - v**2 + 0*v**2.
5*v*(v - 1)**2*(v + 2)**2
Let u(b) be the second derivative of 25*b - 1/6*b**3 - 7/100*b**5 + 0*b**2 + 0 - 11/60*b**4 - 1/150*b**6. Factor u(z).
-z*(z + 1)**2*(z + 5)/5
Let w be (-2)/(-5) + (-16)/(-10). Suppose 0 = -2*n + 4*l + 16, -w*n - 3*l + 3 = 15. Let n*i**2 - 1/2 - i**3 + i + 1/2*i**4 = 0. Calculate i.
-1, 1
Let x(p) be the first derivative of p**4 + 8*p**3/3 + 2*p**2 + 461. Factor x(a).
4*a*(a + 1)**2
Let d(k) = k. Let s(u) = 39*u**2 + 143*u + 51. Let m(b) = -d(b) - s(b). Let l(g) = -3*g**2 - 11*g - 4. Let r(x) = 27*l(x) - 2*m(x). Find t, given that r(t) = 0.
-2, -1
Let t(b) be the third derivative of b**6/120 + b**5/10 + b**4/3 - 29*b**2. Let t(h) = 0. What is h?
-4, -2, 0
Let f(m) = -15*m**2 - 400*m - 7600. Let i(s) = 13*s**2 + 398*s + 7601. Let v(q) = 4*f(q) + 5*i(q). Solve v(c) = 0 for c.
-39
Let y = 41065/3 + -13687. Factor -y - 5/3*s**2 + 1/3*s**3 + 8/3*s.
(s - 2)**2*(s - 1)/3
Suppose 11 = 3*j + 2. Let g(l) = -3*l**2 + 33*l + 3. Let x be g(11). Find z, given that 4 + 4*z**2 + 2*z**j - 6*z - 8*z**2 + x*z + z = 0.
-1, 1, 2
Let x = -1793/7 + 255. Let j = x + 39/28. Factor 1/2 - 3/4*f + j*f**2.
(f - 2)*(f - 1)/4
Let j be (-310)/(-20) + (-1)/(-2) + -1. Factor -20 - 40*a - j*a**2 + 8*a**3 + 10*a**3 - 10*a**2 - 23*a**3.
-5*(a + 1)*(a + 2)**2
Factor -1/6*s**4 - 1/3 + 7/6*s + 5/6*s**3 - 3/2*s**2.
-(s - 2)*(s - 1)**3/6
Suppose 9*m = 6*m + 33. Let f be -1 - 0 - (-33)/m. Factor -f*b - 20*b**2 - 4*b + 17*b**2 + 3*b.
-3*b*(b + 1)
Find q such that -21/2 - 15/2*q**2 + 39/2*q - 3/2*q**3 = 0.
-7, 1
Suppose 153*p**2 - 572 - 1872*p - 918 - 538 - 3*p**3 = 0. Calculate p.
-1, 26
Let t(a) be the third derivative of a**5/90 + 11*a**4/48 + 2*a**3/9 - 15*a**2. Find i, given that t(i) = 0.
-8, -1/4
Let l(i) be the second derivative of -i**5/100 + i**4/15 + 11*i**3/30 + 3*i**2/5 + 2*i - 39. Factor l(a).
-(a - 6)*(a + 1)**2/5
Let a(j) = -2*j**3 - 195*j**2 + 707*j + 2. Let x be a(-101). Factor 0 - 5/2*u**x - 3/2*u + 1/2*u**4 - 1/2*u**3.
u*(u - 3)*(u + 1)**2/2
Let o(t) be the second derivative of 3/4*t**4 - 1/10*t**6 - 3/10*t**5 + 0 + 2*t**3 + 3*t - 6*t**2. Determine r so that o(r) = 0.
-2, 1
Let v(p) = -p**2 + p - 1. Let i be 6/(-9)*6/(-4). Let k = -2 + i. Let y(f) = 3*f**2 - 4*f. Let r(h) = k*y(h) + v(h). Determine m, given that r(m) = 0.
1/4, 1
Let r(b) be the first derivative of 5*b**6/36 - 17*b**5/30 - b**4/6 + 32*b**3/9 - 16*b**2/3 + 8*b/3 - 1. Determine a so that r(a) = 0.
-2, 2/5, 1, 2
Let k be (9/(-108) - (-1)/(-2*2)) + 1. Suppose 2/3 - k*q**2 + 2/3*q**3 - 2/3*q = 0. What is q?
-1, 1
Let h(k) be the first derivative of -5*k**4 + 31*k**3/3 - 29*k**2/2 - 4. Let s(w) = 5*w**3 - 8*w**2 + 7*w. Let u(g) = -2*h(g) - 9*s(g). What is y in u(y) = 0?
0, 1
Let r be 519/8 - (-2)/16. Solve c**3 + c**3 + 2*c**5 + r*c - 6*c**4 - 69*c + 6*c**2 = 0.
-1, 0, 1, 2
Let c = -7 - -9. Determine z, given that 12*z**3 - 3*z**4 + 5*z**c - 2*z**4 - 22*z**3 + 10*z = 0.
-2, -1, 0, 1
Let i(c) be the first derivative of -c**6/6 + c**5 - 25*c**4/12 + 5*c**3/3 - 5*c + 24. Let h(l) be the first derivative of i(l). Solve h(g) = 0 for g.
0, 1, 2
Let t(x) be the first derivative of 7*x**6/3 - 18*x**5/5 - 5*x**4/2 + 6*x**3 - 2*x**2 - 29. Suppose t(h) = 0. Calculate h.
-1, 0, 2/7, 1
Let o(j) = 26*j**3 - 88*j**2 - 19*j. Let m(i) = -i**3 + 2*i**2 - i. Let t(b) = 5*m(b) + o(b). Suppose t(c) = 0. Calculate c.
-2/7, 0, 4
Let n = -36 - -43. Factor -y**3 - 49 + n*y**2 + 97 - 64 - 8*y.
-(y - 4)**2*(y + 1)
Let u(z) = 45*z**2 + 630*z + 240 + 54*z**2 - 24*z**2. Let k(q) = -25*q**2 - 210*q - 80. Let x(l) = 7*k(l) + 2*u(l). Let x(f) = 0. What is f?
-8, -2/5
Let w(n) = -n**2 - 4*n. Let c = -15 - -11. Let x be w(c). Suppose -2 - 4*p**3 + 4*p**4 - 2*p**4 + x + 4*p = 0. Calculate p.
-1, 1
Let f be (24/135)/(-1) + -10*7/(-175). Let 0 - 2/9*p**3 + 4/9*p - f*p**2 = 0. Calculate p.
-2, 0, 1
Let b = -96 - -98. Let q(d) be the second derivative of 4*d**3 + 1/2*d**5 + 0 + 3*d**4 - 8*d**b + 2*d. Factor q(l).
2*(l + 2)**2*(5*l - 2)
Let o(v) = 8*v**2 + v. Let d(h) = -18*h**2 + 52*h + 56. Let u(y) = 2*d(y) + 4*o(y). Factor u(c).
-4*(c - 28)*(c + 1)
Let q(w) be the second derivative of -w**4/84 + 61*w**3/7 - 33489*w**2/14 + w - 50. Suppose q(j) = 0. What is j?
183
Let f(a) be the third derivative of 0*a - 1/18*a**4 + 0*a**3 + 27*a**2 + 0 + 1/90*a**5. Factor f(n).
2*n*(n - 2)/3
Let c(l) be the second derivative of -1/15*l**4 + 1/50*l**5 + 0 + 0*l**2 + 1/15*l**3 - 49*l. Solve c(j) = 0 for j.
0, 1
Let s(i) be the second derivative of i**6/360 - i**4/72 + 8*i**2 - 26*i. Let d(t) be the first derivative of s(t). Factor d(w).
w*(w - 1)*(w + 1)/3
What is z in -4/5*z - 8/5*z**2 + 4/5*z**3 + 2/5*z**4 + 6/5 = 0?
-3, -1, 1
Let f(m) be the first derivative of -3*m**4/16 + 2*m**3 + 3*m**2/8 - 6*m - 361. Factor f(a).
-3*(a - 8)*(a - 1)*(a + 1)/4
Factor 9*y**3 - 14*y + 22*y - 4*y**3 - 13*y - 5 + 5*y**2.
5*(y - 1)*(y + 1)**2
Let g = 2/11 + -39/275. Let r = 53/75 - g. Find c, given that -10/9*c - r*c**2 - 4/9 + 2/9*c**3 + 2/9*c**4 = 0.
-1, 2
Let f = -283 + 287. Let p(g) be the second derivative of -1/75*g**6 - g + 0*g**5 + 0*g**3 + 0*g**2 + 0 + 1/30*g**f. Let p(v) = 0. What is v?
-1, 0, 1
Let o(f) be the first derivative of -f**4 - 112*f**3/3 + 544*f**2 - 2304*f + 500. Factor o(r).
-4*(r - 4)**2*(r + 36)
Let y = 4243/168 + -199/8. Factor y*b - 2/7 - 2/21*b**2.
-2*(b - 3)*(b - 1)/21
Let g(l) be the first derivative of 1/20*l**4 + 0*l - 1/150*l**5 - 2/15*l**3 - 3*l**2 - 5. Let x(w) be the second derivative of g(w). Factor x(f).
-2*(f - 2)*(f - 1)/5
Let x(r) = -2*r**5 + 2*r**4 + 10*r**3 - 2*r**2 - 2*r. Let v(l) = l**4 + l**3 - l**2 - l. Let j(k) = -2*v(k) + x(k). Factor j(u).
-2*u**3*(u - 2)*(u + 2)
Suppose 2 + 398 = 50*l. Let z(v) be the third derivative of 1/8*v**3 + 0*v + 0 + 1/80*v**5 + l*v**2 + 1/16*v**4. Factor z(w).
3*(w + 1)**2/4
Suppose m + 9 = 2*f - 0*m, -3*f = 4*m - 30. Let c = -4 + 8. Factor 2*u**5 + 4*u**2 - 2*u**3 - f*u**2 + 3*u**4 + 0*u**4 - u**c.
2*u**2*(u - 1)*(u + 1)**2
Suppose 0 = -26*s - 22 + 22. Factor -12/7 + 9/7*b**2 + 3/7*b**3 + s*b.
3*(b - 1)*(b + 2)**2/7
Let j(g) = -g**3 - g**2 - 4*g - 2. Let h(i) = -2*i**3 - i**2 - 5*i - 3. Let s(a) = -2*h(a) + 3*j(a). Let y be s(2). Factor y*m + 3*m - 2*m**3 - m**3.
-3*m*(m - 1)*(m + 1)
Suppose 24*u + 9 = 33. Factor u + 1/2*r**2 + 3/2*r.
(r + 1)*(r + 2)/2
Let i(g) be the first derivative of -4/5*g + 1/10*g**4 + 1/5*g**3 - 2 - 2/5*g**2 - 1/25*g**5. Determine h so that i(h) = 0.
-1, 2
Let y(u) = 13*u**3 - 47*u**2 - 72*u - 40. Let h(s) = -38*s**3 + 139*s**2 + 219*s + 119. Let j(n) = -4*h(n) - 11*y(n). Factor j(p).
3*(p - 6)*(p + 1)*(3*p + 2)
Let -56/5 - 168/5*f**2 + 204/5*f + 4*f**3 = 0. Calculate f.
2/5, 1, 7
Let o = -161 - -645/4. Let g = -24 - -24. Factor g*t - o + 1/4*t**2.
(t - 1)*(t + 1)/4
Suppose -2*g = g - 9, 3*k + 2*g = 12. Let h(b) be the first derivative of 0*b**k + 1/5*b**3 - 1/20*b**4 - 4/5*b - 7. Factor h(j).
-(j - 2)**2*(j + 1)/5
Let x(h) = -h**3 + h**2 - h - 1. Let k(w) = 3*w**5 - 54*w**4 + 170*w**3 + 46*w**2 - 718*w + 674. Let g(l) = -k(l) - 2*x(l). Factor g(o).
-3*(o - 14)*(o - 2)**3*(o + 2)
Let k(r) = -355*r**3 + 340*r**2 - 10*r. Let t(w) = w**4 - 177*w**3 + 170*w**2 - 4*w. Let o(d) = -2*k(d) + 5*t(d). Solve o(b) = 0.
0, 1, 34
Let y(o) = 32*o**3 - 54*o**2 + 26*o + 2. Let i(f) = f**4 + f**3 + 1. Let c(u) = -2*i(u) + y(u). Solve c(t) = 0.
0, 1, 13
Let a(n) be the first derivative of n**5/120 + n**4/16 + n**3/6 - 8*n**2 + 13. Let k(u) be the second derivative of a(u). Factor k(x).
(x + 1)*(x + 2)/2
Let a(j) = j**3 + 6*j**2 - 6*j - 53. Let m be a(-5). Factor -8*x - 16/5 + 18/5*x**3 - 12/5*x**m.
2*(x - 2)*(3*x + 2)**2/5
Let d(y) be the first derivative of 2*y**6/9 + 16*y**5/15 - y**4/3 - 64*y**3/9 - 8*y**2 + 14. Determine g, given that 