 3
Let w(n) be the first derivative of -n**4 - 20/3*n**3 - 16*n - 16*n**2 - 15. Factor w(y).
-4*(y + 1)*(y + 2)**2
Factor -3/8*h**4 + 15/8*h**3 + 0 + 0*h - 3/2*h**2.
-3*h**2*(h - 4)*(h - 1)/8
Factor 82*g - 605 + 2646 - 113 + g**2 - 247.
(g + 41)**2
Factor 28/3*k + 16/3*k**2 + 1/3*k**3 + 0.
k*(k + 2)*(k + 14)/3
Let l be (2/4)/((-7)/84)*(-89)/2403. Let q be ((-4)/(-15))/(6/10). Solve q*z + 2/9 + l*z**2 = 0.
-1
Suppose -x + m = 2*m - 2, 5*x + 2*m = 16. Suppose -w**3 + 3*w**x + 3*w**3 + w**2 - 2*w**4 = 0. Calculate w.
-1, 0
Suppose 96*c - 37 = -37. Determine y so that -49/6*y**2 - 7/3*y**3 - 1/6*y**4 + 0 + c*y = 0.
-7, 0
Let f(l) = 0*l**2 + 0 + 3 - 15*l + 7*l**2. Let b(v) = 7*v - v**2 - 19*v + 12*v. Let i(t) = 5*b(t) - f(t). Solve i(k) = 0 for k.
1/4, 1
Let m(u) be the second derivative of 0 - u**2 - 1/24*u**4 + 4*u + 1/3*u**3. Determine k so that m(k) = 0.
2
Let v(m) = 6*m - 30. Let b = -35 + 40. Let z be v(b). Factor 0*d + 2/9*d**2 + z.
2*d**2/9
Suppose 6*d + 7776 = -0*d. Let u be d/(-840) + (-4)/10. Factor 2/7*j**3 - 2/7*j**4 + 0 + 8/7*j**2 - u*j.
-2*j*(j - 2)*(j - 1)*(j + 2)/7
Let u(l) = -14*l**2 + 23*l + 64. Let v(o) = -3*o**2 + 6*o + 16. Let k(a) = -2*u(a) + 9*v(a). Solve k(q) = 0 for q.
-4
Let r(k) be the second derivative of k**5/240 + 5*k**4/48 + 25*k**3/24 - 2*k**2 - 10*k. Let l(c) be the first derivative of r(c). Suppose l(t) = 0. Calculate t.
-5
Let l(q) = -q**3 + 1. Let y(k) = 13 + 7*k**3 + 3*k**2 - 2*k**2 - k**3 + 4*k**4 - 15. Let d(b) = -10*l(b) - 5*y(b). Find v such that d(v) = 0.
-1/2, 0
Let p(n) = -n**2 + 7*n + 2. Let w be p(7). Let x be (w + (-10)/4)*-6. Factor 3*a**2 + 0 + 0 + x*a.
3*a*(a + 1)
Factor 1/4*o**4 + 3/4*o + 1/4*o**2 - 3/4*o**3 - 1/2.
(o - 2)*(o - 1)**2*(o + 1)/4
Suppose -h + 83 = 3*a + 2, -4*h + 310 = -2*a. Solve -84*i**2 - 6*i + 2*i + 0*i**3 + h*i**2 - 2*i**3 = 0 for i.
-2, -1, 0
Determine j, given that 80/3 + 700/3*j**2 - 524/3*j**3 - 132*j + 8/3*j**5 + 44*j**4 = 0.
-20, 1/2, 1
Let k(g) be the second derivative of -1/4*g**5 + 0*g**3 - 2 + 1/3*g**6 - 5/6*g**4 + 5/42*g**7 + 0*g**2 + 7*g. Suppose k(d) = 0. Calculate d.
-2, -1, 0, 1
Find m such that 29/8*m - 5/4 + 93/8*m**2 + 5/8*m**4 + 59/8*m**3 = 0.
-10, -1, 1/5
Let s(m) = -m**2 - 6*m - 1. Let r be s(-4). Find t, given that -1 - r - 16*t - 12*t**2 - 4*t**3 + 4*t + 4 = 0.
-1
Suppose -51*v = 43*v - 86*v - 16. Let 3/5*j**v + 6/5 - 9/5*j = 0. What is j?
1, 2
Let u(j) be the second derivative of j**4/42 + 11*j**3/21 - 12*j**2/7 + 122*j. Suppose u(p) = 0. What is p?
-12, 1
Let p = 131 + -129. Let 7*d - 8*d - 4*d - 6 - d**p = 0. Calculate d.
-3, -2
Let k(h) be the second derivative of -3*h**5/20 - 5*h**4/2 - h + 2. Factor k(a).
-3*a**2*(a + 10)
Let h(q) be the first derivative of q**5/540 - q**4/108 + q**3/54 - 17*q**2/2 + 2. Let b(j) be the second derivative of h(j). Factor b(f).
(f - 1)**2/9
Let i(t) = 5*t**2 + 30*t + 46. Let j(s) = -10*s**2 - 60*s - 91. Let x(k) = -9*k**3 - 2*k. Let v be x(1). Let z(w) = v*i(w) - 6*j(w). Solve z(u) = 0 for u.
-4, -2
Let z = -34 + 41. Let 7*n - z*n - 4*n**3 + 7*n**3 - 3*n**4 = 0. What is n?
0, 1
Let c(u) be the second derivative of -u**6/180 + u**5/24 - u**4/36 - 5*u**3/9 + 2*u**2 - 116*u. Factor c(i).
-(i - 3)*(i - 2)**2*(i + 2)/6
Let r(a) = -2*a + 1. Let t be r(-4). Suppose -x - t = -3*f, -3*x + 7 = 2*x - 2*f. Solve -2*v**2 + 2*v**4 + 3*v**2 - x*v**2 = 0.
-1, 0, 1
Let y be (33/77)/((-1)/(7/(-2))). Let b(p) be the first derivative of -21/25*p**5 + 3/4*p**4 + 9/5*p**3 - 4 - y*p**2 - 6/5*p. Let b(n) = 0. What is n?
-1, -2/7, 1
Let m be -9 - (-15)/50*34. Let i = 369/65 - 66/13. Factor -m + 3/5*l**2 - i*l.
3*(l - 2)*(l + 1)/5
Let f(y) be the second derivative of y**5/30 + 17*y**4/9 + 8*y + 2. Suppose f(x) = 0. Calculate x.
-34, 0
Let j(n) be the first derivative of -8*n**5/5 - 87*n**4/2 + 452*n**3/3 + 237*n**2 - 144*n - 276. Find f, given that j(f) = 0.
-24, -1, 1/4, 3
Let c(u) = u**3 + 4*u**2 - 7*u - 5. Let a be c(-5). Factor 4*z**2 + 22*z**3 + 4*z**a + 12*z**4 - 3*z**3 - 7*z**3.
4*z**2*(z + 1)**3
Determine m, given that -65*m + 312 + 515*m + 260*m + 120*m**2 - 3*m**3 + 186*m**2 - 89*m = 0.
-1, 104
Let q(c) be the second derivative of c**6/120 + c**5/40 - 11*c**4/48 - c**3/2 + 9*c**2/2 + 199*c. Solve q(a) = 0.
-3, 2
Let d be (-6)/(-4)*(-6 + -15 + 23). Let 1/3*v**d + 4/3 - 4/3*v**2 - 1/3*v = 0. What is v?
-1, 1, 4
Suppose -3*c - 22 = -8*c - p, 0 = -c + 3*p + 14. Solve -h**3 + h**c + 4*h**3 - 2*h**5 - 4*h**2 + 6*h**2 = 0.
-1, 0, 2
Suppose 22*c - 26*c = -r + 3, -4*r = -5*c - 12. Factor 0 - 1/4*f**3 + 1/4*f**2 + c*f.
-f**2*(f - 1)/4
Suppose -19*c = -29*c + 15*c. Suppose c = -17*f - 3*f. Determine t, given that 6/7*t**3 + 4/7*t + 10/7*t**2 + f = 0.
-1, -2/3, 0
Let f = 50 - 47. What is b in 4*b**3 - 11*b**3 + 3*b**f = 0?
0
Let v(a) = 9*a**2 + 133*a + 43. Let t(i) = 7*i**2 + 135*i + 44. Let r(o) = -3*t(o) + 2*v(o). Factor r(l).
-(l + 46)*(3*l + 1)
Let h(t) be the third derivative of -t**6/135 - 5*t**5/54 + 29*t**4/54 + 16*t**3/27 + 27*t**2. What is c in h(c) = 0?
-8, -1/4, 2
Suppose 5*n - 11 = 3*h, 5*h - n - 8 = 3. Suppose y - 2 + 4 = h*w, 5*y - 3*w = 14. Suppose 1/3*b**y - 1/3*b + 1/3*b**3 + 2/3 - b**2 = 0. Calculate b.
-2, -1, 1
Let m(u) = -2*u**3 - 2*u**2. Let l(b) = -3*b**3 + 12*b**2 - 175*b - 750. Let q(i) = l(i) - 4*m(i). Factor q(o).
5*(o - 6)*(o + 5)**2
Factor -6*g**3 + 1/3*g**4 + 80/3*g**2 + 6*g - 27.
(g - 9)**2*(g - 1)*(g + 1)/3
Let n = -2/1951 + 93658/9755. Let -n*p**3 + 24/5*p**4 + 8*p**2 - 12/5*p + 0 - 4/5*p**5 = 0. Calculate p.
0, 1, 3
Let c(i) be the first derivative of -i**6/9 + i**5/3 + i**4/6 - 11*i**3/9 + i**2 + 62. Determine m so that c(m) = 0.
-3/2, 0, 1, 2
Let m = 55/36 - 25/36. Let s(o) be the second derivative of -1/4*o**5 + 0*o**2 + 13*o - 5/6*o**3 + 0 - m*o**4. Factor s(k).
-5*k*(k + 1)**2
Let l(u) be the first derivative of -u**4/6 + 4*u**3/3 + 21*u + 15. Let x(y) be the first derivative of l(y). What is o in x(o) = 0?
0, 4
Let t(h) be the third derivative of 0*h**3 - 17*h**2 + 0*h**4 - 4/135*h**5 + 0 + 5/1512*h**8 + 0*h + 7/135*h**6 - 22/945*h**7. Let t(o) = 0. Calculate o.
0, 2/5, 2
Let r = -163 - -183. Factor 5*s**5 - r*s**3 - 10*s**5 + 10*s**2 + 73*s**4 + 10 - 93*s**4 + 25*s.
-5*(s - 1)*(s + 1)**3*(s + 2)
Let m(t) be the second derivative of -t**7/8820 - t**6/504 - t**5/70 + 31*t**4/12 + 3*t - 1. Let w(c) be the third derivative of m(c). Factor w(a).
-2*(a + 2)*(a + 3)/7
Let g(j) be the first derivative of -j**6/24 - 13*j**5/40 - j**4/2 - 5*j**3/24 + 239. Determine v, given that g(v) = 0.
-5, -1, -1/2, 0
Suppose -74 = -8*d + 10*d. Let l = 409/11 + d. Solve 0 - 2/11*s**2 + l*s = 0 for s.
0, 1
Find l, given that 4/11*l**3 - 4/11 - 4/11*l**4 + 8/11*l**2 - 2/11*l**5 - 2/11*l = 0.
-2, -1, 1
Let t(s) = 2*s**2 - 5*s - 21. Let r = 18 - 13. Let l be t(r). Factor 4/5*f**3 + 6/5*f**l + 0 + 0*f**2 - 2*f**5 + 0*f.
-2*f**3*(f - 1)*(5*f + 2)/5
Let k(t) be the second derivative of t**5/130 - 2*t**4/39 + 5*t**3/39 - 2*t**2/13 + 88*t. Factor k(d).
2*(d - 2)*(d - 1)**2/13
Let s(b) be the second derivative of b**6/210 + b**5/105 - 8*b**2 + 3*b. Let v(x) be the first derivative of s(x). Determine j, given that v(j) = 0.
-1, 0
Let w(r) be the first derivative of -r**5/5 + 13*r**4/4 + 10*r**3 + 434. Factor w(t).
-t**2*(t - 15)*(t + 2)
Let m be 14/3*318/371. Let q(n) be the first derivative of 0*n - 2/3*n**3 + 2/5*n**5 - 1/2*n**m + n**2 + 2. Factor q(y).
2*y*(y - 1)**2*(y + 1)
Let j(w) be the second derivative of 0 + 0*w**2 + 0*w**4 + 0*w**3 + 9*w - 1/20*w**5 - 1/30*w**6. Suppose j(d) = 0. Calculate d.
-1, 0
Let j(y) = y**3 + 8*y**2 - 8*y + 12. Let n be j(-9). Factor -8*t**2 + 11*t**2 + 0*t - n*t.
3*t*(t - 1)
Suppose t + 4*v = -v + 21, t - 4*v = -6. Factor -16 + 2*g**3 + 22 - 6 - t*g**2.
2*g**2*(g - 3)
Factor 56*c**3 + 315 - 8*c**3 + 576*c + 3*c**4 + 264*c**2 + 117.
3*(c + 2)**2*(c + 6)**2
Let d = 16 + -14. Let -13*l - 3*l**2 + 17*l + 4*l**4 - l**d - 4*l**3 = 0. Calculate l.
-1, 0, 1
Let l(p) be the first derivative of p**7/2940 - p**6/630 + p**5/420 + 13*p**3/3 + 27. Let j(i) be the third derivative of l(i). Suppose j(r) = 0. What is r?
0, 1
Let w(h) be the third derivative of h**6/60 + h**5/20 - 4*h**4/3 + 5*h**3/2 + 165*h**2 - 2. Factor w(i).
(i - 3)*(i + 5)*(2*i - 1)
Let l = -1/503 - -1015/4527. Factor -4/9*u**2 + 2/9*u + 0 + l*u*