 be c(-15). Let j(k) = -k**3 - 6*k**2 - k - 4. Let g be j(q). Factor f**g - f - 1/3*f**3 + 1/3.
-(f - 1)**3/3
Let r be 31/(-20) - (-231)/132. Find q, given that 2/5 + 3/5*q + r*q**2 = 0.
-2, -1
Find c such that -14/3*c**3 - 16/3*c + 8/9*c**4 + 74/9*c**2 + 8/9 = 0.
1/4, 1, 2
Let w = 18927 - 18923. Factor -5*q + w + 3/2*q**2.
(q - 2)*(3*q - 4)/2
Let s(v) be the first derivative of v**4/10 + 14*v**3/5 - 9*v**2 + 46*v/5 + 6. Suppose s(l) = 0. Calculate l.
-23, 1
Let n = -15/11 + 41/22. Let f(g) be the first derivative of n*g - 1/12*g**3 + 1/8*g**2 + 6. Suppose f(d) = 0. Calculate d.
-1, 2
Let d(c) = -45*c**3 - 690*c**2 - 790*c - 145. Let o(x) = 45*x**3 + 689*x**2 + 788*x + 144. Let b(i) = -4*d(i) - 5*o(i). Factor b(w).
-5*(w + 1)*(w + 14)*(9*w + 2)
Solve 14/3 - 2/15*l**2 + 68/15*l = 0.
-1, 35
Suppose -3*w - 42 + 48 = 0. Factor 2 - 3*g**w - 3*g + 4 + 0 + 0*g**2.
-3*(g - 1)*(g + 2)
Let d(w) be the first derivative of w**3/3 - 42*w**2 + 1764*w + 4. Factor d(v).
(v - 42)**2
Factor 16/9*f + 4/3*f**2 + 2/9*f**3 + 0.
2*f*(f + 2)*(f + 4)/9
Suppose -12 - 6 = -2*l + 4*c, c = -4*l + 27. Suppose -5*g = -5*y + 5, 0 = 3*g - l*g - 5*y + 23. Suppose -24/5*k - 18/5 - 8/5*k**g = 0. Calculate k.
-3/2
Factor 2/5*h**4 + 1960 + 1064*h + 1002/5*h**2 + 76/5*h**3.
2*(h + 5)**2*(h + 14)**2/5
Let p = -124 + 81. Let g = 216/5 + p. Determine f, given that 2/5 - g*f + 1/5*f**3 - 3/5*f**2 + 1/5*f**4 = 0.
-2, -1, 1
Suppose -13*h + 2158 = -26*h. Let v be (h/(-600) + 13/(-52))*5. What is x in 2/15*x**2 + v*x + 0 = 0?
-1, 0
Let o(j) be the second derivative of j**4/54 + 2*j**3/3 + 17*j**2/9 + 92*j + 1. Factor o(n).
2*(n + 1)*(n + 17)/9
Suppose -3 = -5*w - 3. Let s(u) be the third derivative of -u**2 + w + 1/6*u**4 - 1/3*u**3 - 1/30*u**5 + 0*u. What is o in s(o) = 0?
1
Let v(q) = 11*q**2 - 5*q. Let b be v(1). Let y(p) be the second derivative of -1/35*p**5 - 2/21*p**3 + 0*p**2 + 0 + 2/21*p**4 - b*p. Factor y(i).
-4*i*(i - 1)**2/7
Let a be 96/360 + 3*4/30. Let s be (-176)/24 - -5 - -3. Solve -1/3*n**5 + a*n**2 + n - s*n**3 + 1/3 - n**4 = 0.
-1, 1
Let p(l) = -6*l**2 - 5 + 3*l**2 - 2 + 4. Let y(z) = -6*z**2 - z - 6. Suppose -14 = -5*t + 16. Let f(n) = t*y(n) - 11*p(n). Let f(k) = 0. Calculate k.
-1
Let l(f) be the third derivative of f**6/300 - 11*f**5/150 + 7*f**4/12 - 5*f**3/3 - 101*f**2 + 1. Factor l(g).
2*(g - 5)**2*(g - 1)/5
Let c(r) = 5*r - 4*r**3 - 14*r**2 + 2*r**2 - 17*r. Let s(f) = f. Let n be (20/(-12))/5*(4 + -1). Let y(d) = n*c(d) - 4*s(d). Factor y(x).
4*x*(x + 1)*(x + 2)
Let r(b) be the third derivative of -b**11/66528 + b**10/12600 - b**9/15120 - b**5/12 - 3*b**2. Let h(c) be the third derivative of r(c). Factor h(y).
-y**3*(y - 2)*(5*y - 2)
Let t be 86/135 + 27/(-45). Let k(f) be the third derivative of 1/90*f**5 - 10*f**2 + 0*f - 1/540*f**6 + t*f**3 - 1/36*f**4 + 0. Solve k(p) = 0.
1
Let l(g) = 2*g**4 + 10*g**3 + 9*g**2 + 8*g + 7. Let t(q) = q**4 + 5*q**3 + 4*q**2 + 4*q + 4. Let d(r) = -4*l(r) + 7*t(r). Factor d(y).
-y*(y + 1)*(y + 2)**2
Let d be (-6)/10 + 82/105. Let j = 8/21 - d. Factor 0 - 3/5*s + j*s**2.
s*(s - 3)/5
Suppose -17 = -w - 5*q, -3*w + 0*q + 2*q = 0. Solve 900 + 31*j + 89*j + j**w + 3*j**2 = 0.
-15
Find j, given that -1517*j - 544*j + 195*j**2 + 4860 - 99*j - 7*j**3 + 2*j**3 = 0.
3, 18
Let l = 439/306 + 10/153. Let y(t) be the third derivative of 0 + 0*t - 7*t**2 - 3/4*t**4 - 13/180*t**6 - 2/5*t**5 + l*t**3 - 1/210*t**7. Solve y(u) = 0.
-3, 1/3
Let z(r) be the second derivative of r**8/4200 - r**7/2100 - r**3/6 - 2*r. Let p(y) be the second derivative of z(y). Factor p(b).
2*b**3*(b - 1)/5
Let g = 46 + -32. Suppose -g = -4*z + i, -5*z + 2*i = -5 - 14. Solve 23 - 23 + 6*v**z - 3*v**4 = 0 for v.
0, 2
Suppose 0 = -7*s + 12*s - 10. Factor 6 + 0 - q**3 - 2 - q - q**s + 5*q.
-(q - 2)*(q + 1)*(q + 2)
Let f(o) = -o**2 - 6*o - 7. Let a be f(-4). Suppose 7*w = a + 34. Solve -9*s**2 + 2*s**3 + 6*s + w*s**3 - s**3 - 3*s**3 = 0 for s.
0, 1, 2
Let q(h) = 2*h**2 - 6*h - 12. Let f(k) = 4*k**2 + 32*k + 27. Let j be f(-7). Let p(x) = 0 - 2 + 3. Let g(u) = j*q(u) - 4*p(u). Let g(i) = 0. What is i?
-1, 4
Let v = -881/2860 - -18/55. Let w = v - -97/364. Let -w - 3/7*q - 1/7*q**2 = 0. Calculate q.
-2, -1
Factor 5*t**2 + 204 - 330 + 457 + 177*t - 37*t + 649.
5*(t + 14)**2
Factor -15*j**4 + 2916 - 1070*j**2 + 20*j**4 - 104*j**3 - 1944*j + 206*j**2 - 9*j**4.
-4*(j - 1)*(j + 9)**3
Let l = 2246 + -13475/6. Factor 1/6*q**2 + 0 - l*q**3 + 1/6*q - 1/6*q**4.
-q*(q - 1)*(q + 1)**2/6
Let a(o) be the first derivative of o**6/11 + 12*o**5/55 - 4*o**3/11 - 3*o**2/11 - 53. Factor a(c).
6*c*(c - 1)*(c + 1)**3/11
Let q(b) be the third derivative of -b**8/3528 + 4*b**7/2205 + b**6/180 - 11*b**5/315 - 2*b**4/21 - 248*b**2. Determine g so that q(g) = 0.
-2, -1, 0, 3, 4
Let g(f) = 26*f**4 - 42*f**3 + 26*f**2 + 10*f - 4. Let t(m) = -17*m**4 + 28*m**3 - 17*m**2 - 7*m + 3. Let p = 41 - 36. Let d(l) = p*g(l) + 8*t(l). Factor d(v).
-2*(v - 1)**3*(3*v + 2)
Factor -24*p**4 + 0*p**3 - 8140*p**5 - 3*p**3 + 8092*p**5.
-3*p**3*(4*p + 1)**2
Suppose 6*n + 4 = 82. Let p(c) = -c**3 + 15*c**2 - 27*c + 14. Let k be p(n). Suppose 3/4*o**2 - k + 0*o - 1/4*o**3 = 0. What is o?
-1, 2
Factor p**2 - 45*p + 85*p - 7*p**2 + 2*p**4 - 36*p.
2*p*(p - 1)**2*(p + 2)
Let c be ((-305)/(-1464))/(20/16). Factor 35/6*m - 11/6*m**2 + c*m**3 - 25/6.
(m - 5)**2*(m - 1)/6
Suppose -1 = -3*o + 4*u, 5*o + 0*u = -4*u + 23. Factor -v**o - v - 2 - 1 + 2*v**2 + 3.
-v*(v - 1)**2
Let p(s) be the second derivative of -s**5/90 + s**4/54 + s**3/27 - s**2/9 - 109*s. Factor p(b).
-2*(b - 1)**2*(b + 1)/9
Suppose 12*g**2 + 15*g**4 - 21*g**2 + 16*g**2 + 3*g**5 + 24*g**3 + 5*g**2 = 0. What is g?
-2, -1, 0
Let t(z) = 6*z**2 + 7*z + 15. Let j(l) = -2*l**2 - 3*l - 7. Let y(i) = -7*j(i) - 3*t(i). Let y(r) = 0. What is r?
-1, 1
Let d(i) = i**3 - 6*i**2 + 2*i - 8. Let m be d(6). Let o = m + -2. Factor 2*b**o + 6*b + 2 - 1 + 3.
2*(b + 1)*(b + 2)
Let p(z) be the first derivative of -z**5/25 + 3*z**4/10 + 8*z**3/15 - 3*z**2/5 - 7*z/5 + 15. Factor p(l).
-(l - 7)*(l - 1)*(l + 1)**2/5
Solve 2/5*s**5 + 18/5*s**3 + 0 - 8/5*s**2 - 24/5*s + 12/5*s**4 = 0 for s.
-3, -2, 0, 1
Let b = -14 - -16. Suppose -r + b = -0, 2*r - 20 = -p. Factor 4*o**5 + 9*o**2 + 8 - 4*o - o**2 - p*o**4 + 5*o**3 - 16*o + 11*o**3.
4*(o - 2)*(o - 1)**3*(o + 1)
Let z(q) be the third derivative of -q**8/4480 + q**7/1008 - q**6/720 + q**4/8 + 10*q**2. Let h(g) be the second derivative of z(g). Factor h(l).
-l*(l - 1)*(3*l - 2)/2
Let y(x) be the first derivative of -x**7/280 - x**6/15 + 14*x**3/3 - 2*x + 29. Let n(r) be the third derivative of y(r). Factor n(w).
-3*w**2*(w + 8)
Factor 3*t**2 + 84/5*t - 36/5.
3*(t + 6)*(5*t - 2)/5
Factor 48/5*s**2 + 1/5*s**4 + 32/5 + 68/5*s + 13/5*s**3.
(s + 1)*(s + 2)**2*(s + 8)/5
Let g(p) = -8*p**3 - 7*p**2 - 4*p + 9. Let j(n) = -4*n**3 - 3*n**2 - 2*n + 5. Let c(i) = 4*g(i) - 7*j(i). Factor c(s).
-(s + 1)**2*(4*s - 1)
Suppose 3*t - 41 = -5*y, 4*y - 4*t = -0*t + 20. Solve y*o**3 + o**5 - 41*o**2 + 2 - 2 + 5*o**4 + 44*o**2 = 0 for o.
-3, -1, 0
Let l(a) = 4*a + 51. Let h be l(13). Let y = h + -103. Factor y + 2/7*n + 4/7*n**2 + 2/7*n**3.
2*n*(n + 1)**2/7
Suppose 4*z = -4*i, 4*i + 4*z = 9*z + 36. Let d(f) be the second derivative of 3*f + 8/3*f**3 + 16*f**2 + 0 + 1/6*f**i. Factor d(m).
2*(m + 4)**2
Let c(u) be the second derivative of 0*u**4 + 3 + 7/3*u**3 - 7*u - 1/10*u**5 + 6*u**2. Determine o so that c(o) = 0.
-2, -1, 3
Suppose 5*s = 5*j, 5*j + 0*s = -s. Let x = -867 + 873. Factor 4*g - x*g + j*g - 4*g**2 + 0*g**3 - 2*g**3.
-2*g*(g + 1)**2
Let o(q) = q**3 - q**2 - q. Let v = -1 - -3. Let t(d) = -2*d + 5*d - 2*d. Let r(b) = v*t(b) + 2*o(b). Factor r(g).
2*g**2*(g - 1)
Let x(n) be the third derivative of -n**6/600 + 2*n**5/75 - n**4/6 + 8*n**3/15 - 121*n**2. Suppose x(f) = 0. Calculate f.
2, 4
Let s(p) be the second derivative of 2*p**5/45 - p**4/18 - p**3/27 - 4*p - 2. Factor s(w).
2*w*(w - 1)*(4*w + 1)/9
Let b(k) be the first derivative of 0*k - 44 - 1/14*k**2 + 1/21*k**3. Determine a, given that b(a) = 0.
0, 1
Let j be 921/18*(-16)/(-408) - 4/(-36). Suppose 2/17*w**3 + 8/17*w**2 - 6/17*w - j = 0. What is w?
-3, 2
Let x be 24/6 + (-252)/(-3). Factor -4 + x*q**2 - q - 89*q**2 + 6*q.
-(q - 4)*(q - 1)
Suppose -t - 2*t + 2*d + 41 = 0, 32 = 2*t + d. Solve 2*f**5 - 6*f