- 40*c**2.
5*c*(c - 4)**2*(c + 4)/2
Let q(u) = -u**2 - 53*u - 193. Let s be q(-4). Find a such that -3/2*a**2 + 0 - 3/2*a**s + 3/2*a**5 + 3/2*a**4 + 0*a = 0.
-1, 0, 1
Let a(q) be the second derivative of 5/2*q**2 + 5*q + 0*q**3 + 0*q**4 - 1/240*q**5 + 0. Let m(u) be the first derivative of a(u). Factor m(g).
-g**2/4
Let h(r) be the second derivative of r**4/36 - r**3/9 + r**2/6 + 38*r - 2. Suppose h(k) = 0. What is k?
1
What is y in 49*y**2 - 23*y**4 + 55*y**4 - 11*y**2 - 30*y**3 + 2*y**2 - 27*y**4 = 0?
0, 2, 4
Let k = 8830 - 114788/13. Factor k*z**3 + 10/13*z + 8/13*z**2 + 4/13.
2*(z + 1)**2*(z + 2)/13
Let g(c) be the third derivative of -c**7/24 - 43*c**6/48 - 23*c**5/4 - 15*c**4/4 + 167*c**2. Factor g(q).
-5*q*(q + 6)**2*(7*q + 2)/4
Let l(w) be the third derivative of -169*w**7/630 + 13*w**6/60 - w**5/20 - 2*w**2 + 107. Determine k so that l(k) = 0.
0, 3/13
Factor -111537*f + 237*f**4 + 397*f**5 + 6078*f**3 + 46170*f**2 + 59049 + 385*f**5 - 779*f**5.
3*(f - 1)**2*(f + 27)**3
Factor -63*v**3 - 180*v - 111*v**2 - 600 - 2*v**4 + 126*v**2 + 5*v**4 + 339*v**2.
3*(v - 10)**2*(v - 2)*(v + 1)
Let j = 33 - 9. Let z(k) = -k**4 - 7*k**2 - 3*k**4 + j*k**2 - 6 + 5*k - 2*k**4. Let s(g) = 3*g**4 - 9*g**2 - 3*g + 3. Let i(q) = 5*s(q) + 3*z(q). Factor i(h).
-3*(h - 1)**2*(h + 1)**2
Let f(j) be the second derivative of j**7/15120 - j**6/4320 - 7*j**4/12 + 13*j. Let l(q) be the third derivative of f(q). Factor l(z).
z*(z - 1)/6
Let v(g) be the second derivative of g**6/120 - g**5/60 + g**2/2 - 15*g. Let j(m) be the first derivative of v(m). Let j(w) = 0. What is w?
0, 1
Let s be -4*1*33/(-44). Let j(k) be the second derivative of 0*k**2 - 1/75*k**6 - 4*k + 0*k**4 + 0 + 0*k**s - 1/50*k**5. Suppose j(i) = 0. What is i?
-1, 0
Let t(k) = -k**3 + 5*k**2 + 241*k - 122. Let u be t(18). Factor 1/3*i**3 + 0 - 1/3*i**5 + 0*i + 1/3*i**2 - 1/3*i**u.
-i**2*(i - 1)*(i + 1)**2/3
Let b = -5306/145 + 1067/29. Suppose 3/5*f + b*f**2 - 2 = 0. What is f?
-5, 2
Let m = -3 - -5. Suppose 0 = -3*r + 4*f - m, -r = -f - 0*f. Factor 2*o**2 + 2*o**2 + r*o**3 - 2*o + 2 - 6*o**2.
2*(o - 1)**2*(o + 1)
Let m(k) = 4*k**3 - 2*k**2 - 30*k - 20. Let q(u) = 4*u**2 - u. Let p(d) = -m(d) - 4*q(d). Find l such that p(l) = 0.
-5, -1/2, 2
Suppose -4*h - 4*p - 16 = 0, 5*p + 23 = h + 3. Let k = -12212/5 + 2443. Factor h - k*w + 1/5*w**2.
w*(w - 3)/5
Factor -1/3*x**3 + 2/3*x**2 + 0*x + 0.
-x**2*(x - 2)/3
Let t(s) be the first derivative of 2/45*s**3 - 4/5*s + 1/15*s**2 + 55. What is x in t(x) = 0?
-3, 2
Factor 0 + 1/4*q**3 + 3/2*q**2 - 7/4*q.
q*(q - 1)*(q + 7)/4
Let q(x) = 4*x**3 + 2*x - 2. Let r be q(1). Solve -m**2 - 1 - 4*m + r*m + 2 = 0.
-1, 1
Let k(t) = -21*t**3 - 93*t**2 + 78*t + 36. Let l(d) = -21*d**3 - 92*d**2 + 79*d + 34. Let y(p) = -2*k(p) + 3*l(p). Factor y(m).
-3*(m - 1)*(m + 5)*(7*m + 2)
Factor 2*c + 16 - 16*c + 2*c**2 + 38*c + 24.
2*(c + 2)*(c + 10)
Let d(m) be the third derivative of -m**8/1344 - 43*m**7/840 - 95*m**6/96 + 1207*m**5/240 + 3179*m**4/12 - 9826*m**3/3 - 89*m**2 + m. Factor d(u).
-(u - 4)**2*(u + 17)**3/4
Factor -4*u**3 + 2/5*u**4 - 76/5*u - 72/5*u**2 - 26/5.
2*(u - 13)*(u + 1)**3/5
Let m(r) = -r**3 + 15*r**2 - 13*r - 12. Let k be m(14). Factor -3*i**2 + 9*i**2 - 2*i**4 - k*i**3 + 0 - 4 + 0*i + 2*i.
-2*(i - 1)**2*(i + 1)*(i + 2)
Let r = 56 - 54. Factor o - 4*o**2 - 7*o**3 - 6 + 9*o + 2 - r*o**5 + 8*o**4 - o**3.
-2*(o - 2)*(o - 1)**3*(o + 1)
Determine a, given that 2*a**5 - 8/3*a**3 + 0 + 8/3*a**2 + 0*a - 10/3*a**4 = 0.
-1, 0, 2/3, 2
Let u(x) be the first derivative of 0*x + 25 - 2/3*x**3 + 0*x**2. Factor u(z).
-2*z**2
Factor 240 - 231 - 11*r**3 - 4*r - 26*r + r**3 - 8*r**3 + 3*r**4 + 36*r**2.
3*(r - 3)*(r - 1)**3
Factor 203*m**4 + 18*m + 4*m**3 + 4*m**3 - 21*m**2 - 388*m**4 + 184*m**4.
-m*(m - 3)**2*(m - 2)
Factor -680 + k**3 - 4*k**3 - 32*k**2 + k**3 + 3*k**3 + 1258 + 221*k.
(k - 17)**2*(k + 2)
Factor 2/17*c**4 + 0 + 6/17*c**2 + 8/17*c**3 + 0*c.
2*c**2*(c + 1)*(c + 3)/17
Suppose -2*v = 8*v - 30. Let r be v/(3/(-18)*-9). Factor -1/2*t**r - 8 - 4*t.
-(t + 4)**2/2
Let d(f) be the first derivative of f**4/30 + 2*f**3/15 + 3*f - 9. Let k(s) be the first derivative of d(s). Factor k(q).
2*q*(q + 2)/5
Let l(z) be the second derivative of z**6/420 - z**4/7 + 13*z**3/6 + 10*z. Let i(q) be the second derivative of l(q). Solve i(a) = 0.
-2, 2
Solve 8*u**5 + 52*u**2 + 32*u**4 - 16*u**3 - 2*u - 18*u**2 - 10*u - 42*u**4 - 4*u**5 = 0 for u.
-2, 0, 1/2, 1, 3
Let k(b) = -b - 11. Let a(n) = 6. Suppose w + 6 = 1. Let o(d) = w*a(d) - 3*k(d). Let y(j) = j**2 - 6*j - 7. Let h(x) = 5*o(x) + 3*y(x). Solve h(s) = 0 for s.
-1, 2
Let c be (-3)/18 - (-2)/12. Factor 2/11*b**2 + c - 4/11*b.
2*b*(b - 2)/11
Let p(d) = 1445*d**2 + 344*d + 20. Let r(y) = -2890*y**2 - 689*y - 40. Let t(o) = 9*p(o) + 4*r(o). Suppose t(n) = 0. Calculate n.
-2/17
Factor 3/4*a**3 - 1701/4 + 33/4*a**2 - 135/4*a.
3*(a - 7)*(a + 9)**2/4
Let o(x) be the third derivative of -x**7/120 + 3*x**6/160 + 13*x**5/15 - 5*x**4/8 + 275*x**2. What is a in o(a) = 0?
-5, 0, 2/7, 6
Let a be (9/(-72)*4)/(3/(-2)). Suppose -1/6*r**2 - a + 1/2*r = 0. Calculate r.
1, 2
Let i(u) be the second derivative of -u**7/21 - u**6/15 + 3*u**5/5 - u**4/3 - 5*u**3/3 + 3*u**2 - u + 1. Determine f so that i(f) = 0.
-3, -1, 1
Let i be 2/(-4)*1220/(-30). Let t = i + -181/9. Factor -2/9*o**2 + 0*o + t*o**3 + 0.
2*o**2*(o - 1)/9
Let n = 300 + -196. Suppose n*k - 43*k + 4*k**2 - 47*k + 8 - 2*k**3 = 0. What is k?
-1, 4
Let j(n) = -9*n**4 - 21*n**3 - 29*n**2 - 40*n - 23. Let o(q) = -4*q**4 - 10*q**3 - 15*q**2 - 20*q - 11. Let g(m) = -3*j(m) + 7*o(m). Factor g(t).
-(t + 1)*(t + 2)**3
Let o = 7579 - 7577. Find j such that -1/5*j**4 + 8/5 - 6/5*j**o + j**3 - 4/5*j = 0.
-1, 2
Let b be -1 - -10 - (2 + 2). Let t be ((-15)/b)/(-3) + 3. Suppose -1/4*r**t - 1/2*r + 1/2*r**3 + 1/4 + 0*r**2 = 0. What is r?
-1, 1
Let z(k) be the third derivative of -1/36*k**4 + 0*k**3 + 0 + 1/90*k**5 - 8*k**2 + 0*k. What is h in z(h) = 0?
0, 1
Let g(t) be the third derivative of -t**5/390 + t**4/26 - 5*t**3/39 + t**2 + 70. Factor g(q).
-2*(q - 5)*(q - 1)/13
Let f(i) = i**2 + 6. Let d be f(3). Factor 40*x - 17509 + 17509 - d*x**3 + 5*x**4 - 30*x**2.
5*x*(x - 4)*(x - 1)*(x + 2)
Let d(q) be the third derivative of 1/24*q**3 - q**2 + 1/24*q**4 + 1/840*q**7 + 1/120*q**6 + 0*q + 1/40*q**5 + 0. Let d(t) = 0. Calculate t.
-1
Factor -99/2*b**3 + 0 - 9/8*b**5 - 27*b**2 + 0*b - 57/4*b**4.
-3*b**2*(b + 6)**2*(3*b + 2)/8
Let d(s) be the second derivative of -s**9/6720 + s**8/8960 + s**7/1680 - 7*s**4/6 + 14*s. Let h(a) be the third derivative of d(a). Factor h(q).
-3*q**2*(q - 1)*(3*q + 2)/4
Suppose 0 = 3*g + 4*r - 18, -71*g + 72*g + r - 5 = 0. Let k(p) be the first derivative of 1/4*p**4 + 6*p**g - 6 - 8*p - 2*p**3. Solve k(q) = 0.
2
Let p = 23/4 + -111/20. Let v(r) be the first derivative of 0*r**4 + 0*r - 3 - 1/3*r**3 + 0*r**2 + p*r**5. Factor v(x).
x**2*(x - 1)*(x + 1)
Let b(t) be the second derivative of -t**6/40 - t**5/10 + 11*t**4/16 - 5*t**3/12 - 37*t + 4. Find o such that b(o) = 0.
-5, 0, 1/3, 2
Let l(t) = 2*t**4 - 4*t**3 - 4*t**2 - 3*t. Let d(q) = -q**3 - q**2 - q. Let y(u) = -3*d(u) + l(u). Suppose y(x) = 0. Calculate x.
-1/2, 0, 1
Let v(h) = -7*h**2 - 66*h - 77. Let f be v(-8). Factor -2/3*y**4 - 16/3*y**2 - 10/3*y**f + 0 - 8/3*y.
-2*y*(y + 1)*(y + 2)**2/3
Let f(k) be the third derivative of k**5/690 + k**4/46 + 5*k**3/69 - 97*k**2 + 1. Find u such that f(u) = 0.
-5, -1
Let u = -3165/26 - -1602/13. Let m(o) be the second derivative of u*o**2 + 0 + 1/4*o**3 - 1/8*o**4 - 7*o. Find q, given that m(q) = 0.
-1, 2
Let z(i) = i**3 - 4*i**2 + 2*i - 2. Let q(d) = 5*d**3 - 17*d**2 + 9*d - 9. Let j(a) = -4*q(a) + 18*z(a). Factor j(c).
-2*c**2*(c + 2)
Find z, given that 59/5*z**3 - 9/5*z**4 - 142/5*z**2 - 56/5 + 148/5*z = 0.
1, 14/9, 2
Let q(m) be the first derivative of 675/4*m**4 - 22 + 60*m**3 + 0*m + 6*m**2. Factor q(y).
3*y*(15*y + 2)**2
Factor -197 + 11*a**3 - 60*a + 75*a**2 + 57 + 11*a**3 - 27*a**3.
-5*(a - 14)*(a - 2)*(a + 1)
Suppose s - 38 = -30. Suppose 12*x + 3*x - s - 2*x**2 + 12*x - 35*x = 0. What is x?
-2
Factor 2/3*o**5 + 6*o - 4*o**4 - 4/3 + 28/3*o**3 - 32/3*o**2.
2*(o - 2)*(o - 1)**4/3
Let 4*m**2 - 1 + 4 - 3 - 22*m**3 + 21*m**3 = 0. What is m?
0, 4
Let b(q) be the second derivative of -q**7/2