erivative of 65*c**4/72 + 61*c**3/36 - c**2/3 + 289*c - 2. Factor x(q).
(q + 1)*(65*q - 4)/6
Let i(j) = -2*j**2 - 17*j - 5. Let w be i(-5). Factor -5*m**4 + 68*m + 10*m**3 - 5*m**2 - 38*m - w*m.
-5*m**2*(m - 1)**2
Let p(t) be the second derivative of t**6/72 + t**5/24 - 5*t**4/12 + 2*t**3/3 - t. Let r(l) be the second derivative of p(l). What is s in r(s) = 0?
-2, 1
Let i(j) = 27*j**4 - 200*j**3 - 194*j**2 + 11*j + 33. Let s(h) = -5*h**4 + 40*h**3 + 39*h**2 - 2*h - 6. Let k(b) = 4*i(b) + 22*s(b). Solve k(x) = 0.
-1, 0, 41
Let m(q) be the third derivative of -q**5/60 - q**4/6 - q**3/2 + 2*q**2 - 18. Solve m(j) = 0.
-3, -1
Let b(o) be the second derivative of -11*o**4/12 + 3*o**3/2 + o**2 - 6*o - 1. Let b(s) = 0. What is s?
-2/11, 1
Let i(p) = 9*p**4 - 6*p**3 + p**2 - 4*p - 4. Let a(h) = -10*h**4 + 5*h**3 + 5*h + 5. Let d(f) = 4*a(f) + 5*i(f). What is y in d(y) = 0?
0, 1
Let f = -14 + 15. Let t(k) = k**5 - k**3 + k**2 - k - 1. Let v(x) = -4*x**5 - 2*x**4 + 4*x**3 - 4*x**2 + 6*x + 6. Let z(b) = f*v(b) + 6*t(b). Factor z(g).
2*g**2*(g - 1)**2*(g + 1)
Suppose 0 = -2*m + 2 + 14. Let p be -4*(-3)/(-6)*-49. Factor -4*r + m*r - 3*r + p*r**3 - 9*r.
2*r*(7*r - 2)*(7*r + 2)
Let u be ((-2016)/448)/(6/(-4)). Factor 3 - 1/3*g**u - 5*g + 7/3*g**2.
-(g - 3)**2*(g - 1)/3
Let k(i) be the third derivative of i**6/40 - 4*i**5/5 + 13*i**4/8 + 15*i**3 + 11*i**2 + i. What is j in k(j) = 0?
-1, 2, 15
Let y(f) be the first derivative of f**3/15 - f**2/20 - 3*f/5 + 151. Find r, given that y(r) = 0.
-3/2, 2
Let w(o) = -2*o**2 - 8*o + 16. Let b(k) = -6*k**2 - 23*k + 47. Let j(v) = 4*b(v) - 14*w(v). Let i(u) = 1. Let f(g) = 12*i(g) + j(g). Factor f(p).
4*(p - 1)*(p + 6)
Suppose 3*h - h + 5*h = 0. Factor -24*b + 0*b**2 + h*b**2 + 3*b**2 + 18*b + 3.
3*(b - 1)**2
Let f(a) be the third derivative of 1/16*a**4 - 1/160*a**5 + 0*a - 3/16*a**3 - 3*a**2 + 0. Determine w so that f(w) = 0.
1, 3
Find t such that 4*t**2 + 6*t**2 - 5*t - 6*t**2 - 5*t**2 + 2*t**3 - 2 = 0.
-1, -1/2, 2
Factor -12/17*r**4 - 18/17*r**3 - 2/17*r**5 + 0*r**2 + 0*r + 0.
-2*r**3*(r + 3)**2/17
Let x = -44491/15 + 8939/3. Factor -x*q**4 + 2/5*q + 18/5*q**5 + 92/5*q**3 - 48/5*q**2 + 4/5.
2*(q - 1)**4*(9*q + 2)/5
Let z(u) be the first derivative of -u**6/30 - 128*u**5/25 - 1321*u**4/5 - 12496*u**3/3 + 158752*u**2/5 - 340736*u/5 + 515. Factor z(w).
-(w - 2)**2*(w + 44)**3/5
Let h(i) = -i**3 - i**2 + i + 1. Suppose m - 3 = 0, -4*v - 18 + 5 = -3*m. Let r(f) = 4*f**3 + 10*f**2 - f - 13. Let u(s) = v*r(s) - h(s). Factor u(t).
-3*(t - 1)*(t + 2)**2
Let v(t) be the first derivative of t**3/12 + 29*t**2/8 + 77*t/2 - 65. Factor v(d).
(d + 7)*(d + 22)/4
Let y(q) = 11*q**3 + 24*q**2 - 35*q - 5. Let d(k) = -6*k**3 - 12*k**2 + 18*k + 3. Let x(u) = 5*d(u) + 3*y(u). What is i in x(i) = 0?
-5, 0, 1
Let j(k) = -k**2 + 5*k + 20. Let z(n) = -n**2 + 11*n + 41. Let r(i) = -5*j(i) + 2*z(i). Factor r(h).
3*(h - 3)*(h + 2)
Let x(t) be the first derivative of -t**5/420 - 19*t**2/2 + 3. Let z(s) be the second derivative of x(s). Find k, given that z(k) = 0.
0
Let x = -90/13 + 1839/260. Let k(z) be the second derivative of 0*z**3 + 0 - 7*z - x*z**5 + 0*z**4 - 1/14*z**7 + 0*z**2 - 1/5*z**6. Find n, given that k(n) = 0.
-1, 0
Let j be -4 - 176/33*(-9)/6. Let l(z) be the second derivative of 0 + 1/2*z**3 - 3/20*z**5 + 0*z**j + 0*z**2 - 6*z. Find d, given that l(d) = 0.
-1, 0, 1
Let h(t) = 3*t**3 + 11*t**2 - t - 5. Let c be h(-5). Let d be (-2)/8 - 65/c. Determine z, given that d*z**2 - 2/15*z + 2/15*z**4 - 2/5*z**3 + 0 = 0.
0, 1
Let k(j) be the second derivative of -3/20*j**5 - j**3 + 0*j**2 + 3/4*j**4 + 0 - 7*j. Determine n, given that k(n) = 0.
0, 1, 2
Let l(c) be the third derivative of c**5/100 + c**4/10 - 21*c**3/10 + 2*c**2 - 52. Factor l(s).
3*(s - 3)*(s + 7)/5
Let b(k) be the second derivative of k**5/300 - k**4/12 + 5*k**3/6 - 9*k**2 - 41*k. Let q(c) be the first derivative of b(c). Factor q(h).
(h - 5)**2/5
Let q(p) = -13*p**2 + 15*p + 2. Let v(m) = -224*m - 1 + 439*m - 220*m + 4*m**2. Let f(r) = -4*q(r) - 14*v(r). Find h, given that f(h) = 0.
-1/2, 3
Let d(m) = m + 1. Let c(y) = -9*y**2 - 13*y - 4. Let a = 3 + -9. Let l be (42/(-63))/((-2)/(-3)). Let z(h) = a*d(h) + l*c(h). Solve z(j) = 0 for j.
-1, 2/9
Let f(q) = -q**3 + 21*q**2 + 57*q + 57. Let t(r) = 2*r**3 - 62*r**2 - 170*r - 170. Let a = -38 + 41. Let j(n) = a*t(n) + 8*f(n). Factor j(h).
-2*(h + 3)**3
Suppose -7*b + b = -12. Factor -16*p**2 + 15*p**b - p + 2 + 2*p.
-(p - 2)*(p + 1)
Let h(m) be the first derivative of 3*m**4/16 - 3*m**2/8 - 86. Let h(f) = 0. What is f?
-1, 0, 1
Let h be ((-4)/6)/2*(24 + -78). Let d be 6/h*(-3 - 54/(-15)). Factor 0 - d*f - 1/5*f**2.
-f*(f + 1)/5
Let z(l) be the first derivative of l**5/90 - 2*l**4/27 + 5*l**3/27 - 2*l**2/9 - 22*l + 3. Let c(d) be the first derivative of z(d). Solve c(n) = 0 for n.
1, 2
Factor -33*h + 3*h**2 + 24*h + 4 + 8 - 6*h**2.
-3*(h - 1)*(h + 4)
Let f(q) be the second derivative of -q**5/300 + q**4/30 - q**3/10 + 13*q**2/2 - 4*q. Let x(j) be the first derivative of f(j). Factor x(p).
-(p - 3)*(p - 1)/5
Factor -12*s**2 + 40/3*s - 16/9 + 26/9*s**3.
2*(s - 2)**2*(13*s - 2)/9
Let r be 2/((-2016)/(-2700)) - 6/14. Determine q, given that -3/4*q**2 + r*q + 27/4 - 1/4*q**3 = 0.
-3, 3
What is c in 12 + 0*c**2 - 2*c**2 - 8*c**2 - 7*c**2 - 8*c**3 + 4*c**3 - c = 0?
-4, -1, 3/4
Let i = 15 + -18. Let a = i - -5. Let p(t) = 13*t**2 + 36*t + 54. Let l(n) = -4*n**2 - 12*n - 18. Let f(m) = a*p(m) + 7*l(m). Factor f(x).
-2*(x + 3)**2
Let p(w) be the second derivative of -w**4/4 - 3*w**3 - 15*w**2/2 + 31*w - 4. Factor p(x).
-3*(x + 1)*(x + 5)
Let 2/5*x**2 + 32/5 + 16/5*x = 0. Calculate x.
-4
Let h be 20/40*32/12. Determine z so that h*z**3 + 0 + 4/3*z**2 + 0*z = 0.
-1, 0
Let j(q) be the third derivative of 3*q**6/40 - q**5/20 - 4*q**4 + 22*q**3 + 37*q**2. Find g, given that j(g) = 0.
-11/3, 2
Let t(x) be the second derivative of -x**7/21 - 4*x**6/15 - 3*x**5/5 - 2*x**4/3 - x**3/3 + 5*x - 2. Factor t(y).
-2*y*(y + 1)**4
Factor g**5 - g**2 - 13/3*g**4 + 17/3*g**3 + 4/3 - 8/3*g.
(g - 2)*(g - 1)**3*(3*g + 2)/3
Let x(t) = -56*t**2 + 10*t + 115. Let g(h) = -26*h**2 + 4*h + 58. Let b(u) = -13*g(u) + 6*x(u). Let b(w) = 0. What is w?
-8, 4
Let g(h) be the third derivative of 0*h - 1/135*h**5 + 0 + 0*h**3 - 1/315*h**7 + 1/108*h**6 + 0*h**4 - 15*h**2. Solve g(c) = 0 for c.
0, 2/3, 1
Let t(p) be the second derivative of p**6/150 + 8*p**5/5 + 320*p**4/3 + 481*p. Find j, given that t(j) = 0.
-80, 0
Factor -15/8*a**3 + 3/2 - 3/8*a**2 + 15/2*a.
-3*(a - 2)*(a + 2)*(5*a + 1)/8
Factor 4/5*o**2 - 4/5 - 4/5*o + 4/5*o**3.
4*(o - 1)*(o + 1)**2/5
Let l(s) be the second derivative of -s**5 - 208*s**4/3 - 1414*s**3 + 1764*s**2 + 170*s. Solve l(u) = 0 for u.
-21, 2/5
Let g(h) be the third derivative of 0*h + 1/600*h**6 + 0 + 1/100*h**5 - 1/15*h**3 + 11*h**2 - 1/1050*h**7 - 1/120*h**4. Suppose g(t) = 0. What is t?
-1, 1, 2
Let m(u) be the second derivative of -3/35*u**5 - 3/4*u**4 - 5/14*u**3 + 25*u + 0 + 0*u**2. Determine n, given that m(n) = 0.
-5, -1/4, 0
Let g(k) be the third derivative of -k**7/350 + k**6/40 - 7*k**5/100 + 3*k**4/40 + 33*k**2 - 1. Solve g(v) = 0 for v.
0, 1, 3
Let u be ((-1228)/(-921))/(5/3 + -1). Let i be 2/3 + (-1)/3. Factor 0*y + i - 1/3*y**u.
-(y - 1)*(y + 1)/3
Let d be ((-2)/(48/9))/(-3). Let j = d - -7/72. Factor -2/9*v**4 + 0 - j*v**5 + 2/9*v**3 + 2/9*v**2 + 0*v.
-2*v**2*(v - 1)*(v + 1)**2/9
Factor 0*g**2 - 1/5*g**5 + 0*g**3 + 0*g + 0*g**4 + 0.
-g**5/5
Suppose -4*r - 4*w = 12, -2*r + 12 = 2*r - 4*w. Let s(z) be the second derivative of r*z**2 + 1/160*z**5 - 12*z - 1/48*z**4 + 0 + 0*z**3. Factor s(i).
i**2*(i - 2)/8
Suppose 2*z - 22 = h + 20, -5*h = -2*z + 50. Determine w, given that z - 18*w - 10 + 92*w**2 + 11 - 95*w**2 = 0.
-7, 1
Let y(u) be the first derivative of -u**6/150 + u**5/50 - u**4/60 - 10*u - 14. Let g(f) be the first derivative of y(f). Determine j, given that g(j) = 0.
0, 1
Factor -1/3*r**2 + 2/3*r + 5.
-(r - 5)*(r + 3)/3
Let a be ((-480)/(-189))/16*3. Let c(x) be the second derivative of -6*x + 0 + 4/7*x**2 + 2/21*x**4 + a*x**3. Let c(l) = 0. What is l?
-2, -1/2
Suppose -2 = -6*k + 7*k. Let x be (k + 3 - 2)*-2. Factor -105*t**2 + 100*t**x - 32 - 30*t - 13.
-5*(t + 3)**2
Let r(t) = -16*t - 7. Let m be r(-1). Suppose -m - 31 =