/2 - 8*k + 25. Let i(y) be the first derivative of v(y). Factor i(n).
-3*(n - 1)**2*(n + 1)
Let a(g) = 9*g**4 + 99*g**3 + 18*g**2 - 4*g + 2. Let m(r) = r**4 + 2*r**2 - 2*r + 1. Let s(t) = -2*a(t) + 4*m(t). Determine h so that s(h) = 0.
-14, -1/7, 0
Let h be ((-46)/10 - 4) + 70 + -61. What is n in -2 - h*n**3 + 18/5*n - 6/5*n**2 = 0?
-5, 1
Let d(c) = -4*c**5 + c**4 + c**3 + c**2 + c - 2. Let l(a) = -25*a**5 + 14*a**4 + 2*a**3 - 20*a**2 + 43*a - 26. Let g(t) = 30*d(t) - 5*l(t). Factor g(v).
5*(v - 7)*(v - 1)**3*(v + 2)
Let l(q) = 6*q**3 - 59*q**2 + 190*q - 52. Let b(t) = -5*t**3 + 58*t**2 - 173*t + 52. Let h(f) = -5*b(f) - 4*l(f). Let h(c) = 0. What is c?
1, 52
Let b be -1*(-7 + (-20)/(-4)). Let -845 - 5*t**b + 143*t + 0*t**2 - 13*t = 0. What is t?
13
Suppose p - 4*w - 20 = -0*p, 49 = 3*p - w. Suppose 13 = 4*m - 5*m - 5*c, 2*m = 4*c + p. Factor 2*b + b**2 + 5*b + 3*b**m - 3*b.
4*b*(b + 1)
Let b(n) be the second derivative of n**8/16800 - n**6/600 - n**5/150 + 31*n**4/6 - 2*n - 40. Let w(g) be the third derivative of b(g). Factor w(u).
2*(u - 2)*(u + 1)**2/5
Let l(f) be the first derivative of -f**5/360 - f**4/9 - 5*f**3/12 - 53*f**2/2 - f + 29. Let d(h) be the second derivative of l(h). Let d(m) = 0. What is m?
-15, -1
Let s(w) be the third derivative of 2/735*w**7 + 2/105*w**5 - 2*w + 0*w**3 - 3/140*w**6 + 0 + 0*w**4 - 2*w**2. Factor s(t).
2*t**2*(t - 4)*(2*t - 1)/7
Let t be (6/(3 + -5))/(4/(-4)). Factor -t + 0*y - 6*y**2 + 8*y - 2*y + 1 + 2*y**3.
2*(y - 1)**3
Suppose -3*r + 62*g - 166 = 64*g, 3*g = -3*r - 165. Let i be 5/r - (4 + 455/(-104)). Factor -1/7*p + i - 1/7*p**2.
-(p - 1)*(p + 2)/7
Let q(a) = -3*a**3 + 2*a**2 + a + 2. Let g = -5 - -8. Let o(l) = 4*l**3 - 3*l**2 - l - 3. Suppose -43*c = -36*c - 14. Let v(x) = c*o(x) + g*q(x). Factor v(u).
-u*(u - 1)*(u + 1)
Factor 12/5*n**2 + 3/5*n**3 + 0 - 3*n.
3*n*(n - 1)*(n + 5)/5
Let l(z) be the first derivative of z**6/39 - 4*z**5/13 - 9*z**4/13 + 216*z**3/13 - 783*z**2/13 + 972*z/13 - 2150. Suppose l(h) = 0. Calculate h.
-6, 1, 3, 9
Let b(g) be the third derivative of g**5/60 - 19*g**4/8 + 175*g**3/3 + 52*g**2 + 12. Solve b(j) = 0 for j.
7, 50
Let p(k) be the second derivative of 4/45*k**6 + 11/30*k**5 + 0*k**2 - 1/63*k**7 + 0 + 95*k + 0*k**3 + 1/3*k**4. Factor p(s).
-2*s**2*(s - 6)*(s + 1)**2/3
Let t(x) be the first derivative of -53 + 3/2*x**2 + 0*x**4 - 2*x**3 + 0*x + 6/5*x**5 - 1/2*x**6. Factor t(n).
-3*n*(n - 1)**3*(n + 1)
Let f(o) be the third derivative of o**5/390 + 45*o**4 + 315900*o**3 - 4*o**2 - 9*o + 1. Suppose f(p) = 0. Calculate p.
-3510
Let z(i) be the first derivative of -i**4 - 464*i**3/3 - 5978*i**2 + 89304*i - 2332. Determine s so that z(s) = 0.
-61, 6
Let j be 2*135/(-9) - (2 + -6). Let q be (-183)/(-78) + (-4)/j. Find u, given that 3/2*u + 1/2*u**3 - q*u**2 + 9/2 = 0.
-1, 3
Suppose -2*t + 5 = -7. Suppose -k - 3 = -4*h - h, t = k + 4*h. Solve -3*r**k - 5 - r + 4*r - 12*r - 1 = 0.
-2, -1
Suppose -16*a - 6563 = -6675. Let t(v) be the third derivative of 0*v - 1/10*v**4 - 1/50*v**6 - 1/350*v**a + 0 - 3/50*v**5 + 19*v**2 - 1/10*v**3. Factor t(u).
-3*(u + 1)**4/5
Let m = 12 + -4. Determine i, given that -16 - 12*i**2 - 36*i - 6 - m*i**2 + 6 - 3*i**3 = 0.
-4, -2, -2/3
Let a(l) = 10*l**3 + 16*l**2 - 38*l. Let i = -555 + 549. Let x(y) = 14*y**3 + 17*y**2 - 39*y. Let p(f) = i*a(f) + 4*x(f). Solve p(n) = 0.
-9, 0, 2
Suppose 1/3*i**2 - 49/3*i - 90 = 0. Calculate i.
-5, 54
Suppose 162 = -44*z - 102. Let w be ((-20)/z)/(5/3). Find h, given that 0*h + 0*h**w + 0 - 4/7*h**4 + 8/7*h**3 = 0.
0, 2
Factor 2293/5*r + 1146/5 + 1/5*r**3 + 1148/5*r**2.
(r + 1)**2*(r + 1146)/5
Let i(q) be the third derivative of q**7/105 - 4*q**6/15 + 3*q**5 - 50*q**4/3 + 125*q**3/3 + 31*q**2 - 16*q. Factor i(v).
2*(v - 5)**3*(v - 1)
Let h be (-10)/45 + 46/45. Let w(u) = 1708*u - 13661. Let g be w(8). Factor 0 - h*d**2 - 8/5*d + 2/5*d**g + 1/5*d**4.
d*(d - 2)*(d + 2)**2/5
Let q(p) be the second derivative of p**4/30 - 4988*p**3/15 + 6220036*p**2/5 + p + 2583. Solve q(l) = 0.
2494
Suppose 2847 - 19534 = 41*d. Let i = 2048/5 + d. Factor 1/5*y**2 + 12/5 - i*y.
(y - 12)*(y - 1)/5
Let t(k) be the second derivative of -2*k**6/15 - 5*k**5 - 200*k**4/3 - 1000*k**3/3 - 200*k. Factor t(v).
-4*v*(v + 5)*(v + 10)**2
Let r(p) be the first derivative of -6*p**2 + 27 + 3*p**4 - 4/5*p**5 - 4/3*p**3 + 8*p. Solve r(v) = 0 for v.
-1, 1, 2
Let m be 54/(-15)*(-335)/2211 - 16/110. Factor 0 + 8/5*q**2 + 8/5*q + m*q**3.
2*q*(q + 2)**2/5
Let a(p) be the first derivative of 87 + 22/7*p**2 + 10/21*p**3 + 16/7*p. Factor a(j).
2*(j + 4)*(5*j + 2)/7
Let l(a) = 4 - 17 + 9 + 7 + 2*a. Let x be l(6). Factor -5*k - 20*k**4 + 0*k**2 - 15*k**3 - x*k**3 - 5*k**5 - 20*k**2.
-5*k*(k + 1)**4
Let h be (3600/5152 - (-6)/4) + 4/46. Factor 0 - 2/7*a**2 + h*a.
-2*a*(a - 8)/7
Let l = -22919/24 + 955. Let f(p) be the first derivative of -1/20*p**5 - 7 + 1/12*p**3 + 3/16*p**4 - l*p**6 - 1/4*p**2 + 0*p. Find y such that f(y) = 0.
-2, -1, 0, 1
Suppose -7*t + t = 0. Suppose -u + 4 + t = 0. Factor -2*l**4 - u*l**5 + l - 3*l**5 + 6*l**5 + 2*l**2.
-l*(l - 1)*(l + 1)**3
Let a be -38 + (-5617)/3157*-22. Factor 0 - 22/7*w**3 + a*w**4 + 24/7*w**2 - 9/7*w - 1/7*w**5.
-w*(w - 3)**2*(w - 1)**2/7
Factor 0*x - 30*x**3 + 0 - 201/2*x**4 + 0*x**2 - 93/4*x**5.
-3*x**3*(x + 4)*(31*x + 10)/4
Suppose 42 = -0*y + 6*y. Suppose -x = -2*q + 3*q - y, -3*x = 5*q - 27. Let 120*c + 4*c**3 + 276*c**2 - 231*c**2 + 2*c**3 + 80 - c**q = 0. Calculate c.
-4, -1
Let w(r) be the first derivative of -2*r**3/27 + 19*r**2/3 - 424*r/9 - 2805. Determine c so that w(c) = 0.
4, 53
Let t(v) be the first derivative of v**3/15 - 394*v**2/5 - 789*v/5 + 2360. Let t(z) = 0. Calculate z.
-1, 789
Let p be 1 + -2 + (-532)/(-5). Let b = p - 2083/20. Factor -2*q - 1/4*q**3 + 1 + b*q**2.
-(q - 2)**2*(q - 1)/4
Let i(f) be the third derivative of f**6/240 + 11*f**5/24 - 29*f**4/24 - 28*f**3/3 - 2*f**2 + 1640. Factor i(a).
(a - 2)*(a + 1)*(a + 56)/2
Let c(k) be the third derivative of k**6/24 + 29*k**5/45 - k**4/2 - 16*k**3/9 - 1672*k**2. Suppose c(i) = 0. What is i?
-8, -2/5, 2/3
Let d(b) = 4*b**3 - 21*b**2 + 69*b - 56. Let p(a) = -5*a**3 + 22*a**2 - 72*a + 56. Let u(r) = -4*d(r) - 3*p(r). Factor u(o).
-(o - 14)*(o - 2)**2
Factor 8*z - 24 + 15*z**2 - 17*z**2 + 18*z + 17*z**2.
(3*z - 2)*(5*z + 12)
Let o = 21 - 21. Suppose -2*y - v + 13 = o, -5 = -4*y + 3*v + 2*v. Factor 54*s**4 - 15*s**2 - 57*s**4 - 2*s - 11*s**3 + 20*s - y*s**3.
-s*(s + 3)**2*(3*s - 2)
Let y(x) be the second derivative of -x**4/12 + 157*x**3/3 - 24649*x**2/2 + 38*x + 5. Factor y(t).
-(t - 157)**2
Let y(h) = -11*h**2 - 69*h + 276. Let g(l) = 3*l**2 - 4. Let o(q) = -4*g(q) - y(q). Factor o(b).
-(b - 65)*(b - 4)
Let j(t) be the third derivative of -t**6/420 + 8*t**5/105 - 11*t**4/12 + 14*t**3/3 + 4*t**2 - 14*t - 4. Determine q, given that j(q) = 0.
2, 7
Let f(x) be the second derivative of 100/3*x**3 + 0 - 5/12*x**4 - 190*x**2 + 80*x. Factor f(j).
-5*(j - 38)*(j - 2)
Let r(p) be the second derivative of -2/39*p**3 + 0*p**2 + 105*p + 0*p**5 - 1/195*p**6 + 0 + 1/26*p**4. Factor r(l).
-2*l*(l - 1)**2*(l + 2)/13
Suppose -5 = 5*t + 5*a, 8*t - a = 11*t + 13. Let m(n) = 2*n**2 + 0*n**2 - 5*n**2 - 13*n. Let j(g) = g**2 + 4*g. Let r(w) = t*m(w) - 21*j(w). Factor r(l).
-3*l*(l + 2)
Suppose -6*f + 3*y = 8*y - 33, -3*y + 12 = f. Let s(a) = -a**3 + a**2 + a + 3. Let m be s(0). Factor -26 + 2 + 9 + m*z**4 - 9*z**2 - f*z**3 + 15*z + 9.
3*(z - 1)**3*(z + 2)
Let p(u) be the first derivative of 5*u**4/4 - 25*u**3 + 195*u**2/2 + 275*u - 3717. Suppose p(v) = 0. Calculate v.
-1, 5, 11
Let l(p) = -p**2 - 11*p + 30. Let j be l(2). Let n(m) be the first derivative of -1/4*m**j - m**2 - 9 + m**3 + 0*m. Find h, given that n(h) = 0.
0, 1, 2
Suppose 0 = q + 5*v - 11 - 2, -4*q + 10 = -v. Suppose n + q*n - 56 = 0. Find y such that -10*y**2 + n*y**3 + 7 + 3 - 4*y - 10 = 0.
-2/7, 0, 1
Let v(h) be the first derivative of 3*h**4/20 + 248*h**3/5 + 4758*h**2 + 178608*h/5 + 2912. Solve v(z) = 0 for z.
-122, -4
Let a(d) be the second derivative of -5*d**4/6 - 422*d**3/3 - 168*d**2 + 1268*d + 2. Determine s, given that a(s) = 0.
-84, -2/5
Let z(g) be the first derivative of -51/11*g**2 - 15/2*g**4 - 126/55*g**5 - 12/11*g - 98/11*g**3 - 70. Suppose z(l) = 0. What is l?
-1, -1/3, -2/7
Let h(u) 