he third derivative of 20*d**2 + 0*d + 0 - 1/120*d**5 + 0*d**4 + 0*d**3. Find s, given that w(s) = 0.
0
Let t(d) be the third derivative of 0*d + 1/24*d**6 + 24*d**2 + 5/3*d**3 - 5/8*d**4 + 0 + 0*d**5. Factor t(y).
5*(y - 1)**2*(y + 2)
What is i in 2*i**3 - 10 - 37*i + i + 10 + 14*i**2 = 0?
-9, 0, 2
Suppose -2/5*q**2 - 2/5 - 4/5*q = 0. Calculate q.
-1
Suppose -18*a = -65 + 29. Let k(f) be the second derivative of 0*f**4 + 1/80*f**5 + 0*f**a + 0*f**3 - 6*f + 1/120*f**6 + 0. Suppose k(m) = 0. Calculate m.
-1, 0
Let 1/2*q + 11/2*q**2 - 1/2*q**3 - 11/2 = 0. What is q?
-1, 1, 11
Let c = 21 + -21. Let i be (c - -2*(-2)/8)*-4. Factor -2*m - 6*m**i - 3*m**4 - 13/2*m**3 + 0 - 1/2*m**5.
-m*(m + 1)**2*(m + 2)**2/2
Factor 2*g**5 - 6*g**3 + 4*g**2 - 2756*g**4 + 0*g**5 + 2756*g**4.
2*g**2*(g - 1)**2*(g + 2)
Suppose -4*i - 68 = -76. Find p, given that -5*p**5 - 24/5*p**3 + 0*p - 9*p**4 + 0 - 4/5*p**i = 0.
-1, -2/5, 0
Suppose 24*r - 29*r = 0. Suppose r = 4*y + 4*f - 20, -y - 2*f = -5 - 2. Let -12/5*k**y + 8/5*k**2 + 0*k + 0 = 0. Calculate k.
0, 2/3
Let v = -57 - -58. Let a be (3/2)/(v - 1/2). Factor 0*s**2 + 2/5*s - 2/5*s**a + 0.
-2*s*(s - 1)*(s + 1)/5
Let m(z) = 21*z - 84. Let p be m(4). Let j(q) be the first derivative of p*q + 3 + 1/3*q**3 + 0*q**2 - 5/12*q**6 - 9/8*q**4 + 6/5*q**5. Factor j(n).
-n**2*(n - 1)**2*(5*n - 2)/2
Let j(p) be the second derivative of -1/12*p**4 + 0 - 4/5*p**6 + 8/21*p**7 + 0*p**2 + 9/20*p**5 + 13*p + 0*p**3. Find v such that j(v) = 0.
0, 1/4, 1
Let h(k) be the third derivative of 0*k + 22*k**2 - 9/52*k**4 - 3/26*k**5 - 17/780*k**6 + 9/13*k**3 - 2/1365*k**7 + 0. Find p, given that h(p) = 0.
-3, 1/2
Let v(g) = g**5 - g - 1. Let a(l) = -l**5 + 3*l**4 - 9*l**3 + 5*l**2 + 2*l + 2. Let t(h) = -a(h) - 2*v(h). Factor t(x).
-x**2*(x - 1)**2*(x + 5)
Let g(c) be the third derivative of c**6/240 - 2*c**5/15 + 13*c**4/48 + 5*c**3/2 - 2*c**2 + 85*c. Determine z, given that g(z) = 0.
-1, 2, 15
Let z(d) be the third derivative of 1/330*d**5 + 0 - 3/11*d**3 + 0*d + 32*d**2 + 0*d**4. Factor z(i).
2*(i - 3)*(i + 3)/11
Let i(f) be the third derivative of -f**6/24 - 2*f**5 + 275*f**4/24 + 65*f**3 + 44*f**2 + 6*f. Factor i(m).
-5*(m - 3)*(m + 1)*(m + 26)
Suppose -84*b = -83*b - 8. Let w(r) be the second derivative of -3/10*r**5 + 0 + 3/4*r**4 + 0*r**2 - 1/2*r**3 + b*r. Solve w(m) = 0 for m.
0, 1/2, 1
Let z(n) be the first derivative of -9*n**4 - 140*n**3 - 134*n**2 - 44*n + 866. Factor z(v).
-4*(v + 11)*(3*v + 1)**2
Factor -2/9*q**2 + 20/3 - 14/9*q.
-2*(q - 3)*(q + 10)/9
Factor -38/5*d**4 - 102/5*d**2 + 4/5 + 26/5*d + 22*d**3.
-2*(d - 1)**3*(19*d + 2)/5
Let -1/5*q**3 - 8/5*q**2 + 0 + 4*q = 0. What is q?
-10, 0, 2
Suppose 83 + 37 = 15*f. Let q(y) = y**3 - 7*y**2 - 9*y + 12. Let g be q(f). Suppose 4*p**4 - 4/3*p**5 + 4/3*p**2 - g*p**3 + 0 + 0*p = 0. What is p?
0, 1
Factor 25*a**2 + 9 + 2*a - 28*a**2 + 4*a.
-3*(a - 3)*(a + 1)
Factor 14/3*r**2 + 0 - 4*r - 4/9*r**3 - 2/9*r**4.
-2*r*(r - 3)*(r - 1)*(r + 6)/9
Suppose 2/11*c**3 - 56/11*c + 10/11*c**4 + 0 - 64/11*c**2 = 0. Calculate c.
-2, -1, 0, 14/5
Let m(p) = -p + 10. Let z be m(7). Find n such that -3*n + 51*n**3 + 3*n - 46*n**z - 5*n**4 = 0.
0, 1
Let d(b) be the third derivative of -b**5/12 - 15*b**4/8 - 20*b**3/3 - 5*b**2 - 2. Determine n, given that d(n) = 0.
-8, -1
Let p(z) be the third derivative of -z**6/840 - z**5/28 - 25*z**4/56 - z**3/6 + 12*z**2. Let w(g) be the first derivative of p(g). What is k in w(k) = 0?
-5
Factor -2/9*h**3 - 26/9*h**2 - 94/9*h - 70/9.
-2*(h + 1)*(h + 5)*(h + 7)/9
Let t(v) = 4*v**3 - 72*v**2 + 312*v - 314. Let o(j) = -6*j**3 + 72*j**2 - 312*j + 312. Let s(d) = -3*o(d) - 4*t(d). Factor s(b).
2*(b - 2)**2*(b + 40)
Let b(j) be the first derivative of 0*j + 1/8*j**4 + 1/10*j**5 - 1 - 1/4*j**2 - 1/6*j**3. Factor b(l).
l*(l - 1)*(l + 1)**2/2
Solve -25*z**3 + 5*z**2 + 10*z**2 + 280*z + 50*z**2 + 100 = 0.
-2, -2/5, 5
Let i = 40427/3 + -13469. Factor -50/3 + i*z - 2/3*z**2.
-2*(z - 5)**2/3
What is s in -5*s**3 + 0*s**2 + 10*s**2 - 3*s**2 - s**2 - 8*s**4 - 8*s**3 = 0?
-2, 0, 3/8
Factor -1/3*u**4 + 144 + 72*u - 63*u**2 + 26/3*u**3.
-(u - 12)**2*(u - 3)*(u + 1)/3
Let b(j) = -5*j**4 - 18*j**3 + 2*j**2 + 18*j + 3. Let t(d) = d**3 + d**2 - d - 1. Let k(f) = b(f) + 3*t(f). Solve k(l) = 0 for l.
-3, -1, 0, 1
Suppose -14*k + 2*k - 60 = 0. Let s be k + 104/16 - (1 + 0). Determine t so that 1/2*t**2 + 0 + s*t**3 - t = 0.
-2, 0, 1
Let j be -1 + -4 + (-40)/(-4). Determine a so that -2*a**2 - 3 - 4*a + a + j*a**2 - a**3 + 4*a**3 = 0.
-1, 1
Let w be (9/9)/(10/(-6) + 2). Let o = 242/57 - -8/19. Factor -11/3*b**2 + 5/6*b**w - 4/3 + o*b.
(b - 2)**2*(5*b - 2)/6
Let k = 11 - 6. Suppose -22 = -k*q - 4*u, 4*u = -3*q - 0*q + 18. Find o such that 4*o**3 + 0*o**4 + 4*o**4 - 2*o**5 - q*o**3 - 2*o**2 - 2*o**2 = 0.
-1, 0, 1, 2
Let z(h) be the first derivative of -2*h**3/15 - 19*h**2/5 - 36*h/5 + 191. Factor z(a).
-2*(a + 1)*(a + 18)/5
Let y be ((-276)/(-322))/(1 - (-38)/(-42)). Let p(z) be the first derivative of y - 15/4*z**4 - 5/4*z**5 - 5/4*z**2 + 0*z - 15/4*z**3. What is f in p(f) = 0?
-1, -2/5, 0
What is i in 1/2*i**2 - 31*i + 961/2 = 0?
31
Suppose 4*u - 2*g - 78 = 0, -5*u + 0*g - 2*g + 111 = 0. Suppose 21*v**2 - 6*v**3 + u*v + 15*v**3 - 5*v + 4 = 0. Calculate v.
-1, -2/3
Determine t so that 4/7*t - 10/7*t**2 - 2/7*t**4 + 0 + 8/7*t**3 = 0.
0, 1, 2
Factor 129*l**4 - 5*l**2 + 0*l**2 + 2*l**2 - 33*l**5 - 9*l**2 - 120*l**3.
-3*l**2*(l - 2)**2*(11*l + 1)
Let y(l) be the first derivative of 0*l - 13 + 2/5*l**2 - 2/15*l**3 - 1/10*l**4. Find c such that y(c) = 0.
-2, 0, 1
Let m(b) be the third derivative of -b**5/20 + 93*b**4/8 + 47*b**3 - 2*b**2 + 119*b. Suppose m(s) = 0. Calculate s.
-1, 94
Suppose 13*d + 136 = 17*d. Let w be -4*((-35)/d + 1). Factor 4/17*a - 2/17 - w*a**2.
-2*(a - 1)**2/17
Solve -48*x - 64*x**3 + 10*x**4 + 393*x**2 - 289*x**2 + 16*x = 0 for x.
0, 2/5, 2, 4
Let n = 0 - -1. Let k be n/(1/(-2) + 1). Factor 9*b**2 + 7*b + 3*b**3 + 2*b + 5 - k.
3*(b + 1)**3
Let t(q) be the first derivative of q**6/360 + q**5/40 - 5*q**4/12 + 32*q**3/3 + 18. Let c(u) be the third derivative of t(u). Suppose c(x) = 0. Calculate x.
-5, 2
Let f(t) be the third derivative of 0*t - 28*t**2 + 0 + 1/24*t**4 + 1/945*t**7 + 1/120*t**6 + 7/270*t**5 + 1/27*t**3. Factor f(x).
(x + 1)**2*(x + 2)*(2*x + 1)/9
Suppose -10 = -n - 5*a + 6*a, -6 = -3*a. Let l be (n/195)/(-1*2/(-10)). Factor 0 + l*q - 2/13*q**2.
-2*q*(q - 2)/13
Let h = 28 - 26. Suppose h*y = -0 + 12. Factor -4*d + 1 + 2*d**3 + 2*d - 7 + y*d**2.
2*(d - 1)*(d + 1)*(d + 3)
Let o(w) = -2*w**3 - 36*w**2 - 162*w - 8. Let a(p) = 2*p**3 + 36*p**2 + 162*p + 10. Let j(s) = -8*a(s) - 10*o(s). Factor j(f).
4*f*(f + 9)**2
Let n(k) be the third derivative of k**6/30 + k**5/15 - k**4/24 - k**3/6 + 72*k**2. Determine t so that n(t) = 0.
-1, -1/2, 1/2
Let d(q) be the third derivative of 3/160*q**6 + 4*q**2 - 1/48*q**4 + 1/48*q**5 + 0 + 0*q + 0*q**3 - 1/168*q**7 - 1/192*q**8. Solve d(g) = 0.
-1, 0, 2/7, 1
Let p(l) = 23*l**2 + 69*l. Let f be p(-3). Let g(a) be the second derivative of -3*a + 0 - 1/24*a**4 + f*a**2 + 0*a**3 - 1/40*a**5. Factor g(n).
-n**2*(n + 1)/2
Factor -33/2*l**2 + 51/4*l - 15/4*l**3 + 15/2.
-3*(l - 1)*(l + 5)*(5*l + 2)/4
Let p be ((-1)/(-4))/(46 + 9924/(-216)). Let i = 4 + -1. Let i*d**2 + 0*d + 0 + 3/2*d**4 + p*d**3 = 0. Calculate d.
-2, -1, 0
Let o(a) be the third derivative of a**7/1260 - a**6/60 - a**5/360 + a**4/12 + 54*a**2. Factor o(g).
g*(g - 12)*(g - 1)*(g + 1)/6
Let l = 200/17 + -532/51. Let r(q) be the second derivative of 0 - 7/5*q**4 - 6*q - 8/15*q**2 + 49/150*q**5 + l*q**3. What is t in r(t) = 0?
2/7, 2
Let v(w) be the second derivative of 0*w**2 + 1/28*w**7 + 3/8*w**4 - 3/20*w**6 + 3/40*w**5 - 1/2*w**3 + 0 - 4*w. Determine o, given that v(o) = 0.
-1, 0, 1, 2
Let q(m) be the second derivative of 200*m**4/9 - 20*m**3/3 + 3*m**2/4 + m + 351. Factor q(g).
(40*g - 3)**2/6
Let u(b) be the third derivative of b**6/72 + b**5/6 + 5*b**4/8 - 5*b**3/6 + 4*b**2. Let t(f) be the first derivative of u(f). Factor t(a).
5*(a + 1)*(a + 3)
Solve 0*y + 200/11*y**2 - 2/11*y**5 - 160/11*y**3 + 0 - 38/11*y**4 = 0.
-10, 0, 1
Let f(b) be the second derivative of 2*b**7/21 - b**5/5 + 48*b. Factor f(t).
4*t**3*(t - 1)*(t + 1)
Let n(m) = -21*m**4 - 8*m**3 + 11*m**2 + 8*m - 1