y. Let v(n) be the third derivative of a(n). Factor v(k).
-k**3*(k - 1)*(k + 1)/2
Let j(x) be the second derivative of x**8/1176 - x**6/210 + x**4/84 + x**2/2 + 3*x. Let a(h) be the first derivative of j(h). Solve a(y) = 0.
-1, 0, 1
Suppose -1/3*m**2 + 10/3*m - 3 = 0. Calculate m.
1, 9
Let r(d) be the first derivative of d**7/105 + 2*d**6/75 + d**5/50 + d + 5. Let p(q) be the first derivative of r(q). Determine j so that p(j) = 0.
-1, 0
Let x be 3 - 4*(-2)/(-4). Let p(r) = 6*r**3 + 10*r**2 + 6*r. Let s(m) = m**2 + m. Let a(n) = x*p(n) - 6*s(n). Find t, given that a(t) = 0.
-2/3, 0
Let n(d) be the first derivative of 0*d**3 + d**2 - 1/5*d**5 + d + 1 - 1/2*d**4. Factor n(r).
-(r - 1)*(r + 1)**3
Let s be (-8)/(-5) - 6/(-15). Let k(n) be the first derivative of 0*n**s + 0*n - 1/4*n**4 + 1/5*n**5 - 1 + 0*n**3. Factor k(r).
r**3*(r - 1)
Let z(p) be the third derivative of -1/1050*p**7 - 1/600*p**6 + 0 + 0*p**3 + 1/300*p**5 + 0*p + 1/120*p**4 - 5*p**2. Determine n so that z(n) = 0.
-1, 0, 1
Let x(a) = -a**2 - 25*a - 97. Let l be x(-20). Factor 9/2*v**3 - l*v**4 - 3/2*v**5 - 6*v + 0 + 6*v**2.
-3*v*(v - 1)**2*(v + 2)**2/2
Determine s so that 0*s + s**3 - s - s**2 + 2*s**2 - 1 + 0*s**2 = 0.
-1, 1
Factor 5*n + 16*n + 4*n**3 + 2 - 10*n + 18*n**2 - 8*n**4.
-(n - 2)*(2*n + 1)**3
Let s(u) be the third derivative of 0*u + 4/105*u**7 + 0 + 0*u**3 + 0*u**4 - 1/75*u**5 + 4*u**2 + 1/100*u**6. Factor s(o).
2*o**2*(4*o - 1)*(5*o + 2)/5
Let g(f) = f + 13. Let u be g(-9). Suppose 2*r + 1 + 7 = u*b, b + 2*r - 7 = 0. Solve 0*m**b - 2/3*m**5 + 0*m**2 + 0 + 2/3*m**4 + 0*m = 0.
0, 1
Let c(o) = 3*o**2 - o**3 - o + 0*o**2 - 12*o**3 - 7*o. Let x(m) = m**3 + m. Let g(y) = -2*c(y) - 18*x(y). What is t in g(t) = 0?
-1/4, 0, 1
Let z(h) be the second derivative of 5*h**7/168 + 11*h**6/60 + 33*h**5/80 + 5*h**4/12 + h**3/6 + 46*h - 2. Solve z(x) = 0 for x.
-2, -1, -2/5, 0
Let b = -22 + 24. Let l(c) be the first derivative of -1/9*c**3 - 1/12*c**4 - 2 + 1/6*c**b + 1/3*c. Factor l(j).
-(j - 1)*(j + 1)**2/3
Suppose -4 = z - 8. Factor -l**2 - 2*l**3 - z*l**2 + 2*l + 5*l**2.
-2*l*(l - 1)*(l + 1)
Let b be (-3)/(-4) - 2/(-8). Let 4*s + s - 4*s - 3*s - b - s**2 = 0. Calculate s.
-1
Let t be 0 - -1*(-2 + 7). Determine k so that k**5 - k - k**2 - t*k**3 + k**3 + 4*k + 2 - k**2 = 0.
-1, 1, 2
Let d(p) be the third derivative of -p**5/120 - p**4/24 - 4*p**2. Factor d(x).
-x*(x + 2)/2
Suppose -3*y + 31 = 7. Suppose 14 = 2*w - y. Factor 2*z**5 + 2*z**2 + 11*z - w*z - 2*z**3 - 2*z**4.
2*z**2*(z - 1)**2*(z + 1)
Let w(h) be the first derivative of -h**3/15 - h**2 - 5*h - 3. Determine r, given that w(r) = 0.
-5
Let y be 108/(-135) + (0 - -1). Solve -1/5*r**2 + 1/5*r**4 - y*r**3 + 1/5*r + 0 = 0 for r.
-1, 0, 1
What is k in -15/7*k**3 - 24/7 + 54/7*k**2 - 36/7*k = 0?
-2/5, 2
Let f(k) be the third derivative of 0 + 0*k - 1/16*k**4 - 5*k**2 - 1/120*k**5 - 1/6*k**3. Factor f(m).
-(m + 1)*(m + 2)/2
Let y(o) be the second derivative of 3*o - 2/21*o**3 - 1/210*o**5 + 1/28*o**4 + 0 - o**2. Let t(p) be the first derivative of y(p). Factor t(z).
-2*(z - 2)*(z - 1)/7
Let r(d) = 2*d**2. Let q be r(1). Factor -4*g**2 - g - 19*g - 7*g**3 - 8 + 30*g**q.
-(g - 2)**2*(7*g + 2)
Let z be -17 + 16 - 1/(1/(-3)). Solve 0*r - 1/4*r**z + 1/4 = 0 for r.
-1, 1
Let l(q) = -2*q - 16. Let m be l(-9). Let n(h) be the first derivative of -9/10*h**5 + 0*h + 0*h**m - 1 + 3/4*h**4 - 1/6*h**3. Suppose n(y) = 0. Calculate y.
0, 1/3
Let z be (-69)/115*1/((-27)/60). Suppose 2*i - z - 2/3*i**2 = 0. Calculate i.
1, 2
Let c(h) be the first derivative of 1 + 0*h - 2/3*h**3 + h**2. Find f, given that c(f) = 0.
0, 1
Let j be (6/(-8))/(27/(-72)). Let z be j - 5/(60/16). Determine u so that 0 + 0*u - 2/3*u**2 + z*u**3 - 2/3*u**5 + 2/3*u**4 = 0.
-1, 0, 1
Let b be (-4)/14 + (-69)/(-21). Let y(p) be the third derivative of 1/60*p**4 + p**2 + 1/30*p**b + 0*p + 1/300*p**5 + 0. Factor y(m).
(m + 1)**2/5
Let h(w) = 25*w**2 + 45*w + 20. Let k(m) = m**2 + 1. Let n(o) = -h(o) + 20*k(o). Factor n(j).
-5*j*(j + 9)
Factor 2/7*q**4 + 0*q + 0*q**2 + 2/7*q**3 + 0.
2*q**3*(q + 1)/7
Let b = 2 + 1. Factor 2*k - 3*k + 3*k - b*k**3 + k**3.
-2*k*(k - 1)*(k + 1)
Let t = -4 - 2. Let o be (-1 - -3) + t/12. What is m in o*m**3 - 7/2*m**2 - 5/2*m**5 + 0 + 7/2*m**4 + m = 0?
-1, 0, 2/5, 1
Suppose 0 = -w + y + 4, 3*y = -w + 7*y - 11. Suppose -10*o = -w*o - 4. Determine i, given that -1/3*i**o - 4/3*i**5 - 4/3*i + 8/3*i**3 + 2/3*i**2 - 1/3 = 0.
-1, -1/4, 1
Suppose 0 = -11*i + 7 + 15. Let 0 + 1/4*b**i - 1/2*b + 1/2*b**3 - 1/4*b**4 = 0. What is b?
-1, 0, 1, 2
Let u(l) be the third derivative of 0 + 4*l**2 - 9/40*l**6 + 0*l**3 + 0*l + 3/10*l**5 - 1/8*l**4 + 2/35*l**7. Factor u(f).
3*f*(f - 1)**2*(4*f - 1)
Let h(b) be the third derivative of -b**6/60 - b**5/15 - 24*b**2. Suppose h(a) = 0. What is a?
-2, 0
Let p = 516708445/339 - 1524209. Let b = p - 4/113. Determine t so that -22*t - 94/3*t**3 + b*t**4 - 12 + 182/3*t**2 = 0.
-2/7, 1, 3
Determine p, given that -2/3*p**3 + 2/3*p + 2/9*p**4 + 2/9*p**2 - 4/9 = 0.
-1, 1, 2
Let x be -2 + 0 - (-4 - 2). Let z = x + -4. Suppose 1/2*j**2 + 0 + 1/2*j**3 + z*j = 0. Calculate j.
-1, 0
Let j be 4 - (-14 + 10 - -2*4). Factor j + 0*v + 1/2*v**3 - v**2.
v**2*(v - 2)/2
What is k in -2/13*k**2 + 6/13*k + 0 = 0?
0, 3
Let s(c) be the first derivative of 5/8*c**2 - 1/2*c - 1/3*c**3 + 3 + 1/16*c**4. Let s(p) = 0. Calculate p.
1, 2
Let l(q) be the second derivative of 0 + 1/8*q**3 + 3*q - 5/168*q**7 - 1/6*q**4 - 11/40*q**5 + 1/4*q**2 - 3/20*q**6. Find h, given that l(h) = 0.
-1, 2/5
Let g be 5 + -4 + (-1 - -2). Let c be -1*3/((-42)/8). Factor 6/7*t**g + 0 - c*t.
2*t*(3*t - 2)/7
Factor 1/5*l - 1/10*l**2 - 1/10.
-(l - 1)**2/10
Let z(n) = -n**2 + 6*n - 6. Let l be z(3). Let s(m) be the second derivative of 0 - 1/12*m**l + 1/120*m**6 - 1/8*m**2 - 2*m + 0*m**4 + 1/40*m**5. Factor s(i).
(i - 1)*(i + 1)**3/4
Suppose g = -4*l - 17 - 1, 2*l = 5*g + 2. Let x be g/8 - (-17)/4. Let 0*n + 0 - 2/3*n**x + 2/3*n**3 + 0*n**2 = 0. Calculate n.
0, 1
Let k(x) be the second derivative of x**5/30 + x**4/9 - x**3/9 - 2*x**2/3 - 22*x. Factor k(z).
2*(z - 1)*(z + 1)*(z + 2)/3
Factor 1/4*i**4 - i**3 - 1/2*i + 0 + 5/4*i**2.
i*(i - 2)*(i - 1)**2/4
Factor -8/3*b**2 - 10/3 + 1/3*b**3 - 19/3*b.
(b - 10)*(b + 1)**2/3
Let s = 2 - 2. Suppose s*m + 3 = m. Factor 0*o**2 + 0 + 0*o**m + 1/2*o**4 + 0*o + 1/4*o**5.
o**4*(o + 2)/4
Let k be 4/(-22) - 24/(-11). Determine x, given that -x**4 - 6*x**k + 9*x**4 - x**3 + x - 2*x**4 = 0.
-1, 0, 1/6, 1
Let k(h) be the second derivative of h**6/105 - h**5/14 + h**4/14 + 3*h**3/7 - 2*h. Factor k(g).
2*g*(g - 3)**2*(g + 1)/7
Let n = 7/9 + -5/9. Factor n*w**2 - 4/9*w + 2/9.
2*(w - 1)**2/9
Let t = 641/7 - 91. Factor -2*w**3 - t*w**2 + 0 + 0*w - 6/7*w**4.
-2*w**2*(w + 2)*(3*w + 1)/7
Factor -4*z**3 - 7*z**4 - 3*z + 3*z + 11*z**4.
4*z**3*(z - 1)
Let h(r) be the first derivative of -9*r**4/4 + 7*r**3/3 + 13*r**2/2 - 7*r + 6. Let m(j) = 9*j**3 - 6*j**2 - 12*j + 6. Let p(s) = -3*h(s) - 4*m(s). Factor p(y).
-3*(y - 1)*(y + 1)*(3*y - 1)
Factor 1/11*a**4 + 6/11 + 5/11*a**3 - 5/11*a - 7/11*a**2.
(a - 1)**2*(a + 1)*(a + 6)/11
Let i(p) = -3*p**2 - 17*p - 12. Let h(v) = -3*v**2 - 18*v - 12. Let q(b) = -5*h(b) + 6*i(b). Factor q(g).
-3*(g + 2)**2
Suppose -3*m = 2*v + 9, m - 15 = -5*v + 6*m. Let p(u) be the first derivative of v*u - 2/9*u**3 + 1 + 0*u**2 - 2/15*u**5 + 1/3*u**4. Solve p(r) = 0 for r.
0, 1
Let l(t) be the first derivative of 21*t**5/20 + 57*t**4/16 - 3*t**3/2 - 60. Determine p so that l(p) = 0.
-3, 0, 2/7
Let n(l) be the first derivative of 2 + 6/5*l**5 + 0*l + 1/6*l**6 + 2*l**2 + 13/4*l**4 + 4*l**3. Factor n(q).
q*(q + 1)**2*(q + 2)**2
Let m(c) = c**2 + 4*c + 9. Let n be (2 - 14*-1) + 0. Suppose 4*j + n = -0*j. Let k(s) = s**2 + 4*s + 8. Let t(u) = j*m(u) + 5*k(u). Factor t(y).
(y + 2)**2
Find w, given that -w**2 - w - 7*w + 0*w - w**4 + 2 + 5*w + 3*w**3 = 0.
-1, 1, 2
Let o(s) be the third derivative of -s**5/120 + s**4/4 - 3*s**3 + 16*s**2. Solve o(b) = 0.
6
Let i be (-34)/85*(-5)/4. Determine q so that -1/2*q**3 + 1/2*q - i*q**2 + 1/2 = 0.
-1, 1
Let g(u) = u**3 + 5*u**2 + 3. Let t = 13 + -18. Let r be g(t). Find j, given that 18/7*j + 48/7*j**2 + 2/7 + 32/7*j**r = 0.
-1, -1/4
Let j = 9 - 5. Suppose -8 = -8*h + j*h. Suppose -1/4*v**h - 1/2*v - 1/4 = 