1/45*f**5 + 1/504*f**8 + 0*f + 0 + 0*f**3 + 4*f**2 + 0*f**4. Factor n(d).
2*d**2*(d - 2)*(d - 1)**2/3
Let z be (-1*1)/((-2)/50*5). Suppose s**z + 4/3*s + 6*s**2 - 8/3 - 8/3*s**4 - 5/3*s**3 = 0. Calculate s.
-1, 2/3, 2
Let t(a) be the third derivative of -5*a**8/336 - a**7/21 + 12*a**2. Factor t(y).
-5*y**4*(y + 2)
Factor 1/6*w**2 + 1/2*w + 0.
w*(w + 3)/6
Suppose -w + 4 = l, 7 = -w + 3*l - 5. Solve w*k - 1/7*k**2 + 0 = 0.
0
Suppose -9 - 10 = -2*k - 5*a, 0 = -5*a + 15. Find t such that 0*t + 3/2 - 3/2*t**k = 0.
-1, 1
Let y(x) = -6*x + 0*x**2 + 10*x + 4*x**2 + 2 + 0. Let h(g) = -g**2 + g - 1. Let o(c) = 2*h(c) + y(c). Suppose o(u) = 0. Calculate u.
-3, 0
Suppose -d = 3, -7*d + 12*d = 3*m - 15. Let k(r) be the second derivative of 2*r + 0*r**3 + 1/4*r**4 - 1/10*r**6 + 0*r**2 + m + 0*r**5. Factor k(z).
-3*z**2*(z - 1)*(z + 1)
Let t(b) be the third derivative of -1/90*b**5 - 1/36*b**4 + 1/315*b**7 + b**2 + 1/180*b**6 + 0*b + 0*b**3 + 0. Factor t(d).
2*d*(d - 1)*(d + 1)**2/3
Let i = 217/3 + -71. Let v(n) be the third derivative of 0*n - 4*n**2 + 0 - i*n**3 - 13/30*n**5 + 1/10*n**6 - 1/105*n**7 + n**4. Suppose v(l) = 0. What is l?
1, 2
Let s(c) = -c**3. Let j(a) = -6*a**3 + 15*a**2 + 21*a + 9. Let y(p) = j(p) - 9*s(p). Factor y(m).
3*(m + 1)**2*(m + 3)
Suppose 0 = 5*a + 5*n + 35, 3 = -n + 2. Let q = a + 10. Factor -u**3 - q*u**5 - 5*u**2 - u**4 + 2*u**2 + 4*u**2 + 5*u**5.
u**2*(u - 1)**2*(u + 1)
Let a be 55/(-15) + 1/(-3). Let k = a + 7. Let 0*r + 0 + 2/7*r**4 - 2/7*r**5 + 2/7*r**k - 2/7*r**2 = 0. Calculate r.
-1, 0, 1
Let o(c) be the third derivative of -c**8/840 + 2*c**7/525 + c**6/75 - c**5/75 - c**4/20 - 58*c**2. Solve o(s) = 0.
-1, 0, 1, 3
Let r(a) be the second derivative of -a**4/4 + 3*a**2/2 - 26*a. Factor r(f).
-3*(f - 1)*(f + 1)
Suppose r - 3*v + 0 = 17, 2*v = -8. Let k(n) be the second derivative of n - 24*n**2 + 2058/5*n**r + 0 - 294*n**4 + 112*n**3 - 2401/10*n**6. Factor k(b).
-3*(7*b - 2)**4
Suppose 9 = -4*s + 3*n, -3*s + 2*n = -3*n + 15. Suppose -5*o + q - 4*q + 5 = s, -4*o - 2*q = -4. Let 1/2*u + o - 1/2*u**2 = 0. What is u?
-1, 2
Let i be -10*(-3)/(-6)*-2. Determine d so that 5 - 100*d**3 + i*d**4 + 6 - 3 - 66*d**2 - 52*d**4 = 0.
-1, -2/3, 2/7
Suppose 0*u - 1/7*u**5 - u**2 + 1/7*u**3 + 4/7 + 3/7*u**4 = 0. What is u?
-1, 1, 2
Let u = -9 + 20. Determine g, given that 0 + 3*g**4 - u*g**3 - 6*g**3 + 2*g**3 - 21*g + 27*g**2 + 6 = 0.
1, 2
Factor -2*v**2 + 3*v - 7*v + 2 - 4.
-2*(v + 1)**2
Let m(x) be the first derivative of -x**7/3360 + x**6/288 - x**5/60 + x**4/24 + 7*x**3/3 - 5. Let o(j) be the third derivative of m(j). Factor o(c).
-(c - 2)**2*(c - 1)/4
Find k, given that 0 - 1/5*k**4 - 1/10*k + 1/10*k**5 + 1/5*k**2 + 0*k**3 = 0.
-1, 0, 1
Let u = -28/9 - -139/36. Factor 0*v - 1/4*v**2 + 0 - 1/4*v**5 - 3/4*v**3 - u*v**4.
-v**2*(v + 1)**3/4
Let i(g) be the third derivative of -g**5/42 - g**4/12 - 2*g**3/21 - 2*g**2. Factor i(j).
-2*(j + 1)*(5*j + 2)/7
Let -6*v**3 + 4*v**3 + 4*v**3 + 4*v**2 - 4*v**3 = 0. What is v?
0, 2
Let r(z) be the first derivative of 0*z + 6 - 1/15*z**3 - 1/10*z**2. Factor r(q).
-q*(q + 1)/5
Suppose 0 = -5*v - 0*v + 5. Let n(d) be the first derivative of 2*d**4 - 2/3*d**2 - 14/15*d**5 - 2/3*d**3 + v + 0*d. Let n(r) = 0. Calculate r.
-2/7, 0, 1
Find q, given that -4*q + 0*q - 4*q + 6*q**3 + 2*q**4 = 0.
-2, 0, 1
Let u(o) be the third derivative of o**5/20 - 2*o**4 + 32*o**3 + 17*o**2. Factor u(n).
3*(n - 8)**2
Suppose 0 = -h - 4 + 8. Factor 2/13*s**2 + 0*s + 0 + 0*s**3 - 2/13*s**h.
-2*s**2*(s - 1)*(s + 1)/13
Let d be -4 + -5*81/(-90). Factor -m**4 - 3/2*m**2 - d*m + 1/2 + 5/2*m**3.
-(m - 1)**3*(2*m + 1)/2
Let f = -71 - -359/5. Factor 2/5*b**3 - 6/5*b - f + 0*b**2.
2*(b - 2)*(b + 1)**2/5
Let i(m) be the second derivative of 5*m + 0 + 0*m**2 + 1/130*m**5 + 4/39*m**3 + 2/39*m**4. Solve i(x) = 0 for x.
-2, 0
Let l(k) be the first derivative of -2/3*k**3 - 1/2*k**4 + 2*k**2 - 4 + 0*k. Factor l(i).
-2*i*(i - 1)*(i + 2)
Let b(d) be the first derivative of -d**5/25 + 3*d**4/20 - d**3/15 - 3*d**2/10 + 2*d/5 - 7. Determine p so that b(p) = 0.
-1, 1, 2
Factor -h**4 - 4*h - 4*h + h**5 - 12*h**2 + 4*h**4 - 2*h**3 + 0*h**4.
h*(h - 2)*(h + 1)*(h + 2)**2
Let s be (-1)/4*4*(-4)/10. Factor 1/5*t**2 + 0 + s*t.
t*(t + 2)/5
What is g in 2/3*g**2 + 4 - 10/3*g = 0?
2, 3
Let q(a) be the second derivative of -a**6/135 - a**5/10 - 4*a**4/9 - 16*a**3/27 - a. Factor q(i).
-2*i*(i + 1)*(i + 4)**2/9
Let r = -1463/92 - -65/4. Let b = 86/115 - r. Factor 0*v + 0 + 0*v**2 + 2/5*v**3 - b*v**4.
-2*v**3*(v - 1)/5
Let g(z) be the first derivative of z**6/240 - z**4/16 + z**3/6 + z**2 - 3. Let b(u) be the second derivative of g(u). Suppose b(p) = 0. What is p?
-2, 1
Let y(j) be the third derivative of -4/105*j**7 + 0 + 0*j**3 - 1/60*j**6 + 0*j + 0*j**4 + 1/56*j**8 + 1/15*j**5 - j**2. Find t, given that y(t) = 0.
-2/3, 0, 1
Suppose 5*y - u - 10 = 0, -u - 3*u = 2*y - 26. Factor 6*j**3 - 6*j**3 + 2*j**y - 2*j.
2*j*(j - 1)*(j + 1)
Let y be ((-3)/(-36))/(36/8). Let z(n) be the second derivative of -2/27*n**3 + 0 + y*n**4 + 1/9*n**2 + 2*n. Factor z(g).
2*(g - 1)**2/9
Let c(t) = 4*t**2 + 7*t. Let b(r) = 4*r**2 + 6*r. Let k(z) = 5*b(z) - 6*c(z). Factor k(u).
-4*u*(u + 3)
Suppose 0 = 4*g + 4*o - 80, 0*o - 2*o + 61 = 3*g. Let z be ((-14)/g)/(2/(-4)). Factor -z*v**2 - 2/3*v**5 + 2/3 + 4/3*v**3 + 2/3*v**4 - 2/3*v.
-2*(v - 1)**3*(v + 1)**2/3
Let k(y) = -y**2 + 6*y - 5. Let n(d) = -2*d**2 + 9*d - 8. Let g(p) = 8*k(p) - 5*n(p). Determine r so that g(r) = 0.
-3/2, 0
Let o(n) = -n - 1 + 2*n**3 - 2*n**2 + 5 + 0*n**3 - 3*n**3. Let a(b) = 1. Let v be 0/(1 + 0) + 1. Let q(z) = v*o(z) - 4*a(z). Determine s, given that q(s) = 0.
-1, 0
Let h(f) be the third derivative of -f**8/28 + f**7/42 + 3*f**6/20 - f**5/15 - f**4/4 - f**3/6 + 7*f**2. Let h(u) = 0. Calculate u.
-1, -1/3, -1/4, 1
Let m(k) = -2*k**2 - 7*k + 3. Let r be m(-4). Let x(t) = -3*t**4 - 3*t**3 - 3*t**2 - 3*t. Let y(b) = -b**3 - b**2 - b. Let c(u) = r*x(u) + 3*y(u). Factor c(z).
3*z**4
Suppose -3*b = -b + 2*p - 8, -5*b + 2*p = 1. Let n be b*(0 - 2/(-1)). Factor 7*d**2 - 7*d**4 - 11*d + n*d**3 + 8*d + d.
-d*(d - 1)*(d + 1)*(7*d - 2)
Suppose -q + 2*q + 60 = 0. Let t = 302/5 + q. What is y in 2/5*y**4 + t*y**3 + 0 - 2/5*y**2 - 2/5*y = 0?
-1, 0, 1
Let h be -7 + (7 - 0/6). Find f such that 16/7 - 4*f**2 + 12/7*f**4 - 4/7*f**5 + h*f + 4/7*f**3 = 0.
-1, 1, 2
Let c(d) be the first derivative of d**6/360 + d**5/120 - 2*d**3/3 - 3. Let k(z) be the third derivative of c(z). Solve k(m) = 0.
-1, 0
Let n(a) be the first derivative of -a**9/3024 - a**8/840 - 8*a**3/3 + 1. Let m(v) be the third derivative of n(v). Find o, given that m(o) = 0.
-2, 0
Let d(l) be the third derivative of l**6/24 - l**5/4 + 5*l**4/12 + 24*l**2. Factor d(c).
5*c*(c - 2)*(c - 1)
Let 24 - 12*y**2 - 8 - 28*y + 8*y**3 + 4*y**4 + 12*y = 0. Calculate y.
-2, 1
Let r(i) be the first derivative of 20*i**3/21 + 4*i**2 - 12*i/7 + 3. Factor r(f).
4*(f + 3)*(5*f - 1)/7
Let v(u) be the first derivative of 0*u**3 + 0*u - 3/4*u**4 - 1/2*u**6 + 6/5*u**5 + 2 + 0*u**2. Let v(h) = 0. Calculate h.
0, 1
Let b(o) = 2*o - 42. Let d be b(21). Let m(s) be the first derivative of d*s - 1/3*s**3 + 0*s**2 + 1/4*s**4 + 4. Determine i so that m(i) = 0.
0, 1
Let l be ((-5)/(-3))/(30/108). Let u(z) be the first derivative of l*z - 39/2*z**2 + 20*z**3 - 2 - 27/4*z**4. Factor u(j).
-3*(j - 1)**2*(9*j - 2)
Solve -9*l**3 + l - 3*l**4 - 3*l + 14*l = 0 for l.
-2, 0, 1
Let x(t) be the second derivative of -t**6/75 + 26*t**5/25 - 169*t**4/5 + 8788*t**3/15 - 28561*t**2/5 + 37*t. What is y in x(y) = 0?
13
Let l(n) be the second derivative of -1/120*n**6 + 1/48*n**4 - 1/80*n**5 + 1/168*n**7 - 3*n + 0*n**2 + 0*n**3 + 0. Factor l(i).
i**2*(i - 1)**2*(i + 1)/4
Factor 1/3*f**2 + 1/3*f**3 + 0 - 1/3*f**4 - 1/3*f.
-f*(f - 1)**2*(f + 1)/3
Let t = 50 + -50. Factor t*d + 2/5*d**3 + 0 + 8/5*d**4 + 0*d**2.
2*d**3*(4*d + 1)/5
Let w(a) be the third derivative of 1/2*a**4 + 1/2*a**3 + 0 - 3*a**2 + 0*a + 1/5*a**5. Let w(k) = 0. Calculate k.
-1/2
Suppose -12 + 15 = -i. Let v = 5 + i. Let -6/5*d - 2/5 + 2*d**v - 8/5*d**4 + 6/5*d**3 = 0. What is d?
-1, -1/4, 1
Suppose -8 = 2*u, -5*u - 32 = -5*j + 3. Suppose -j*k - 18 = -3*r, 2*k = 2*r + 7*k + 16. Let 4/7*z**3 + 6/7*z**r - 8/7*z - 8/7 - 2/7*z**4 = 0. Calculate z.
-1, 2