g**3/15 + 48*g**2/5 - 151*g. Solve i(z) = 0 for z.
-4, 1, 3
Let v = -21/155 + 376403/465. Let f = v + -798. Determine s so that -8/3*s**4 + 8/3*s + f*s**3 - 40/3*s**2 + 0 = 0.
0, 1/4, 2
Solve 5/3*t**3 + 15*t**2 - 180 + 0*t = 0.
-6, 3
Let v(k) be the first derivative of -k**6/3 - 18*k**5/5 - 23*k**4/2 + 6*k**3 + 108*k**2 + 216*k - 63. Determine z so that v(z) = 0.
-3, -2, 2
Let v = -179 - -182. Let y(w) be the second derivative of -1/4*w**4 + w**3 - v*w + 0*w**2 + 0. Find h such that y(h) = 0.
0, 2
Let a(x) = -55*x**3 - 305*x**2 - 360*x - 75. Let l(f) = -26*f**3 - 153*f**2 - 180*f - 37. Let i(c) = 3*a(c) - 5*l(c). Factor i(q).
-5*(q + 2)**2*(7*q + 2)
Find i, given that 1/4*i**2 - 31/4*i + 0 = 0.
0, 31
Let r(n) be the third derivative of -n**6/180 - n**5/12 - n**4/3 - 35*n**3/6 - n**2 + 21*n. Let p(m) be the first derivative of r(m). Solve p(c) = 0.
-4, -1
Determine u so that -1/5*u**4 - 1/5*u**5 - u + 3/5 - 2/5*u**2 + 6/5*u**3 = 0.
-3, -1, 1
Let a be ((4/(-224))/1)/((-24)/192). Factor 0*v**3 + 1/7*v + 2/7*v**4 + 0 - a*v**5 - 2/7*v**2.
-v*(v - 1)**3*(v + 1)/7
Let f be (-52)/6*(-3)/2. Suppose 4 = 5*b - 11. Factor r + 16*r**3 - f*r**b - 3*r**4 - r.
-3*r**3*(r - 1)
Suppose -5 = t, -2*t + 1 = 4*l + t. Let o(z) be the second derivative of 9/4*z**l - 7/2*z**3 - 3*z**2 + 6*z + 0. Factor o(b).
3*(b - 1)*(9*b + 2)
Let b(u) be the second derivative of u**8/57120 + u**7/7140 - 5*u**4/6 + 16*u. Let p(v) be the third derivative of b(v). Factor p(l).
2*l**2*(l + 3)/17
Let f(m) be the first derivative of m**7/2100 - m**6/900 - m**5/150 - 4*m**3 - 21. Let a(s) be the third derivative of f(s). Solve a(y) = 0.
-1, 0, 2
Let n = 8/677 - -653/2031. Factor 0 - n*j + 1/3*j**2.
j*(j - 1)/3
Let k = -77 + 76. Let f be -1 + -2 + 2 - 3*k. Factor 3/2 - 3/4*y**3 - 15/4*y + 3*y**f.
-3*(y - 2)*(y - 1)**2/4
Let o = 87 - 62. Suppose -o = f - 6*f. Factor f*m**3 + 0*m**3 - 4*m**3.
m**3
Let z(c) be the first derivative of c**5/20 + 5*c**4/16 + c**3/2 - c**2/2 - 2*c - 68. Factor z(m).
(m - 1)*(m + 2)**3/4
Let o = -581 + 29051/50. Let i(z) be the second derivative of -4/15*z**3 + 0*z**2 - o*z**5 - 2/15*z**4 - 5*z + 0. Factor i(h).
-2*h*(h + 2)**2/5
Let p(o) be the first derivative of 4*o**5/55 - 67*o**4/22 + 46*o**3 - 275*o**2 + 242*o + 556. Factor p(q).
2*(q - 11)**3*(2*q - 1)/11
Factor 2/13*b**3 + 28/13 + 46/13*b + 20/13*b**2.
2*(b + 1)*(b + 2)*(b + 7)/13
Let y(q) be the third derivative of 0 + 1/96*q**4 + 0*q - 1/480*q**6 + 1/120*q**5 - 8*q**2 - 1/12*q**3. Factor y(t).
-(t - 2)*(t - 1)*(t + 1)/4
Suppose -12*l + 5*l = 4*l. Let f(w) be the first derivative of 0*w**4 + 2/25*w**5 - 2/15*w**3 + 1 + 1/10*w**2 - 1/30*w**6 + l*w. Solve f(s) = 0 for s.
-1, 0, 1
Let k = 12979/9738 - -5/9738. Factor 4/3*x**3 - 4/3*x**2 - k*x + 4/3*x**4 + 0.
4*x*(x - 1)*(x + 1)**2/3
Let q(i) be the third derivative of -11*i**2 - 1/6*i**4 + 1/30*i**5 - i**3 + 0*i + 0. Factor q(d).
2*(d - 3)*(d + 1)
Let c = 138 - 134. Let o(u) be the first derivative of -1/3*u**3 + 0*u**2 + 6 + 1/10*u**5 + 0*u + 1/8*u**c. Find i such that o(i) = 0.
-2, 0, 1
Let i(a) be the first derivative of -a**6/18 + 4*a**5/15 + a**4/12 - 4*a**3/9 + 6. Determine k so that i(k) = 0.
-1, 0, 1, 4
Suppose -3*r = 3, 4*q = -r + 6 + 5. Let u(t) be the second derivative of 1/5*t**5 + 0 + 0*t**q + 0*t**2 + 1/6*t**4 - 5*t + 1/15*t**6. Factor u(k).
2*k**2*(k + 1)**2
Suppose 0 = c - 2*c + 9. Let m be ((-7)/6 + (10 - c))*-2. Factor m*b**2 + 1/3*b**3 + 0 - 1/3*b**4 + 0*b - 1/3*b**5.
-b**2*(b - 1)*(b + 1)**2/3
Let h(d) = -2*d**2 + 2*d - 3. Let i(t) = -3*t**2 + 3*t - 4. Let f = -10 + 14. Let q(j) = f*h(j) - 3*i(j). Factor q(k).
k*(k - 1)
Let w(n) be the second derivative of -1/4*n**5 - 12*n + 0 + 0*n**2 + 0*n**3 + 5/6*n**4 - 1/6*n**6. Factor w(v).
-5*v**2*(v - 1)*(v + 2)
Let j be -12 - 4/(-56)*172. Determine a, given that j*a**2 + 4/7 - 6/7*a = 0.
1, 2
Suppose n - 6*n = -l, 0 = 5*l - 3*n - n. Factor 15/4*j**4 - 3*j**5 + 0*j**2 + 0 - 3/4*j**3 + l*j.
-3*j**3*(j - 1)*(4*j - 1)/4
Let x(m) = -5*m**4 + 10*m**3 + 6*m**2 - 31*m - 7. Let d(w) = 9*w**4 - 19*w**3 - 14*w**2 + 61*w + 17. Let j(f) = -6*d(f) - 10*x(f). Let j(u) = 0. What is u?
-2, -1/2, 2, 4
What is w in -28*w**2 + w**4 + 19*w**2 + w**2 - w**3 - w**3 - 4*w + w**2 = 0?
-1, 0, 4
Suppose 2*f + f = -6. Let p be (5 - -1)*f/(-6). Let -p*a**5 + 5*a**4 + 3*a**5 - 3*a**4 + 2*a**3 - a**3 = 0. What is a?
-1, 0
Suppose -59 = -16*t + 5. Suppose -j = 5*f - 17, -3 = f - 4*j + 2. Factor -1/3*i - 1/3 + 4/3*i**t - 11/3*i**f + 3*i**2.
(i - 1)**3*(4*i + 1)/3
Let w(d) be the second derivative of -5/2*d**3 + 10*d - 9/20*d**5 - 3/2*d**2 + 0 - 7/4*d**4. Let w(q) = 0. What is q?
-1, -1/3
Let z(p) = -p**2 + 6*p - 8. Let w(v) = 0*v**2 + 24*v - 32 - 5*v**2 - 5*v**2 + 5*v**2. Let q(l) = 6*w(l) - 26*z(l). What is j in q(j) = 0?
-4, 1
Let f be ((-9)/2*100/(-225))/(10/4). Suppose 4/5*r**2 + 0 - f*r**4 + 0*r - 2/5*r**3 + 2/5*r**5 = 0. Calculate r.
-1, 0, 1, 2
Let p(w) be the first derivative of w**6/120 + w**5/60 + w**4/72 + 8*w**3/3 - 3. Let n(k) be the third derivative of p(k). Let n(o) = 0. Calculate o.
-1/3
Let j be (-27)/(-5) - (-4)/(-10). Let q(u) be the first derivative of 1/4*u**2 + 3/8*u**4 + 0*u - 1/2*u**3 - 6 - 1/10*u**j. Factor q(t).
-t*(t - 1)**3/2
Let k be 12/(-5)*((-42)/9 + -2). Factor k*r + 3*r**2 + 0*r + 8*r + 48.
3*(r + 4)**2
Let q(z) = z**3 - 1. Let l(b) = 4*b**4 - 26*b**3 + 32*b**2 + 64*b - 2. Let v(o) = l(o) - 2*q(o). Factor v(r).
4*r*(r - 4)**2*(r + 1)
Let -2*b**4 + 48/5*b**2 + 12/5*b**3 + 4*b - 6/5 = 0. What is b?
-1, 1/5, 3
Suppose 4*p = -n + 4, -4*n - 2 = -2*p - 3*n. Let m(c) = -2*c**2 + 4*c + 4. Let r(u) = -u**2 + 1. Let a(t) = p*m(t) - 4*r(t). Factor a(x).
2*x*(x + 2)
Let j be 16/88 - (-2)/(-11). Let z(n) be the third derivative of 1/35*n**5 + 0*n**3 + 0*n - 6*n**2 + j + 1/21*n**4 + 1/210*n**6. Find s such that z(s) = 0.
-2, -1, 0
Let v(w) be the first derivative of -w**6/12 - 3*w**5/5 + w**4/8 + w**3 + 339. Find i such that v(i) = 0.
-6, -1, 0, 1
Suppose 2/5*z**3 + 72/5*z**2 - 78/5*z - 148/5 = 0. Calculate z.
-37, -1, 2
Let n(s) = s**2 - s - 16. Let o be n(-4). Let l be (-15)/(-6)*4/5. Suppose -2*i**2 - i**4 + i**4 + l*i**3 - i + 2*i**o - i = 0. What is i?
-1, 0, 1
Let u(b) be the second derivative of -22*b + 1/2*b**5 - 2*b**2 + 0 - 3/2*b**4 - 1/15*b**6 + 7/3*b**3. Let u(w) = 0. What is w?
1, 2
Determine g, given that 44 + 21*g - 3*g**2 + 28*g - 2 - 10*g = 0.
-1, 14
Let i(s) be the third derivative of s**6/40 - 23*s**5/10 + 89*s**4/8 - 22*s**3 + 12*s**2 + 2*s. Find f, given that i(f) = 0.
1, 44
Let -8/3*z**2 + 4 - 2/3*z**3 - 2/3*z = 0. What is z?
-3, -2, 1
Let f(h) be the third derivative of h**6/480 + h**5/120 - h**2 + 65. Solve f(w) = 0.
-2, 0
Let w(y) be the second derivative of -1/15*y**5 + 1/3*y**2 - 1/63*y**7 + 24*y + 0 + 1/9*y**4 + 1/3*y**3 - 1/15*y**6. Suppose w(s) = 0. Calculate s.
-1, 1
Let j = -23 + 25. Factor 12*z + 10 + 20*z**2 - 24*z**j - 4*z**4 - 2 - 12*z**3.
-4*(z - 1)*(z + 1)**2*(z + 2)
Let m be ((-14)/(-3) + -2)/(-2)*-3. Let g(q) be the third derivative of 0 - 6*q**2 + 0*q + 1/32*q**m + 1/4*q**3 - 1/160*q**6 - 1/40*q**5. Factor g(u).
-3*(u - 1)*(u + 1)*(u + 2)/4
Let t(w) = w**2 - 4. Let f be (-11 + 9)*(-2 - -1). Let l be t(f). Solve l*y + 1/2*y**3 + 1/2*y**2 + 0 = 0.
-1, 0
Let i = -11 + 4. Let q(k) = 6*k**4 + 14*k**3 + 14*k**2 + 14*k + 8. Let t(s) = -11*s**4 - 27*s**3 - 29*s**2 - 28*s - 15. Let r(w) = i*q(w) - 4*t(w). Factor r(a).
2*(a + 1)**3*(a + 2)
Let p(c) be the first derivative of -c**8/784 + c**7/490 + c**2 - 9. Let m(x) be the second derivative of p(x). Solve m(j) = 0.
0, 1
Find t such that 20*t**5 + 49*t**2 + 33*t**2 - 20*t**4 - 5*t**4 - 27*t**2 - 59 + 115*t - 135*t**3 + 29 = 0.
-2, -1, 1/4, 1, 3
Suppose v - 2 = 0, 2*v = -x - 2*v - 2. Let u be (3/12)/1*(-48)/x. Factor 2/5*h**4 + 0 + 0*h**2 + u*h**3 - 8/5*h.
2*h*(h - 1)*(h + 2)**2/5
Let a(p) be the first derivative of p**5/30 - p**4/9 - 7*p + 33. Let t(y) be the first derivative of a(y). Solve t(u) = 0.
0, 2
Let -15 + 5/4*m + 5/4*m**2 = 0. What is m?
-4, 3
Let o = -15704/33 + 476. Let z = o + 289/66. Factor 6*r**2 + 1 - z*r - 5/2*r**3.
-(r - 1)**2*(5*r - 2)/2
Suppose -115 = 12*i - 250 + 99. Factor u**i + u + 1/4 + 1/4*u**4 + 3/2*u**2.
(u + 1)**4/4
Let v(w) be the second derivative of w**4/54 - 77*w**3/27 - 26*w**2/3 - 206*w + 1. 