c + 2/3*c**3 + 0. Factor t(p).
2*(p + 1)**2
Let z(w) be the third derivative of -w**5/60 + 5*w**4/6 - 50*w**3/3 + 41*w**2. Suppose z(y) = 0. Calculate y.
10
Suppose 0 - 2 = -z. Let c(d) be the first derivative of 0*d + 1/3*d**3 + d**z - 1. Determine s, given that c(s) = 0.
-2, 0
Let n = -53 + 380/7. Factor 4/7 - 4*k + n*k**4 - 6*k**3 + 61/7*k**2.
(k - 2)**2*(3*k - 1)**2/7
Solve 0 - 2/7*r - 2/7*r**2 = 0.
-1, 0
Let u(m) be the first derivative of -m**5/25 + m**4/5 - 2*m**3/5 + 2*m**2/5 - m/5 + 10. Factor u(z).
-(z - 1)**4/5
Suppose -2*q = 4*u, q + 0 = -u + 1. Suppose 3*c**q - 2 + 3*c**2 - 8*c**2 + c**4 + 3 = 0. Calculate c.
-1, 1
Suppose -6*m + 2 = -16. Factor m*k + 3*k**4 - k + 3*k**2 - 6*k**3 - 2*k.
3*k**2*(k - 1)**2
Let y(z) be the third derivative of z**5/450 - z**4/180 + 7*z**2. Determine l, given that y(l) = 0.
0, 1
Factor -1/3*g + 1/3*g**3 - 1/3*g**2 + 0 + 1/3*g**4.
g*(g - 1)*(g + 1)**2/3
Let u(o) be the second derivative of -o**6/15 - 3*o**5/10 - o**4/3 - 11*o. Find y such that u(y) = 0.
-2, -1, 0
Let f(w) be the first derivative of -2*w**5/15 + w**4/2 - 2*w**3/3 + 3*w**2 + 9. Let m(t) be the second derivative of f(t). Suppose m(n) = 0. What is n?
1/2, 1
Let c = 1454 - 7267/5. Factor -9/5 - 12/5*j - c*j**2.
-3*(j + 1)*(j + 3)/5
Let x = 20 - 16. Let b(m) be the third derivative of 0 - 1/60*m**x - 1/300*m**6 + m**2 - 1/75*m**5 + 0*m**3 + 0*m. Factor b(z).
-2*z*(z + 1)**2/5
Let w = 67/255 + 6/85. Solve 0*q + 0 + w*q**3 + 0*q**2 = 0 for q.
0
Let c(a) be the first derivative of -a**5/240 - a**4/96 - 3*a**2/2 - 2. Let k(s) be the second derivative of c(s). Factor k(g).
-g*(g + 1)/4
Suppose -r = 3*r. Suppose -3*k + 5*f + 21 = 2*f, -4*k - 5*f - 17 = r. Factor 1/3*j**4 - 1/3*j**k + 0 + 1/3*j**3 - 1/3*j.
j*(j - 1)*(j + 1)**2/3
Let z(s) be the second derivative of -s**4/60 + 2*s**2/5 + 12*s. Solve z(t) = 0 for t.
-2, 2
Let u be 2*2/4 + 6/(-12). Let u + 0*c - 1/2*c**2 = 0. What is c?
-1, 1
Let h = -2 - -6. Suppose 2*i - 3*i = 5*s - 29, -3*s = -3*i - 3. Factor 0*z**3 - 7*z - i*z**h - 18*z**2 + 3*z**4 - 7*z**4 - 20*z**3 - 1.
-(z + 1)*(2*z + 1)**3
Let h = -163 + 163. Determine t, given that 1/4*t + h + 1/4*t**2 = 0.
-1, 0
Let 1/2*y**3 + 0*y**2 + 0*y + 1/2*y**4 + 0 = 0. Calculate y.
-1, 0
Let z(u) = -3*u**4 - 17*u**3 + 23*u**2 + 5. Let m(l) = -5*l**4 - 26*l**3 + 35*l**2 + 8. Let h(n) = 5*m(n) - 8*z(n). Find o such that h(o) = 0.
0, 3
Let u(g) be the first derivative of -3/4*g**4 - g**3 + 0*g + 0*g**2 - 4. Let u(j) = 0. Calculate j.
-1, 0
Let k(s) = -s**5 + 25*s**4 - 49*s**3 + 47*s**2 - 7*s + 5. Let x(u) = 12*u**4 - 24*u**3 + 24*u**2 - 3*u + 3. Let i(y) = 3*k(y) - 5*x(y). Factor i(t).
-3*t*(t - 2)*(t - 1)**3
Factor -6*o**3 - 4*o**5 + 93*o**4 + 7*o**5 - 90*o**4.
3*o**3*(o - 1)*(o + 2)
Let x = 11 + -8. Let a(h) be the first derivative of 0*h - 14/15*h**5 - 3/2*h**4 + 3 + 0*h**2 - 4/9*h**x. Factor a(j).
-2*j**2*(j + 1)*(7*j + 2)/3
Let n(u) be the third derivative of u**6/120 + u**5/20 + u**4/12 + 5*u**2. Factor n(l).
l*(l + 1)*(l + 2)
Suppose 3*u + j - 4 = 0, 10*j = -3*u + 5*j + 20. Let 12/7*q**4 + u - 3/7*q**3 + 0*q - 9/7*q**5 + 0*q**2 = 0. Calculate q.
0, 1/3, 1
Let t = -1743 + 5237/3. Factor -t + 4/3*z**4 - 20/3*z + 4/3*z**3 - 4*z**2.
4*(z - 2)*(z + 1)**3/3
Let l(s) = -s**3 + s**2 + 2. Let v be l(0). Solve 4*n + n**v - 4*n**3 - 9*n**2 + 8*n**3 = 0 for n.
0, 1
Let f(z) = z**2 - 16*z + 2. Let y be f(16). Let -3/4*b**y - 3/2 - 9/4*b = 0. Calculate b.
-2, -1
Let m(p) be the first derivative of 3*p**4/4 - 3*p**3 + 3*p**2 + 16. Factor m(k).
3*k*(k - 2)*(k - 1)
Find o, given that -50/7 - 20/7*o - 2/7*o**2 = 0.
-5
Let g(w) = 8*w + 5. Let u be g(-5). Let d = u + 141/4. Solve d*k + 0 - 1/4*k**2 = 0 for k.
0, 1
Let o(c) be the first derivative of -c**3/9 - 2*c**2/3 - c + 9. Factor o(d).
-(d + 1)*(d + 3)/3
Factor -6 + 5*n**2 - 4*n**2 + 4 - 7.
(n - 3)*(n + 3)
Let a be 9/(-7) - 12/(-42). Let r(q) = -1. Let w(h) = -h**2 + h + 7. Let v(b) = a*w(b) - 5*r(b). Factor v(t).
(t - 2)*(t + 1)
Let g = 2/1675 + 6678/18425. Determine f, given that 2/11*f**3 + 2/11*f**4 - g*f**2 + 0 + 0*f = 0.
-2, 0, 1
Let x be 10/8 + 2/24. Factor -1/3*p**3 + 2/3 - 5/3*p + x*p**2.
-(p - 2)*(p - 1)**2/3
Let i(b) be the first derivative of 0*b**4 - 1/30*b**5 + 1/36*b**6 - 7 + 0*b + 0*b**2 + 0*b**3. Factor i(o).
o**4*(o - 1)/6
Determine q, given that -1/5*q**2 - 3/5 - 4/5*q = 0.
-3, -1
Let n = -20 + 21. Factor 4*b**5 - 1 - 30*b**4 + n + 34*b**4.
4*b**4*(b + 1)
Let x(w) be the second derivative of w**6/2 - 2*w**5 + 5*w**4/2 - 5*w**2/2 + 5*w. Let x(f) = 0. What is f?
-1/3, 1
Let g(y) be the third derivative of y**9/20160 - y**8/1680 + y**7/336 - y**6/120 - y**5/15 - 2*y**2. Let f(w) be the third derivative of g(w). Factor f(a).
3*(a - 2)*(a - 1)**2
Let b(x) be the second derivative of x**6/1080 + x**5/180 + x**4/72 - 5*x**3/6 + 3*x. Let j(l) be the second derivative of b(l). Factor j(f).
(f + 1)**2/3
Let b(m) be the second derivative of m**7/147 - m**5/70 - 11*m. Factor b(h).
2*h**3*(h - 1)*(h + 1)/7
Let l(n) = 11*n**5 - 23*n**4 + 13*n**3 + 9*n**2 - 5. Let z(y) = -16*y**5 + 34*y**4 - 20*y**3 - 14*y**2 + 8. Let a(g) = -8*l(g) - 5*z(g). Factor a(r).
-2*r**2*(r - 1)**2*(4*r + 1)
Suppose 5*i = s + 49, 5*s + 3*i - i = -218. Let r = 177/4 + s. Factor -1/4*b**5 + 0*b + 0*b**4 + 0*b**2 + r*b**3 + 0.
-b**3*(b - 1)*(b + 1)/4
Factor 2/15*c + 0*c**2 + 0 - 2/15*c**3.
-2*c*(c - 1)*(c + 1)/15
Let y be (32/(-88))/((-4)/22). Find t, given that -2/15 + 2/15*t**y + 0*t = 0.
-1, 1
Let u = 19 + -17. Let q(g) be the first derivative of 2 - 5/3*g**3 - 1/2*g - 1/2*g**5 + 5/4*g**4 + 5/4*g**u + 1/12*g**6. Suppose q(x) = 0. Calculate x.
1
Let r be (5 - 14/4)*(-4)/(-3). Let 4/3*k**3 - 2/3 + r*k**4 - 4/3*k**2 - 2*k + 2/3*k**5 = 0. What is k?
-1, 1
Let a(g) be the first derivative of -4 + 0*g**2 + 0*g**3 + 0*g - 5/12*g**4 + 5/18*g**6 + 0*g**5. Suppose a(f) = 0. Calculate f.
-1, 0, 1
Let r(s) be the third derivative of 1/8*s**4 + 0*s + 0 + 1/3*s**3 - 1/40*s**6 + 6*s**2 - 1/60*s**5 - 1/210*s**7. Find a, given that r(a) = 0.
-2, -1, 1
Let s(d) = -d**2 + d - 1. Let v(i) = -9*i**2 + 42*i - 114. Let k(u) = -6*s(u) + v(u). Determine n, given that k(n) = 0.
6
Let t = 326/11 - 324/11. Suppose 0 - 2/11*k**4 + 0*k - 4/11*k**3 - t*k**2 = 0. What is k?
-1, 0
Let g(b) = -16*b**4 + 11*b**3 + 2*b**2 - 11*b + 7. Let u(h) = 11*h**4 - 7*h**3 - h**2 + 7*h - 5. Let t(i) = -5*g(i) - 7*u(i). Factor t(q).
3*q*(q - 2)*(q - 1)*(q + 1)
Let b(p) = 3*p**5 - 7*p**4 + 2*p**3 - 4*p**2 - 3*p + 3. Let q(h) = h**3 + h**2 + h - 1. Suppose 8*l + 3 = 9*l. Let r(o) = l*q(o) + b(o). Solve r(y) = 0 for y.
0, 1/3, 1
Let z be (-20)/6 + (2 - -1). Let r = 1/6 - z. Factor 1/2*q**2 + 0 - r*q.
q*(q - 1)/2
Let k be 0 - 40/7 - 1. Let y = k + 53/7. Factor 6/7*l**2 - y*l**3 + 2/7*l**4 + 0 - 2/7*l.
2*l*(l - 1)**3/7
Let n(c) = -2*c**2 + 2*c + 2. Let z(q) be the first derivative of q + 2. Let x(u) = -n(u) + 2*z(u). Suppose x(f) = 0. Calculate f.
0, 1
Factor -k + k**3 - 10*k**3 - k - 3*k**4 - 9*k**2 - k.
-3*k*(k + 1)**3
Let m(l) = -5*l + 79. Let q be m(15). Let -2/9*i**3 - 2/9*i**q + 2/9*i + 0 + 2/9*i**2 = 0. Calculate i.
-1, 0, 1
Suppose -2*m + 2*s - 6 = 0, 0 = -5*m - 3*s + 1 + 24. Factor 5*f**3 - 6*f**3 - 3*f - f**4 + m*f**2 - f**2 + 4*f**3.
-f*(f - 3)*(f - 1)*(f + 1)
Let o = 20 + -16. Let a(f) be the third derivative of 2/165*f**5 + 0*f + 0 + 2/33*f**3 + 5/132*f**o + f**2 + 1/660*f**6. Suppose a(x) = 0. Calculate x.
-2, -1
Let l(x) be the first derivative of 4*x**3/3 - 4*x + 5. Find k such that l(k) = 0.
-1, 1
Let q(d) be the third derivative of -d**5/30 - d**3 - 2*d**2. Let n(t) = -4*t**2 - t - 13. Let p = -5 - -9. Let a(w) = p*n(w) - 9*q(w). Factor a(r).
2*(r - 1)**2
Factor 0*k + 0 + 10/7*k**4 + 8/7*k**2 - 16/7*k**3 - 2/7*k**5.
-2*k**2*(k - 2)**2*(k - 1)/7
Let c(r) = 2*r - 2. Let f be c(2). Factor 2*i - 5*i - i**3 - i**2 + 4*i**2 + f*i**2 - i**4.
-i*(i - 1)**2*(i + 3)
Let c(f) be the second derivative of -f**6/30 + f**5/5 + f**4/4 - 3*f**3 + 32*f. Factor c(t).
-t*(t - 3)**2*(t + 2)
Suppose -15 = f - 6*f. Factor -k**f - 2*k + 3 - 3*k**2 + 5*k - 2*k**3.
-3*(k - 1)*(k + 1)**2
Let n(y) = y**2 + y. Let c(m) = 3*m**3 - 28*m**2 - 31*m. Let j(u) = -c(u) - 4*n(u). Factor j(x).
-3*x*(x - 9)*(x + 1)
Let w(f) = 2*f**2 - 17*f - 7. Let m be w(9). Suppose -d - d - 2 = r, -3*r = m*d + 6. Fact