et o(t) = 0. Calculate t.
-1, 0, 1
Let r(v) be the first derivative of -4*v**5/5 + v**4 + 4*v**3/3 - 2*v**2 - 24. Factor r(m).
-4*m*(m - 1)**2*(m + 1)
Let z(f) be the first derivative of 2*f**2 - 4*f - 1. Let k be z(2). Factor 81/5*g**3 + 19/5*g - 2/5 - 27/5*g**k - 63/5*g**2.
-(g - 2)*(3*g - 1)**3/5
Let n(b) be the first derivative of 2*b**5/25 - b**4/10 - 2*b**3/15 + b**2/5 - 2. Factor n(q).
2*q*(q - 1)**2*(q + 1)/5
Determine z, given that 1/5*z**2 - 6/5 - 1/5*z = 0.
-2, 3
Let p(q) be the first derivative of 0*q - 1 + 1/180*q**5 - 1/18*q**3 + 1/2*q**2 + 0*q**4. Let a(k) be the second derivative of p(k). Factor a(o).
(o - 1)*(o + 1)/3
Let z(k) = k**3 - k**2 + 1. Let g be z(-1). Let d be ((-10)/(-15))/(g/(-3)). Find x such that -d - 1/2*x**2 + 2*x = 0.
2
Factor -2/11*f**5 + 0 + 0*f + 0*f**2 - 4/11*f**4 - 2/11*f**3.
-2*f**3*(f + 1)**2/11
Let x be ((-48)/(-84))/(1/7). Suppose 4*r = 2*u, -6*u - x*r = -2*u. Factor u - 2/7*s**3 - 8/7*s + 8/7*s**2.
-2*s*(s - 2)**2/7
Let j(l) be the second derivative of -361*l**4/60 + 38*l**3/15 - 2*l**2/5 - 24*l. Factor j(f).
-(19*f - 2)**2/5
Let c(n) = -7*n**3 - 5*n**2 - 3*n - 5. Let i(w) = -3*w**3 - 2*w**2 - w - 2. Let m(g) = 6*c(g) - 15*i(g). Factor m(r).
3*r*(r - 1)*(r + 1)
Let c(a) = -2*a**2 + 10*a - 8. Let k be c(4). Factor -8/9*z**2 + k*z - 8/9*z**3 - 2/9*z**4 + 0.
-2*z**2*(z + 2)**2/9
Let v(i) be the second derivative of -i**8/336 + i**7/105 - i**6/120 + i**2/2 + 2*i. Let y(l) be the first derivative of v(l). Factor y(f).
-f**3*(f - 1)**2
Let k be 4/(13/(26/28)). Factor -k*w**4 + 10/7*w - 2/7*w**3 + 4/7 + 6/7*w**2.
-2*(w - 2)*(w + 1)**3/7
Let m(j) be the second derivative of -j**7/11340 + j**6/1620 - j**4/12 - 9*j. Let o(z) be the third derivative of m(z). Factor o(f).
-2*f*(f - 2)/9
Let y = 1 + 1. Suppose y*j + 2*j = 0. Factor 5*s**2 + 3*s - 2*s**2 + j + 3 + 3*s.
3*(s + 1)**2
Let z(d) be the first derivative of d**4/2 + 10*d**3/3 - 27. What is o in z(o) = 0?
-5, 0
Let y(b) be the second derivative of 2*b**6/15 - b**5/5 - 2*b. Factor y(u).
4*u**3*(u - 1)
Let a(g) = g**4 + 14*g**3 - 35*g**2 + 24*g + 4. Let v(f) = f**4 - f**3 - f - 1. Let p(i) = a(i) + 4*v(i). Find y, given that p(y) = 0.
-4, 0, 1
Let p(y) be the first derivative of -5*y**6/3 + 22*y**5/35 + 10*y**4/7 + 8*y**3/21 + 3. Let p(h) = 0. What is h?
-2/5, -2/7, 0, 1
Let s be 7/2*(-16)/(-28). Let u(x) be the first derivative of 1/4*x + 1/12*x**3 + 1/4*x**s + 3. Suppose u(p) = 0. Calculate p.
-1
Let x be 2/(-5) - (-62)/5. Suppose -4*p = -p - x. Find n, given that 4*n**4 + p - 7*n - 14*n**4 + 21*n + 6*n**2 - 14*n**3 = 0.
-1, -2/5, 1
Let r = -5 + 8. Suppose 3*y - r*f - 8 = -f, 4*f = 5*y - 16. Factor y*b**2 + 2/3*b**4 - 4/3*b**3 - 2/3 + 4/3*b.
2*(b - 1)**3*(b + 1)/3
Suppose 2*t = -2*t - 20. Let u be (6/(-15))/((-2)/20). Let l(p) = p**2 + 7*p - 2. Let h(f) = f**2 + 8*f - 3. Let n(k) = t*l(k) + u*h(k). Solve n(d) = 0.
-2, -1
Let u(m) be the first derivative of -m**3/15 - 11*m**2/5 - 121*m/5 - 11. Determine h so that u(h) = 0.
-11
Suppose 16 - 16 = 3*p. Solve p*n + 0*n**4 - 2/5*n**5 + 2/5*n**3 + 0 + 0*n**2 = 0.
-1, 0, 1
Let j(r) be the first derivative of -r**3/3 + 3*r**2 - 9*r + 18. Determine f so that j(f) = 0.
3
Let c(u) = -8*u**3 + 10*u**2 + 2*u - 10. Let r(i) = 23*i**3 - 29*i**2 - 6*i + 29. Let p(m) = -17*c(m) - 6*r(m). Let p(h) = 0. What is h?
-1, 1, 2
Let y be -2 + 2 - (-24)/72. Factor 1/6*s**2 - y - 1/2*s + 1/6*s**4 + 1/2*s**3.
(s - 1)*(s + 1)**2*(s + 2)/6
Let o be (1*0/3)/1. Let d(z) be the third derivative of 0*z**3 - 1/120*z**6 + 0*z + 1/60*z**5 + 0*z**4 + 1/336*z**8 - z**2 - 1/210*z**7 + o. Factor d(v).
v**2*(v - 1)**2*(v + 1)
Let c(a) be the third derivative of a**8/420 - 4*a**7/105 + 11*a**6/50 - 8*a**5/15 + 8*a**4/15 - 7*a**2 - a. Factor c(p).
4*p*(p - 4)**2*(p - 1)**2/5
Let j(l) be the second derivative of 0*l**2 + 3/10*l**5 - 4/3*l**3 + 1/15*l**6 + 0*l**4 + 0 - 2*l. Factor j(s).
2*s*(s - 1)*(s + 2)**2
Let y(g) be the third derivative of 0 + 2/3*g**3 + 1/15*g**5 + 0*g + 1/3*g**4 + 7*g**2. What is z in y(z) = 0?
-1
Let d(p) = p**5 + p**4 + p. Let f(r) = r**5 + 4*r**4 + 4*r. Let q(l) = 4*d(l) - f(l). Let q(x) = 0. Calculate x.
0
Let f(k) be the first derivative of -k**8/240 - 19*k**7/840 - k**6/24 - k**5/120 + k**4/12 + k**3 - 9. Let l(n) be the third derivative of f(n). Factor l(c).
-(c + 1)**3*(7*c - 2)
Let z(v) = -4*v**4 + 56*v**3 + 20*v**2 - 48*v + 8. Let l(f) = -3*f**4 + 37*f**3 + 13*f**2 - 32*f + 5. Let b(s) = 8*l(s) - 5*z(s). Solve b(g) = 0.
-1, 0, 1, 4
Let l(m) be the first derivative of -5*m**4/4 - 5*m**3/3 + 10*m**2 + 20*m + 20. Factor l(y).
-5*(y - 2)*(y + 1)*(y + 2)
Let d(n) = n**3 - n**2 - 1. Let r be 1/(-2*(-3)/(-36)). Let t(k) = 7*k**3 - 9*k**2 + 2*k - 6. Let x(u) = r*d(u) + t(u). Solve x(q) = 0 for q.
0, 1, 2
Factor -3*g**2 + 3*g - 6*g + 15*g.
-3*g*(g - 4)
Let p be (8/(-3))/((-2)/(-6)). Let g(a) = -a**3 - 9*a**2 - 8*a. Let i be g(p). Factor 4/3*t - 4/3*t**3 + i*t**2 + 2/3*t**4 - 2/3.
2*(t - 1)**3*(t + 1)/3
Suppose -2*o + 2*w - 5 = -w, 0 = -4*o + 3*w + 5. Suppose 5*f - 17 = -h, -h = -o*h + 5*f - 7. Factor x + 0*x**2 + 0*x + x**h.
x*(x + 1)
Determine y, given that -4/5*y**3 - 4/5*y**2 + 4/5 + 4/5*y = 0.
-1, 1
Let i(y) be the third derivative of y**8/3360 - y**7/420 + y**6/180 - 2*y**3/3 - 7*y**2. Let j(z) be the first derivative of i(z). Factor j(p).
p**2*(p - 2)**2/2
Let -120*h - 3*h**2 - 6*h**3 + 48*h**2 + h**3 + 80 = 0. Calculate h.
1, 4
Find x such that 18/11*x**2 - 102/11*x**3 + 182/11*x**4 - 98/11*x**5 + 0 + 0*x = 0.
0, 3/7, 1
Determine g so that -2/9*g**2 - 2 - 4/3*g = 0.
-3
Let s(r) = r**4 - 24*r**3 + 25*r**2 - 6*r - 4. Let l(g) = g**4 + g**3 - g + 1. Let a(w) = -4*l(w) - s(w). Factor a(i).
-5*i*(i - 2)*(i - 1)**2
Factor 7*r**2 + 5 + 24*r - 9*r**2 - 77.
-2*(r - 6)**2
Factor 1/5*d**2 + 6/5 + d.
(d + 2)*(d + 3)/5
Factor 120*j - 13*j**2 + 80 + 18*j**2 + 10*j**4 - 30*j**3 - 5*j**4.
5*(j - 4)**2*(j + 1)**2
Factor -17*f**2 - 6 + 1 - 1 - 8*f + 15*f**2.
-2*(f + 1)*(f + 3)
Suppose 0*j - 1050 = 5*b + 4*j, -j - 423 = 2*b. Let o = -1494/7 - b. Determine x, given that -2/7 - 4/7*x**2 + 2/7*x**5 + 6/7*x**4 + o*x**3 - 6/7*x = 0.
-1, 1
Let t be (10 - 1)*(-6)/(-18). Factor -4*d + 4*d**4 + 52*d**2 - 3 + 52*d - 1 + 20 + 24*d**t.
4*(d + 1)**2*(d + 2)**2
Find f such that 0*f**4 - f**3 - 1/2*f**2 + 3/4*f + 1/4*f**5 + 1/2 = 0.
-1, 1, 2
Let g(a) be the first derivative of -3*a**4/28 + a**3/3 - 2*a**2/7 - 4. Factor g(u).
-u*(u - 1)*(3*u - 4)/7
Let n be 0/(6/51 - (-180)/(-85)). Let a(d) be the third derivative of 0*d + 1/36*d**4 - d**2 + 0 - 1/60*d**6 + n*d**3 - 1/45*d**5. Let a(q) = 0. What is q?
-1, 0, 1/3
Let j(v) be the third derivative of v**7/70 - 7*v**6/40 - v**5/20 + 7*v**4/8 - 41*v**2. Find z, given that j(z) = 0.
-1, 0, 1, 7
Suppose u - 5*v - 7 = 0, -u = -3*v - v - 6. Find d, given that 2/7*d + 0 + 18/7*d**3 - 12/7*d**u - 8/7*d**4 = 0.
0, 1/4, 1
Let h(l) be the third derivative of -l**8/840 - l**7/75 - 19*l**6/300 - l**5/6 - 4*l**4/15 - 4*l**3/15 + 19*l**2. Factor h(r).
-2*(r + 1)**3*(r + 2)**2/5
Let y(s) = s + 1. Let a(w) be the first derivative of 2*w**3/3 - 4*w**2 - 10*w - 4. Let j = 1 + -2. Let n(t) = j*a(t) - 12*y(t). Solve n(p) = 0.
-1
Factor 0 - 3*r**2 - 6/5*r.
-3*r*(5*r + 2)/5
Let s(z) be the first derivative of z**4/14 - 4*z**3/21 - 3*z**2/7 + 4. Factor s(u).
2*u*(u - 3)*(u + 1)/7
Suppose -21 + 21 + 2*l**3 + 4*l**2 - 12*l**4 = 0. What is l?
-1/2, 0, 2/3
Suppose a + a = 0. What is r in -r**2 + 3 - 4 + a - 2*r = 0?
-1
Suppose 4/7*c**2 + 0 + 2/7*c - 2/7*c**5 - 4/7*c**4 + 0*c**3 = 0. Calculate c.
-1, 0, 1
Let w = -5 - -6. Let g be (-2 - -3)*(w - -2). Factor 4*r - 2*r**2 - r + 2 - g*r.
-2*(r - 1)*(r + 1)
Let v(y) be the second derivative of -y**6/21 + 4*y**5/35 + 4*y**4/7 - 32*y**3/21 - 16*y**2/7 - y. Determine b, given that v(b) = 0.
-2, -2/5, 2
Let k(r) be the third derivative of 0*r**6 - 4*r**2 - 1/3*r**3 + 0*r + 1/15*r**5 + 0*r**4 + 0 - 1/105*r**7. Determine t, given that k(t) = 0.
-1, 1
Let b = -140 + 1401/10. Let j(v) be the second derivative of -1/3*v**3 - b*v**5 + 2*v + 0*v**2 - 1/3*v**4 + 0. Factor j(y).
-2*y*(y + 1)**2
Let z(y) be the third derivative of -y**6/160 + y**5/40 + 7*y**2. Suppose z(x) = 0. Calculate x.
0, 2
Let d(w) be the second derivative of -w**5/80 + w**4/24 - 7*w. Find p such that d(p) = 0.
0, 2
Let g = 3