 t**7/840 - t**5/240 - 2*t**3/3 - 3. Let q(y) be the third derivative of v(y). Factor q(u).
-u*(u - 1)**2*(u + 1)**2/2
Let i(t) be the second derivative of -3*t**5/80 - 3*t**4/16 + 13*t**3/8 + 45*t**2/8 + 8*t + 2. Factor i(f).
-3*(f - 3)*(f + 1)*(f + 5)/4
Let x(t) = -t**3 - 4*t**2 + 2. Let m be x(-4). Suppose -2*c - m*l - 8 = 0, 4*c + l - 4 + 8 = 0. Factor 5 - 3 + c*z**2 - 2*z**2.
-2*(z - 1)*(z + 1)
Let s(h) be the second derivative of h**5/50 - 2*h**4/15 + h**3/5 - 12*h. What is m in s(m) = 0?
0, 1, 3
Let p = -472 + 472. Factor 12/7*o**5 - 16/7*o**4 + 8/7*o**2 + 0*o + p - 4/7*o**3.
4*o**2*(o - 1)**2*(3*o + 2)/7
Factor 3/5*p**3 + 6/5*p**2 - 3/5*p - 6/5.
3*(p - 1)*(p + 1)*(p + 2)/5
Let k be (0/3)/2 + (-6)/(-18). Suppose -k*j + 1/3*j**3 + 0 - 1/3*j**4 + 1/3*j**2 = 0. What is j?
-1, 0, 1
Suppose -6/5 - 9/5*c**4 + 3/5*c**3 + 3*c**2 - 3/5*c = 0. Calculate c.
-1, -2/3, 1
Let x = 0 - -3. Suppose 4*y - 2*l = -l + 14, y + x*l = -3. Factor 3*a + 2*a**2 - 2*a - 2*a - a**y.
-a*(a - 1)**2
Let x be -2 + (3 - 2 - (-3 - -2)). Determine r so that 0 - 1/3*r**4 + 0*r**2 + 0*r + x*r**3 = 0.
0
Let x = 133 + -70. Let r = 253/4 - x. Suppose r*n**2 + 0 + 0*n - n**3 = 0. Calculate n.
0, 1/4
Let w(z) = -z**3 + 4*z**2 + 3*z + 4. Let a be w(5). Let r = 8 + a. Find g, given that 2*g**2 + g**2 + g**2 - 6*g**r = 0.
0
Let i(q) = -3*q**3 - 3*q**2 - 7*q. Let n(h) = -3*h**3 - 3*h**2 - 6*h. Let f(x) = 6*i(x) - 7*n(x). Factor f(t).
3*t**2*(t + 1)
Let n(s) = 3*s**2 - 3*s - 5. Let a(p) = p**2 - p - 1. Let w be (-4)/10 - 128/80. Let f(h) = w*n(h) + 10*a(h). Let f(q) = 0. Calculate q.
0, 1
Suppose 2*q = 3*i - 2*q - 13, 4*q + 4 = 0. Suppose 0 = 5*t, 2*t = 2*d + 2*d - 8. Let -16/3*m**5 - 10/3*m**d + 2/3*m + 4*m**i + 8/3*m**4 + 0 = 0. Calculate m.
-1, 0, 1/2
Suppose 2*r = -5*v + 8, -2*v + r = -3*v + 4. Let 8/7*o**4 + 32/7*o - 288/7*o**3 + v + 10*o**5 - 32/7*o**2 = 0. Calculate o.
-2, -2/5, 0, 2/7, 2
Suppose -4*h - 4*h = 0. Let x(t) be the second derivative of -t + h*t**2 + 1/12*t**3 + 0 - 1/16*t**4 + 1/80*t**5. Determine z, given that x(z) = 0.
0, 1, 2
Let y(l) = 6*l**5 + 24*l**4 + 38*l**3 - 2*l + 2. Let c(o) = -7*o**5 - 24*o**4 - 39*o**3 + 3*o - 3. Let m(z) = -2*c(z) - 3*y(z). Find j, given that m(j) = 0.
-3, 0
Let h(j) be the third derivative of -1/3*j**3 + 1/180*j**6 - 1/30*j**5 + 0*j + 1/12*j**4 + 0 - 2*j**2. Let g(v) be the first derivative of h(v). Factor g(t).
2*(t - 1)**2
Let b be 1/((-3)/6) + 2. Suppose 6*o - 4*o - 16 = b. Factor 2*a**2 - 2 - 2*a + 4*a**4 - o*a**2 + 2*a**3 + 4.
2*(a - 1)*(a + 1)**2*(2*a - 1)
Let c be -4 + 9 + 5/(-5). Let h(z) be the first derivative of 2/3*z**3 + 0*z - 5/4*z**c + 0*z**2 + 4. What is u in h(u) = 0?
0, 2/5
Let p(j) be the third derivative of 0 - 9*j**2 - 1/150*j**5 + 0*j + 1/525*j**7 + 1/30*j**4 - 1/150*j**6 + 0*j**3. Factor p(f).
2*f*(f - 2)*(f - 1)*(f + 1)/5
Let z be (-1)/(-4)*2*0. Let m be 2/6 - (-1 + 1). Factor u**3 - u**2 + z - 1/3*u**4 + m*u.
-u*(u - 1)**3/3
Suppose 2*t + 2*t + 3*j = -6, -10 = t + 5*j. Solve t*g**2 - 4/11*g + 2/11 + 4/11*g**3 - 2/11*g**4 = 0 for g.
-1, 1
Let f(b) be the first derivative of -b**4/14 + 3*b**2/7 + 4*b/7 + 7. Solve f(s) = 0 for s.
-1, 2
Let q(o) be the second derivative of -o**2 - 1/20*o**4 + 0 + 1/10*o**3 - 1/50*o**6 - 7/100*o**5 + o. Let y(s) be the first derivative of q(s). Factor y(v).
-3*(v + 1)**2*(4*v - 1)/5
Let h be 30/(-9)*12/(-10). Factor -2 - 4*d**3 - 3*d**4 + d**4 + 0*d**4 + h*d**4 + 4*d.
2*(d - 1)**3*(d + 1)
Let i(s) be the third derivative of s**5/30 + s**4/24 - s**2. Let a be i(1). Determine t, given that 0*t**2 + 6*t**3 + t**2 - t**a + 4*t**4 = 0.
-1, -1/4, 0
Let x(k) = 5*k**2 + k - 8. Let j(d) = -5*d**2 + 8. Let q(r) = 4*j(r) + 5*x(r). Let o(v) = 6*v**2 + 6*v - 9. Let m(i) = -2*o(i) + 3*q(i). Factor m(z).
3*(z - 1)*(z + 2)
Determine q, given that 7*q**4 + 4*q**2 + 4 + 31*q - 2*q**3 - 39*q - 25*q**2 = 0.
-1, 2/7, 2
Let k(y) = -y**2 - 4*y. Let c(w) = w**2 - w. Let d(h) = -3*c(h) + k(h). Solve d(f) = 0 for f.
-1/4, 0
Let k(r) be the first derivative of -r**4/4 + r**3 - 46. What is a in k(a) = 0?
0, 3
Let m = 41 - 18. Suppose 10*q**2 - m*q**4 + 4*q**2 + 7*q**4 + 7*q**5 - 8*q + 4*q**3 + 2 - 3*q = 0. What is q?
-1, 2/7, 1
Let s(v) be the second derivative of 1/10*v**5 + 3*v + 0*v**2 + 0 - 1/3*v**3 + 0*v**4. Factor s(l).
2*l*(l - 1)*(l + 1)
Let b(a) be the first derivative of -3*a**4/10 + 16*a**3/15 - a**2 + 53. Suppose b(n) = 0. Calculate n.
0, 1, 5/3
Let i = 11 + -21. Let b = i - -14. Find n such that 2*n**2 + 4*n**3 + 2*n**b + 5*n - 5*n = 0.
-1, 0
Let p(w) = w**2 - 5*w + 3. Let b be p(6). Let c be ((-4)/(-15))/(3/b). Factor 0*x + 14/5*x**3 + 0 + c*x**2.
2*x**2*(7*x + 2)/5
Let p(i) = -i**3 - 20*i**2 - 14*i + 100. Let t be p(-19). Find c, given that 2*c - 5/4*c**3 + 1 + 1/4*c**t + 1/4*c**2 - 1/4*c**4 = 0.
-1, 2
Let t(v) be the second derivative of -v**7/42 + v**6/30 + v**5/10 - v**4/6 - v**3/6 + v**2/2 - 10*v. Find l such that t(l) = 0.
-1, 1
Let z(r) = -8*r**3 - 2*r**2 + 4*r. Let u = -3 - -4. Let n be -2 + u - 0/(-4). Let m(t) = t**2. Let c(g) = n*z(g) + 12*m(g). What is b in c(b) = 0?
-2, 0, 1/4
Let q(p) = 2*p - 6. Let d be q(5). Suppose 19*y - 9 = -9. Let 2/9*l**d + y*l + 0 + 0*l**2 + 2/9*l**5 + 0*l**3 = 0. Calculate l.
-1, 0
Let r(b) = -b + 8. Let h be r(0). Let l be (2/4)/(h/80). Suppose -4/5*y**l - 2/5*y**2 + 0*y + 0 - 2*y**4 - 8/5*y**3 = 0. Calculate y.
-1, -1/2, 0
Let f(w) be the first derivative of 1/18*w**4 + 0*w - 2 + 0*w**3 - 1/9*w**2. Factor f(k).
2*k*(k - 1)*(k + 1)/9
Let y(c) be the third derivative of 1/4*c**4 + 0 - 1/20*c**5 - 7*c**2 + 0*c + 0*c**3 - 1/40*c**6. Suppose y(r) = 0. Calculate r.
-2, 0, 1
Let b = -8 + 11. Factor -2*j + 0*j**2 + 0*j + j**2 + b - 2.
(j - 1)**2
Suppose s = 5*u - 3*u + 14, -48 = -2*s - u. Suppose -2*d + s = 3*g - 6*d, -2*g + 16 = -3*d. Factor 0 + 1/2*r**3 + 0*r + 1/2*r**g.
r**2*(r + 1)/2
Find w, given that -3/2*w**4 + 0*w - 3/2*w**3 + 0*w**2 + 0 = 0.
-1, 0
Let o(l) be the second derivative of l**4/6 + l**3/3 + 5*l**2/2 + 3*l. Let t(z) = z**2 + z + 1. Let s(k) = -2*o(k) + 6*t(k). Determine g, given that s(g) = 0.
-2, 1
Let c(n) be the third derivative of -n**7/105 + 7*n**6/48 - 33*n**5/40 + 27*n**4/16 + 9*n**3/4 + n**2. Factor c(w).
-(w - 3)**3*(4*w + 1)/2
Let s(b) be the second derivative of 5*b**4/24 - b**3 + b**2 + 7*b. Let s(g) = 0. What is g?
2/5, 2
Let j(i) be the third derivative of -i**6/24 - i**5/12 + 5*i**4/12 + 12*i**2. Factor j(u).
-5*u*(u - 1)*(u + 2)
Let i(l) be the second derivative of l + 1/3*l**3 + 2/3*l**2 + 0 - 1/9*l**4 - 1/10*l**5. Determine u so that i(u) = 0.
-1, -2/3, 1
Determine c, given that 0*c + 50/7*c**2 + 2/7*c**4 + 0 - 20/7*c**3 = 0.
0, 5
Factor -16*p**2 + 40/3*p - 2/15*p**4 + 0 + 14/5*p**3.
-2*p*(p - 10)**2*(p - 1)/15
Let l(q) = 3*q**2 + q - 1. Let f be l(1). Let h = -7 + 9. Suppose -2*k**h + 2*k**3 + 4*k**2 - f*k**4 + k**5 - 1 + 2 - 3*k = 0. What is k?
-1, 1
Let -2*p**3 - 10 - 10*p - 12*p + 0*p**3 - 14*p**2 = 0. Calculate p.
-5, -1
Let h(x) = x. Let f be -1*(0/1 - 0). Let u be h(f). Let u*p + p**2 + 0*p**2 + p = 0. What is p?
-1, 0
Let k(v) be the first derivative of -v**4/20 + v**3/5 - 3*v**2/10 + v/5 - 7. Factor k(c).
-(c - 1)**3/5
Let q(j) be the third derivative of -j**9/80640 + j**8/13440 - j**7/6720 - j**5/30 - j**2. Let z(m) be the third derivative of q(m). Factor z(v).
-3*v*(v - 1)**2/4
Let f(g) be the second derivative of g**8/23520 + g**7/8820 - g**6/1260 + g**4/12 + 2*g. Let t(d) be the third derivative of f(d). What is p in t(p) = 0?
-2, 0, 1
Suppose 0 = -5*w + 2*w + 6. Let r(n) be the second derivative of 0*n**w + 0 + 3*n - 1/70*n**5 + 1/21*n**3 + 4/105*n**6 - 2/21*n**4. Find g such that r(g) = 0.
-1, 0, 1/4, 1
Let v(z) be the first derivative of -1/4*z**2 + 2/5*z**5 - 3/4*z**4 - 1/12*z**6 + 1 + 0*z + 2/3*z**3. Suppose v(m) = 0. What is m?
0, 1
Suppose -g - 49 = 9. Let k = -170/3 - g. Factor -1/3*r**2 + 4/3*r - k.
-(r - 2)**2/3
Let c(f) be the first derivative of -10*f**6/3 + 8*f**5/5 - 27. Factor c(o).
-4*o**4*(5*o - 2)
Let o(j) = -12*j - 46. Let m be o(-4). Let g be (-42)/(-18) + (-4)/(-6). Find l such that 0 + 1/2*l + 1/2*l**g - l**m = 0.
0, 1
Let y be (3 - (-69)/(-21))/((-1)/7). Factor 0*n - 25/3*n**5 + 15*n**4 + 0 + 4/3*n**y - 8*n**3.
-n**2*(n - 1)*(5*n - 2)**2/3
Suppose g + 4*g = 10. Suppose 3*h = -2*f, g