 3*b. Let p(r) be the first derivative of w(r). Factor p(c).
3*c*(c - 2)*(c - 1)*(4*c + 1)
Suppose 6*b + 27 = 3*b. Let m = -5 - b. Suppose t**5 - 2*t**m + 3*t**4 - 2*t**5 = 0. Calculate t.
0, 1
Let p = -1178/9 + 131. Let a(g) be the third derivative of 1/540*g**6 + 0 + 1/45*g**5 + 0*g + 3*g**2 + 8/27*g**3 + p*g**4. Factor a(d).
2*(d + 2)**3/9
Let m(p) = -p**2 + 5*p - 1. Let z = -10 + 14. Let v be m(z). Determine o, given that 63*o**5 + 75/4*o**4 + 27/4*o**2 - 1/2 + 9/4*o - 161/4*o**v = 0.
-1, -1/4, 2/7, 1/3
Let i(v) be the first derivative of 3/14*v**4 - 3/7*v**2 + 2/21*v**3 + 0*v - 2/35*v**5 + 4. Let i(n) = 0. What is n?
-1, 0, 1, 3
Let p be 2*(25/2 - 0). Let u be 40/p - 4/(-10). Factor 0*j**u - 1/2*j**3 + 0*j + 0.
-j**3/2
Let x(u) be the second derivative of -3*u**5/20 - u**4/6 - u**3/3 + u**2 - 2*u. Let g(b) = -b**3. Let h(n) = 5*g(n) - x(n). Factor h(w).
-2*(w - 1)**2*(w + 1)
Let o = 11 - 8. Suppose -2*l = 2*j - 10, -4*j + 12 = o*l - 5. Factor -5 + 2*p**2 + 5 + 2*p**l.
2*p**2*(p + 1)
Let s = -126 - -507/4. Suppose s*w**2 + 0 - 3/4*w = 0. Calculate w.
0, 1
Let r(p) be the third derivative of 5*p**8/84 - p**7/6 - p**6/4 + 7*p**5/12 + 5*p**4/12 - 13*p**2. Find z such that r(z) = 0.
-1, -1/4, 0, 1, 2
Let j(m) = 10*m**3 - 62*m**2 + 117*m - 45. Let f(b) = -20*b**3 + 125*b**2 - 235*b + 90. Let c(g) = 3*f(g) + 5*j(g). Determine x, given that c(x) = 0.
1/2, 3
Let i(w) be the third derivative of -1/210*w**7 + 0 - 1/60*w**5 - 1/60*w**6 + 0*w + 0*w**3 + 0*w**4 + 4*w**2. Find p such that i(p) = 0.
-1, 0
Let h(a) = -2*a**3 - 11*a. Let r be h(0). Factor r + 1/3*c**5 + 0*c - 4/3*c**2 + 0*c**3 + c**4.
c**2*(c - 1)*(c + 2)**2/3
Let a(c) be the third derivative of -c**6/540 + c**5/270 - c**2. Suppose a(f) = 0. What is f?
0, 1
Let w be (-3)/(-80)*(145/18 + -8). Let m(o) be the third derivative of -w*o**6 + 0*o**5 - 1/12*o**3 + 0 - o**2 + 0*o + 1/32*o**4. Factor m(v).
-(v - 1)**2*(v + 2)/4
Let h = -269 + 8071/30. Let z(n) be the third derivative of -2/45*n**5 + 0 + 0*n - h*n**6 - 4/315*n**7 + n**2 - 1/36*n**4 - 1/504*n**8 + 0*n**3. Factor z(y).
-2*y*(y + 1)**4/3
Let c = 7553/9 - 838. Let y(w) be the second derivative of 13/18*w**4 - 2/15*w**5 + 0 + 3*w + 2/3*w**2 - c*w**3. Factor y(d).
-2*(d - 2)*(d - 1)*(4*d - 1)/3
Determine d, given that 3*d**3 - 2*d**2 + 8*d**2 + 0*d**2 = 0.
-2, 0
Let t(d) = -7*d**3 - 5*d**2 + 25*d - 16. Let p(y) = 8*y**3 + 4*y**2 - 24*y + 16. Let i(a) = -3*p(a) - 4*t(a). Factor i(n).
4*(n - 1)**2*(n + 4)
Let p(w) = 5*w**4 + 5*w**3 + 3*w**2 + w + 2. Let u = 17 + -11. Let i(m) = m**4 - m**3 - m**2 + 1. Let t(x) = u*i(x) - 3*p(x). Factor t(b).
-3*b*(b + 1)**2*(3*b + 1)
Let g(b) = -b**4 - b**3 + 1. Let j(l) = 2*l**4 + l**3 + 2*l - 2. Let m(x) = 3*g(x) + j(x). Find a such that m(a) = 0.
-1, 1
Let u(q) be the second derivative of -49*q**5/90 + 77*q**4/54 - 32*q**3/27 + 4*q**2/9 + 15*q. Factor u(l).
-2*(l - 1)*(7*l - 2)**2/9
Find t such that -8/19 + 2/19*t**2 - 6/19*t = 0.
-1, 4
Let k(r) be the first derivative of -4*r**3/3 + 4*r**2 - 4*r + 25. Factor k(g).
-4*(g - 1)**2
Let k(z) be the third derivative of -7/96*z**4 + 0 + 3*z**2 - 1/30*z**5 + 0*z - 1/160*z**6 - 1/12*z**3. Factor k(s).
-(s + 1)**2*(3*s + 2)/4
Let m = 488/7 + 53/14. Suppose -90*v**2 + 0 - 189*v**3 - 12*v - m*v**4 = 0. Calculate v.
-2, -2/7, 0
Let r(o) = -o**4 + o**3 + o**2 - o. Let a(z) = -14*z**4 + 4*z**3 + 8*z**2 - 4*z + 6. Let p(d) = -a(d) + 12*r(d). Solve p(v) = 0 for v.
-3, -1, 1
Let x(p) = p**2. Let k(b) = -5*b**2 + 7*b + 2. Let t(u) = k(u) + 4*x(u). Let s be t(7). Solve 0 + 2/13*v**s + 0*v = 0 for v.
0
Let i(v) be the first derivative of -5*v**3/3 - 9*v**2 + 8*v - 14. Determine s, given that i(s) = 0.
-4, 2/5
Let q(f) be the third derivative of f**5/270 - f**4/9 + 4*f**3/3 + 16*f**2. Factor q(z).
2*(z - 6)**2/9
Let m(f) = 13*f**4 - 19*f**3 + 32*f. Let j(v) = -6*v**4 + 10*v**3 - 16*v. Let x(w) = -5*j(w) - 2*m(w). Solve x(s) = 0.
-1, 0, 2
Let v = -48 + 51. Let z(i) be the second derivative of 0 - 1/9*i**6 + 0*i**4 + 1/15*i**5 + 3*i + 0*i**v + 0*i**2. Suppose z(t) = 0. Calculate t.
0, 2/5
Let p be 1 - ((-35)/25 - 2/(-5)). Factor 6/5*g + 2/5*g**p + 4/5.
2*(g + 1)*(g + 2)/5
Find g such that -5/3*g**2 + 5/3*g**4 - 2/3*g + 3*g**3 + 0 - 7/3*g**5 = 0.
-1, -2/7, 0, 1
Suppose 0 = -4*h + 12, -w - 3*w = -2*h - 14. Suppose -w*b + 5 = u, -4*b + 46 = -5*u + 13. Let 1/4*x**b + 1/4 + 1/2*x = 0. Calculate x.
-1
Find h, given that -6*h**3 - 16*h - 9*h**3 + 25*h**2 - h**5 + 4 + 7*h**4 - 4*h**3 = 0.
1, 2
Suppose 3/5*k**4 + 1/5*k - 3/5*k**2 - 1/5*k**3 + 0 = 0. What is k?
-1, 0, 1/3, 1
Let v(i) be the first derivative of i**6/360 + i**5/40 + i**4/12 - i**3/3 - 1. Let j(q) be the third derivative of v(q). Determine a, given that j(a) = 0.
-2, -1
Let k(y) be the second derivative of -y**7/18 - y**6/10 + y**5/12 + y**4/4 + y**3/9 - 23*y. Suppose k(b) = 0. Calculate b.
-1, -2/7, 0, 1
Factor 0*j**4 - 10/3*j**3 + 5/3*j**5 + 0*j**2 + 5/3*j + 0.
5*j*(j - 1)**2*(j + 1)**2/3
Let u(r) be the second derivative of -r**4/12 - 5*r**3/24 - r**2/8 - 25*r. Factor u(b).
-(b + 1)*(4*b + 1)/4
Let w = 801/2 + -400. Solve -3/4*c + 0*c**2 - w + 1/4*c**3 = 0 for c.
-1, 2
Let a be (-13)/312*(1 + (-16)/14). Let p(q) be the third derivative of 0*q**3 - 1/1470*q**7 + 0*q + 1/420*q**5 - a*q**4 + 0 + 1/840*q**6 - q**2. Factor p(s).
-s*(s - 1)**2*(s + 1)/7
Let x(z) = z**3 + 9*z**2 - 12*z - 13. Let i be x(-10). Let 0*s - 6*s + 2*s**2 - 3*s**3 + i*s**2 = 0. What is s?
0, 1, 2
Let u be 84/462 + (-68)/11 + 8. Factor 0*m - 1/2*m**u - 1/2*m**4 - m**3 + 0.
-m**2*(m + 1)**2/2
Suppose -b - 5 + 13 = 0. Suppose 0 = -2*p + b, 22 = u + 5*p. Solve 9/4*k**3 + 3/2*k**u - 3/2 - 9/4*k = 0 for k.
-1, -2/3, 1
Let b(j) = -j**3 - 3*j**2 - 2*j + 2. Let s be b(-2). Let r(c) = c**2 + 1. Let h be r(s). Factor -3*t - 4*t**h + t + 2*t**5 + 4*t**3.
-2*t*(t - 1)**2*(t + 1)**2
Let x(q) be the first derivative of q**5/5 + 2*q**4 + 8*q**3 + 16*q**2 + 16*q + 1. Factor x(d).
(d + 2)**4
Let t(q) be the first derivative of 3*q**6/4 + 3*q**5/2 - 3*q**4/2 - 2*q**3 - 16. Suppose t(u) = 0. What is u?
-2, -2/3, 0, 1
Let k = 2/333 - -374/11655. Let r = 34/105 - k. What is u in 10/7*u**2 - r - 6/7*u**3 + 6/7*u - 8/7*u**4 = 0?
-1, 1/4, 1
Factor 2/5*z**4 - 2/5 - 4/5*z**3 + 4/5*z + 0*z**2.
2*(z - 1)**3*(z + 1)/5
Let r be 25*(-5)/(50/(-8)). Suppose 4*o**2 - 24*o - 7 + r + 23 = 0. What is o?
3
Let c(g) be the first derivative of -3*g**5/10 - 3*g**4/4 + g**3/2 + 3*g**2/2 + 2. Factor c(m).
-3*m*(m - 1)*(m + 1)*(m + 2)/2
Suppose -3*t + 3/2*t**2 + 3/2 = 0. What is t?
1
Let i(q) = 2*q**4 + 6*q**3 - 6*q**2 - 2*q + 4. Let d(p) = p**3 - p**2 + 1. Let w(a) = -4*d(a) + i(a). Let w(j) = 0. Calculate j.
-1, 0, 1
Let u(f) be the second derivative of 0*f**2 + 0 + 0*f**3 - 5*f - 1/12*f**4. Let u(m) = 0. Calculate m.
0
Let x(k) = 21*k**4 + 36*k**3 + 29*k**2 + 9*k + 5. Let n(h) = -22*h**4 - 36*h**3 - 30*h**2 - 10*h - 6. Let j(i) = 5*n(i) + 6*x(i). Factor j(z).
4*z*(z + 1)**2*(4*z + 1)
Let b(p) be the first derivative of -22/5*p**5 + 2*p**6 + 0*p - 5 + 1/8*p**2 - p**3 + 51/16*p**4. Solve b(l) = 0 for l.
0, 1/4, 1/3, 1
Let t(a) be the first derivative of 0*a + 1/4*a**4 + 2/3*a**3 + 1/2*a**2 + 3. What is d in t(d) = 0?
-1, 0
Factor -2 - 3*t**3 + 6*t**2 + 3*t**2 - 2 - 8.
-3*(t - 2)**2*(t + 1)
Let m be (-1 - -2) + 1/3. Let r = -106/39 + 44/13. Suppose -m*g + 2/3*g**2 + r = 0. What is g?
1
Suppose -49*p = -52*p + 12. Let l(b) be the third derivative of -1/80*b**6 + 1/140*b**7 - 1/40*b**5 + 5*b**2 + 0*b**3 + 0*b + 1/16*b**p + 0. Solve l(y) = 0.
-1, 0, 1
Suppose 4 = y - 1. Suppose y*w + 10 = 2*o, 0 = 2*w + 2*w. Factor -5*j**2 - 2*j - 3*j**2 - 8*j**4 + 6*j**5 - 8*j**o - 12*j**3.
-2*j*(j + 1)**4
Let -395/2*p**3 - 35/2*p**5 - 10*p - 20 + 100*p**4 + 145*p**2 = 0. Calculate p.
-2/7, 1, 2
Let y = -2 + 5. Let u(l) be the first derivative of -l**4 - 1 + 1/3*l**6 + 0*l**y + 0*l**5 + 0*l + l**2. What is g in u(g) = 0?
-1, 0, 1
Let x(d) be the first derivative of 4*d**4 + 16*d**3/3 + 2*d**2 + 10. What is k in x(k) = 0?
-1/2, 0
Let r(z) = -z**3 - 12*z**2 + 7*z + 7. Let m(h) be the first derivative of h**4/4 + 8*h**3/3 - 5*h**2/2 - 5*h + 6. Let u(t) = -7*m(t) - 5*r(t). Factor u(s).
-2*s**2*(s - 2)
Let b(l) be the second derivative of 0 - 3*l + 0*l**3 - 1/12*l**4 + 0*l**2. Determine x, given that b(x) = 0.
0
L