4*(a - 1)**3*(a + 1)**2
Let i(s) be the first derivative of -4*s**3/3 - 4*s**2 + 12*s - 26. Factor i(k).
-4*(k - 1)*(k + 3)
Suppose 4*y + 13 = z, 4*z = 6*y - 2*y + 28. Suppose -5*l = 2*d, -d = z*l + 4*d. Factor 5*t**5 + l*t**5 - 6*t**5 + 3*t**5 - 2*t**3.
2*t**3*(t - 1)*(t + 1)
Let x(t) = 8 + 4*t - 3 - 8 - 2*t**2 + t**3. Let z be x(2). Factor 0*n + 0*n**2 + 0 + 1/2*n**3 - 2*n**z + 3/2*n**4.
-n**3*(n - 1)*(4*n + 1)/2
Suppose 0*z + 0*z**3 + 0 + 1/4*z**4 - 1/4*z**2 = 0. What is z?
-1, 0, 1
Let u(i) = i**3 + 4*i**2 - 3*i + 4. Let n be u(-5). Let b(f) = -f - 2. Let l be b(n). Factor 1/3*j**3 - 8/3 + l*j - 2*j**2.
(j - 2)**3/3
Let a(x) be the third derivative of 0 - 1/90*x**5 - 5*x**2 + 0*x - 1/36*x**4 + 0*x**3. Factor a(l).
-2*l*(l + 1)/3
Let o(c) be the second derivative of -c**6/150 - c**5/25 - c**4/30 + 2*c**3/15 + 3*c**2/10 + 2*c. Factor o(g).
-(g - 1)*(g + 1)**2*(g + 3)/5
Suppose 4*w = 4 + 4. Let a = 2 + w. Factor -2*n**2 + a*n**2 - 1 - n**2.
(n - 1)*(n + 1)
Let i(b) be the first derivative of -b**5 + 5*b**4/4 + 10. Factor i(p).
-5*p**3*(p - 1)
Suppose -y - 4 = 4*y + p, -5*p - 20 = -y. Let u(w) be the third derivative of y*w**4 + 0*w + 0 + 0*w**3 - 1/360*w**5 + 4*w**2. Factor u(s).
-s**2/6
Let w(d) be the first derivative of 0*d**3 - 1/20*d**5 - 4 - 1/4*d**2 + 1/4*d + 1/8*d**4. Let w(l) = 0. Calculate l.
-1, 1
Let u(i) = i**3 + 9*i**2 + 6*i - 17. Let r be u(-8). Let f be r + 4 - (2 + 1). Factor x**2 + f + 2/3*x - 1/3*x**4 + 0*x**3.
-x*(x - 2)*(x + 1)**2/3
Factor 0*s - 1/5*s**3 + 0 - 1/5*s**2.
-s**2*(s + 1)/5
Let l(y) = 17*y - 1. Let w be l(1). Let f be (-2)/7*(-28)/w. Factor 0 - 3/2*o**2 - 1/2*o**4 - f*o - 3/2*o**3.
-o*(o + 1)**3/2
Let j(t) = -18*t + 9. Let x be j(-4). Let c be x/18 + 2/(-4). Factor -2/3*q**3 - 2/3*q**2 + 0 - 2/9*q - 2/9*q**c.
-2*q*(q + 1)**3/9
Factor -5*k - 299*k**4 + 0*k**3 + 5*k**2 + 294*k**4 + 5*k**3.
-5*k*(k - 1)**2*(k + 1)
Suppose 4 = -2*o + 4. Determine a so that -2/5*a**4 + 0 - 1/5*a**5 + 0*a - 1/5*a**3 + o*a**2 = 0.
-1, 0
Let r(c) be the first derivative of c**3/21 - 3*c**2/14 - 4*c/7 - 2. Find n, given that r(n) = 0.
-1, 4
Find q, given that -33*q**2 + 3 + 18*q - 6*q**2 + 110*q**2 - 35*q**2 + 24*q**3 = 0.
-1/2
Determine d so that 8/5 + 2/5*d**4 + 6/5*d**3 - 2*d**2 - 6/5*d = 0.
-4, -1, 1
Let o(u) be the second derivative of -1/15*u**3 - 1/150*u**6 + 1/50*u**5 + 0*u**4 + 0 + 4*u + 1/10*u**2. Factor o(z).
-(z - 1)**3*(z + 1)/5
Let h(b) = -4*b**2 + 12*b + 22. Let t(s) = -5*s**2 + 11*s + 21. Let m(k) = -7*h(k) + 6*t(k). Factor m(a).
-2*(a + 2)*(a + 7)
Let w be -6*(2/(-30))/((-72)/(-40)). Solve 0*a - w*a**2 + 2/9 = 0 for a.
-1, 1
Let s be 143/55 - (2/10 - 0). What is g in s*g**2 + 8/5*g**3 + 8/5*g + 2/5*g**4 + 2/5 = 0?
-1
Let j(q) = -q - 4. Let c be j(-7). Suppose 0 = -k - 1 + 4. Determine z so that -k*z**4 + 3*z**3 - 3*z**4 - 9*z**c - 2*z**5 - 2*z**2 = 0.
-1, 0
Let t(f) be the third derivative of f**7/10080 + f**6/2880 - f**4/6 - 4*f**2. Let d(s) be the second derivative of t(s). Factor d(k).
k*(k + 1)/4
Let d(r) be the first derivative of 3/8*r**2 + 1/4*r**3 + 0*r - 3. Factor d(i).
3*i*(i + 1)/4
Let y(w) be the first derivative of -4*w**5/15 + 2*w**4/3 - 4*w**3/9 - 7. Factor y(o).
-4*o**2*(o - 1)**2/3
Let p(y) be the second derivative of -y**7/1680 - y**6/720 + y**5/120 - y**3/2 - 3*y. Let c(f) be the second derivative of p(f). Determine s so that c(s) = 0.
-2, 0, 1
Find r, given that -16*r**3 + 4 + 8 + 10*r**4 - 18*r**2 + 16*r - 4 = 0.
-1, -2/5, 1, 2
Let u = -89/80 - -17/15. Let a(y) be the second derivative of -2*y - u*y**4 + 0 - 1/8*y**2 + 1/12*y**3. Let a(q) = 0. What is q?
1
Let j(s) be the third derivative of 0*s**3 - 5*s**2 + 0*s - 1/24*s**4 + 0 + 1/60*s**5. Factor j(b).
b*(b - 1)
Let x(c) = -45*c**4 + 510*c**3 - 1262*c**2 - 1017*c - 180. Let w(f) = 90*f**4 - 1020*f**3 + 2525*f**2 + 2035*f + 360. Let h(s) = 3*w(s) + 5*x(s). Factor h(p).
5*(p - 6)**2*(3*p + 1)**2
Let p(h) be the first derivative of -h**4/24 - 17*h**3/18 - 21*h**2/4 + 27*h/2 - 14. Factor p(r).
-(r - 1)*(r + 9)**2/6
Let h(n) = -21*n**4 + 39*n**3 - 39*n**2 + 12*n. Let i(z) = z**5 - 20*z**4 + 39*z**3 - 38*z**2 + 12*z. Let c(l) = 2*h(l) - 3*i(l). Factor c(v).
-3*v*(v - 2)**2*(v - 1)**2
Let l = -9 - 189. Let q be (-360)/l + (-2)/(-11). Find x, given that 9/2*x**4 + 0*x - 15/2*x**3 + 0 + 3*x**q = 0.
0, 2/3, 1
Let c = -5 + 7. Factor 0 + 0 - 4*i**2 - c*i + 2*i**5 + 4*i**4.
2*i*(i - 1)*(i + 1)**3
Let j(a) be the second derivative of -1/70*a**5 + 0*a**2 + 0*a**3 + 0 + a + 1/42*a**4. Factor j(l).
-2*l**2*(l - 1)/7
Let z(x) be the first derivative of 0*x + 0*x**4 + 3 + 0*x**2 - 1/25*x**5 + 1/15*x**3. Let z(v) = 0. What is v?
-1, 0, 1
Let i(y) = -28*y**2 + 24*y + 28. Let t(f) = -f**2 + f + 1. Let u(j) = -i(j) + 24*t(j). Factor u(d).
4*(d - 1)*(d + 1)
Let n(a) be the first derivative of a**5/15 - 29*a**4/12 + 30*a**3 - 350*a**2/3 - 1000*a/3 + 60. Factor n(d).
(d - 10)**3*(d + 1)/3
Suppose 4*v = 9 + 3. Factor -2*y**2 + 2*y**2 - 3*y**2 + v.
-3*(y - 1)*(y + 1)
Let w(s) = s - 3. Let q be w(5). Factor 1/2*z**4 + 3*z**q + 1/2 - 2*z - 2*z**3.
(z - 1)**4/2
Let q = 14 - 32. Let f = q + 21. Factor -4/3*t**2 + 2/3*t**5 + 4/3*t**4 + 0*t**f - 2/3*t + 0.
2*t*(t - 1)*(t + 1)**3/3
Let b be ((-2)/(-63))/(70/21). Let h(v) be the third derivative of 1/6*v**4 + 0 + 1/3*v**3 - b*v**7 - 1/30*v**6 + 0*v**5 + 0*v + v**2. Factor h(j).
-2*(j - 1)*(j + 1)**3
Let n(q) be the first derivative of 1/130*q**5 + 4 - 4/13*q**2 + 1/26*q**4 + 0*q**3 + q. Let k(v) be the first derivative of n(v). Factor k(g).
2*(g - 1)*(g + 2)**2/13
Let r(g) be the second derivative of -g**4/3 + 10*g**3/3 + 12*g**2 - 16*g + 1. Factor r(l).
-4*(l - 6)*(l + 1)
Let s = 20/3 - 19/3. Let c(z) be the third derivative of 0 - s*z**3 - 1/120*z**6 - 2*z**2 + 1/24*z**4 - 1/210*z**7 + 1/20*z**5 + 0*z. Solve c(x) = 0 for x.
-2, -1, 1
Let l(w) be the third derivative of -w**5/480 - w**4/48 - w**3/16 - 8*w**2. Let l(z) = 0. Calculate z.
-3, -1
Factor -24*v**3 - 91*v**2 - 5*v**2 - 128*v - 13*v**4 + 11*v**4.
-2*v*(v + 4)**3
Suppose 22 = 14*o - 3*o. Let g(h) be the third derivative of 2/15*h**5 + 0 + 5/12*h**4 + 1/60*h**6 + 0*h + 2/3*h**3 - 3*h**o. Solve g(i) = 0 for i.
-2, -1
Factor 13*f**2 - 5*f**4 - 32 - 4*f**2 + 3*f**4 + 7*f**2.
-2*(f - 2)**2*(f + 2)**2
Suppose -3*i - 9 = -6*i. Let t = i + -1. Find f, given that -10/11*f**t + 6/11*f - 6/11*f**3 + 8/11*f**4 + 2/11 = 0.
-1, -1/4, 1
Let d(c) be the third derivative of -2/21*c**3 + 0*c - 3/28*c**4 - c**2 - 1/30*c**5 + 0. What is h in d(h) = 0?
-1, -2/7
Let r(p) be the first derivative of 4/5*p**2 + 1/2*p**4 + 0*p + 16/15*p**3 + 2/25*p**5 - 3. Suppose r(w) = 0. What is w?
-2, -1, 0
Let g(v) be the third derivative of 2*v**7/105 - 11*v**6/40 - 7*v**5/15 + 3*v**4/8 + 33*v**2. Suppose g(w) = 0. Calculate w.
-1, 0, 1/4, 9
Let p be (9 + -9)*(-3)/6*-1. Let f be (-312)/(-189) - (-4)/(-18). Let -f*w**2 + p - 4/7*w = 0. Calculate w.
-2/5, 0
Let b(z) be the third derivative of -z**9/24192 + z**8/3360 - z**7/1120 + z**6/720 - 3*z**5/20 + 3*z**2. Let l(h) be the third derivative of b(h). Factor l(u).
-(u - 1)**2*(5*u - 2)/2
Let z = -3 + 3. Suppose z = 2*j - 0*j. Factor -2/7*b**2 + 2/7*b + j.
-2*b*(b - 1)/7
Let x(d) = -14*d**2 - 21*d - 6. Let h(t) = -6 + 5*t**2 - 10*t + 6*t - 17*t - 20*t**2. Let k(v) = 5*h(v) - 6*x(v). Factor k(m).
3*(m + 2)*(3*m + 1)
Factor 4/3*r**2 + r - 1/3.
(r + 1)*(4*r - 1)/3
Let a(f) be the first derivative of f**5/5 + f**4/2 + f**3/3 + 8. Factor a(t).
t**2*(t + 1)**2
Let h(z) be the first derivative of 7/6*z**2 - 2/3*z - 5/9*z**3 - 2. Factor h(s).
-(s - 1)*(5*s - 2)/3
Let p(i) = -3*i**4 - 2*i**3 + 4*i**2 + 2*i - 3. Let n(f) = 3 - 3 - 1. Let s(o) = -2*n(o) + p(o). Factor s(g).
-(g - 1)*(g + 1)**2*(3*g - 1)
Let a(b) = b**3 - b**2 - b + 1. Let i(v) = -10*v**3 + 16*v**2 + 4*v - 28. Let g(d) = 12*a(d) + i(d). Factor g(k).
2*(k - 2)*(k + 2)**2
Let o(d) = d**2 - 9*d - 7. Let j be o(10). Let 1/2*c**j - 1/2 + 1/2*c**2 - 1/2*c = 0. What is c?
-1, 1
Suppose -2*g - g + 4*w = -5, 3 = 2*g - 3*w. Suppose 3/5*o**2 - 3/5*o**g + 6/5*o + 0 = 0. What is o?
-1, 0, 2
Solve 3/2 + 1/4*y**2 - 7/4*y = 0.
1, 6
Let u(t) = t**3 + 3*t**2 + 4. Let d be u(-3). Suppose -1 - d + 5 - 3*b**3 - 3*b**2 = 0. What is b?
-1, 0
Let z(n) be the second derivative of 0*n**2 - 1/15*n**6 + 0 + 0*n**3 + n + 1/12*n**4