k - 1)*(k + 1)**3/9
Factor 0*u**2 + 0 + 0*u + 5/6*u**3.
5*u**3/6
Let a(n) = -3*n - 4. Let l be a(-2). Let h = 5 - l. Factor -2/7*f - 4/7*f**2 - 2/7*f**h + 0.
-2*f*(f + 1)**2/7
Factor 2/5*a**3 - 4/5*a - 2/5*a**2 + 0.
2*a*(a - 2)*(a + 1)/5
Find i such that -3*i**4 + 15*i**3 + i**4 - 3*i**4 = 0.
0, 3
Suppose 0 = -2*t + t - 2. Let y be (t/10)/((-28)/35). Factor y*n**4 + 1/4*n**3 + 0 + 0*n**2 + 0*n.
n**3*(n + 1)/4
Suppose -3*v + r = 2*r - 5, 0 = r + 1. Suppose -2/5*l**3 + 2/5*l**v + 0*l + 0 = 0. Calculate l.
0, 1
Let p(f) = f**4 + f**3 + f**2 + f - 1. Let a(k) = -9*k**4 - 6*k - 21*k**2 + 3 + 9 - 12*k**3 + 0*k**2. Let o(w) = a(w) + 12*p(w). Factor o(m).
3*m*(m - 1)**2*(m + 2)
Let u(s) be the second derivative of -s + 0 + 0*s**2 + 1/9*s**3 - 1/18*s**4. Let u(g) = 0. What is g?
0, 1
Let w(z) be the first derivative of 25*z**3/21 + 10*z**2/7 + 4*z/7 - 12. Factor w(c).
(5*c + 2)**2/7
Factor 0*m - 2*m**3 - 2/5*m**5 + 4/5*m**2 + 0 + 8/5*m**4.
-2*m**2*(m - 2)*(m - 1)**2/5
Suppose -2*o + o = 0. Let s(v) be the third derivative of 0*v**4 + 1/1155*v**7 - v**2 + 0 + 0*v**6 + 0*v - 1/330*v**5 + o*v**3. Solve s(c) = 0.
-1, 0, 1
Let s(f) = 12*f**2 - 21*f. Suppose -36 = -2*c + 6*c. Let v(u) = -3*u**2 + 5*u. Let m(t) = c*v(t) - 2*s(t). Factor m(b).
3*b*(b - 1)
Let y be ((-160)/(-36) + -4)/(4/18). Factor 6/5*r**3 - 3/5*r**y - 3/5*r**4 + 0*r + 0.
-3*r**2*(r - 1)**2/5
Let -3/7*r**2 - 6/7*r**3 + 0 + 3/7*r = 0. What is r?
-1, 0, 1/2
Let c(o) be the first derivative of -2*o**3/9 + 8*o**2/3 - 14*o/3 - 20. Find i, given that c(i) = 0.
1, 7
Let l(i) = i**2 - i - 1. Let t(n) = -3*n**2 + 3*n + 2. Let j(c) = 2*l(c) + t(c). Factor j(y).
-y*(y - 1)
Let g(w) = 8*w**2 + 38*w + 128. Let p(z) = z**2 + z. Let v(n) = g(n) - 6*p(n). Factor v(b).
2*(b + 8)**2
Let w(o) = 1. Let b(j) = j + 1. Let n(y) = -b(y) - 5*w(y). Let r be n(-6). Factor r + 1/3*u**2 + 2/3*u.
u*(u + 2)/3
Let r(b) be the second derivative of -b**4/6 - b**3 + 4*b**2 - 38*b. Factor r(p).
-2*(p - 1)*(p + 4)
Let c(n) = -n + 9. Let g be c(7). Factor 1 + 0*a**2 + a**2 - 2*a + 2*a**g - 2*a**2.
(a - 1)**2
Let w(p) be the second derivative of 5*p**4/12 - p. Determine y, given that w(y) = 0.
0
Factor -4*c**4 + 10*c + 8*c**3 - 20*c**2 + 8*c**3 - 2*c.
-4*c*(c - 2)*(c - 1)**2
Let k(y) = y**2 + 2*y. Let u be k(-3). Factor 8*z**3 + 2*z**3 - 4*z + u*z**4 - 7*z**3 - 2*z**4.
z*(z - 1)*(z + 2)**2
Factor -40 + 82 + 7*j - 5*j**2 - 44.
-(j - 1)*(5*j - 2)
Let q be 0 - 1 - (-7 - -3). Suppose -h - q*v = -5 - 0, 3*v + 3 = 3*h. Factor 0*l + 0 + 2/7*l**h.
2*l**2/7
Suppose 18*o - 13*o - 5 = 0. Let w be o/2*0 - -2. Factor w*f + 1/2*f**2 + 2.
(f + 2)**2/2
Let q(l) be the second derivative of -l**4/3 + 8*l**3/9 - 2*l**2/3 + 6*l. Factor q(x).
-4*(x - 1)*(3*x - 1)/3
Let k(v) be the second derivative of -v**8/420 - v**7/140 - v**6/180 - 2*v**3/3 - 4*v. Let z(g) be the second derivative of k(g). Solve z(f) = 0 for f.
-1, -1/2, 0
Let n(d) be the first derivative of -3 + 1/3*d**3 + 1/2*d**2 - 2*d. Factor n(f).
(f - 1)*(f + 2)
Let s(n) be the first derivative of 1/2*n**3 - 3/2*n**2 - 6 + 3/2*n. Factor s(c).
3*(c - 1)**2/2
Let d(p) be the second derivative of p**4/3 - 2*p**3 - 8*p**2 + 36*p. Find i, given that d(i) = 0.
-1, 4
Let h(y) be the third derivative of -1/504*y**8 - 1/36*y**4 + 0*y + 1/90*y**6 + 1/9*y**3 + 1/315*y**7 + 0 + 3*y**2 - 1/45*y**5. Factor h(z).
-2*(z - 1)**3*(z + 1)**2/3
Let g(k) = 10*k**4 + 8*k**3 + 4*k**2 + 6*k - 9. Let w(b) = -b**4 + b**2 + 1. Let f(c) = 4*g(c) + 36*w(c). Factor f(u).
4*u*(u + 1)**2*(u + 6)
Factor j**2 + 12*j - 2*j**2 - j**2 - 2*j**2.
-4*j*(j - 3)
Let s(p) = p**3 + 2*p**2 - 2*p + 2. Let u be s(-3). Let m be 2/(-3)*3/u. Factor -2/5*n + 1/5*n**4 + 0*n**m + 2/5*n**3 - 1/5.
(n - 1)*(n + 1)**3/5
Let u(m) be the third derivative of -m**10/201600 + m**9/17280 - m**8/4032 + m**7/2520 - m**5/12 + m**2. Let x(r) be the third derivative of u(r). Factor x(g).
-g*(g - 2)**2*(3*g - 2)/4
Let m(h) = -5*h**3 - 7*h**2 + 12*h. Let k(i) = 5*i**3 + 6*i**2 - 11*i. Let j(t) = -7*k(t) - 6*m(t). Solve j(n) = 0.
-1, 0, 1
Let n be 4/96*6 - (-13)/44. Suppose 4/11 + 2/11*v**2 + n*v = 0. Calculate v.
-2, -1
Let k(f) = 6*f**3 - 4*f**2 - 14*f + 12. Let z(x) = 4*x**3 - 3*x**2 - 9*x + 8. Let i(n) = -5*k(n) + 8*z(n). Factor i(c).
2*(c - 2)*(c - 1)*(c + 1)
Let w = 8 - 5. Solve -2*o - o + w*o**5 + 2*o**3 + 2*o - 4*o**5 = 0.
-1, 0, 1
Suppose 0 = -2*q + 2*v, 4*q = -4*v + 13 + 3. Suppose -2/3*k**q + 0 + 0*k = 0. Calculate k.
0
Let q = 7 - 4. Suppose 2*y - 2*o = -o + 3, 5*o - 6 = q*y. Suppose -2 + 12*j**5 - 16*j**3 + 8*j + 2*j**4 - 4*j**y + 0*j**4 = 0. Calculate j.
-1, 1/3, 1/2, 1
Let t(a) = a**2 - 4*a + 1. Let d be (-1)/(4/(-20)) + -3. Let r(n) = -n + 1. Let x(z) = d*t(z) - 6*r(z). Factor x(y).
2*(y - 2)*(y + 1)
Let i be 3 + (-3 - -3) - 18. Let b be (-2)/2 - 42/i. Solve -b*y**3 - 3*y**2 - 7/5*y - 1/5 = 0.
-1, -1/3
Let a(v) = -5*v - 1. Let p be a(-1). Let t be 30/7 - p/14. Factor x**2 + x - 1 - x**3 - x**t + 1.
-x*(x - 1)*(x + 1)**2
Let z = 17/29 + -547/1131. Let q(l) be the second derivative of -3*l + 1/65*l**5 + 0 - 1/195*l**6 - 4/13*l**2 + 1/26*l**4 - z*l**3. Factor q(f).
-2*(f - 2)**2*(f + 1)**2/13
Factor -4/5*i**2 + 16/5 - 12/5*i.
-4*(i - 1)*(i + 4)/5
Suppose 17 = 4*g + 5*i, -g + 3*g - 8 = -2*i. Suppose -t = g*t - 8. Factor -3*q**3 + 2*q**5 + 2*q**2 + 2*q**4 + q**3 - 4*q**t.
2*q**2*(q - 1)*(q + 1)**2
Let c(b) be the first derivative of 2*b**3/15 + 4*b**2/5 + 9. Factor c(n).
2*n*(n + 4)/5
Let g(i) be the second derivative of i**4/42 + i**3/21 - 2*i**2/7 - 7*i. Find y, given that g(y) = 0.
-2, 1
Suppose -2*y + 2*g + 10 = 0, 4*g + 1 = 3*g. Let c(j) be the second derivative of 0*j**2 + j + 1/12*j**y + 0*j**3 + 0 + 1/20*j**5. Find z, given that c(z) = 0.
-1, 0
Let x = 4 + -1. Suppose -3*b + 15 = x*y - 3, 0 = 5*b - 20. Factor -7*u**2 - 13*u**2 - 12*u - 8*u**3 - 2 + 2*u**y.
-2*(u + 1)**2*(4*u + 1)
Suppose -4/9*u**2 - 64/9 + 32/9*u = 0. Calculate u.
4
Let t(s) be the first derivative of -5*s**7/168 - s**6/60 + s**5/16 + s**4/24 - 2*s + 5. Let b(k) be the first derivative of t(k). Let b(d) = 0. What is d?
-1, -2/5, 0, 1
Let f = 5/66 - -1/11. Let h(k) be the first derivative of 1 + 2/9*k**3 + 0*k + 0*k**2 - f*k**4 - 2/15*k**5 + 1/9*k**6. What is j in h(j) = 0?
-1, 0, 1
Let x(h) be the second derivative of 1/4*h**4 + 0*h**2 + 0 - 5*h + 0*h**5 + 0*h**3 - 1/10*h**6. Factor x(l).
-3*l**2*(l - 1)*(l + 1)
Suppose -10*w = 19*w - 10*w. Let t(q) be the third derivative of -3/20*q**5 + 0*q - 2*q**2 + 0 + w*q**3 - 1/8*q**4. Find g such that t(g) = 0.
-1/3, 0
Let k(p) be the second derivative of p**5/20 - p**4/6 - p**3/2 - p. Factor k(i).
i*(i - 3)*(i + 1)
Factor 61*p**2 - 33*p**2 + 6*p - 3*p**3 - 31*p**2.
-3*p*(p - 1)*(p + 2)
Let m(c) = c**2 + 20*c + 51. Let j be m(-17). Solve -2/7*n + 8/7*n**2 + j = 0 for n.
0, 1/4
Suppose 18/5 + 12/5*d + 2/5*d**2 = 0. Calculate d.
-3
What is h in 0 + 18/5*h**3 - 14/5*h**4 - 4/5*h**2 + 0*h = 0?
0, 2/7, 1
Let l(y) be the third derivative of -y**8/20160 - y**7/1680 - y**6/360 - y**5/15 + 5*y**2. Let r(p) be the third derivative of l(p). What is o in r(o) = 0?
-2, -1
Let a(b) = b**2 - 2*b - 3. Suppose 0 = 14*y - 10*y - 4. Let w(j) = j + 1. Let f(g) = y*a(g) + 4*w(g). Find l such that f(l) = 0.
-1
Let i(v) be the second derivative of -v**4/12 - 4*v**3 - 72*v**2 - 19*v. What is r in i(r) = 0?
-12
Let n(q) be the second derivative of -9/2*q**2 + 0 + q**3 + 1/4*q**4 + 3*q. Factor n(k).
3*(k - 1)*(k + 3)
Let a(t) be the first derivative of -10*t**3/21 - 3*t**2/7 + 4*t/7 - 4. Factor a(u).
-2*(u + 1)*(5*u - 2)/7
Let a(w) be the third derivative of -w**8/224 + w**6/40 - w**4/16 + 2*w**2. Find j, given that a(j) = 0.
-1, 0, 1
Suppose -5*o + 9 = 2*s, -8 - 2 = 2*o. Suppose 1 + 11*g + 2*g**2 + s + 4*g - 3*g = 0. What is g?
-3
Let h(i) = -2*i**3 + 2*i**2 - i - 1. Let k be 2*(0 + 0 + -1). Let f = k - -4. Let n(s) = -s**3 - 1. Let p(q) = f*n(q) - 2*h(q). Factor p(d).
2*d*(d - 1)**2
Factor -243 - 5*q + 223 + 15*q**2 + 16*q + 9*q.
5*(q + 2)*(3*q - 2)
Let -2*d - 2*d**5 + 9*d**3 + 2*d - 3*d**3 + 4*d**2 = 0. What is d?
-1, 0, 2
Let u(i) be the first derivative of i**6/2 + 3*i**5 - 21*i**4/2 + 2*i**3 + 39*i**2/2 - 21*i + 67. Factor u(g).
3*(g - 1)**3*(g + 1)*(g + 7)
Let h(k) be the third derivative of 1/70*k**5 + 0*k - 1/280*k**6 + 0*k**3 - 1/56*k**4 + 0 + 5*