et a(l) = l**3 - 5*l**2 + l - 5. Let t be a(5). Suppose -5*u - 25 = 0, 4*u + t*u + 27 = c. Factor 1 - c*n - 2*n**2 + 5*n - 4*n + 11*n**2 - 4*n**3.
-(n - 1)**2*(4*n - 1)
Let 0*z + 0 + 1/2*z**2 + z**3 + 1/2*z**4 = 0. Calculate z.
-1, 0
Suppose 4*s + 10 = 26. Let c be -2 + (-14)/8 + 4. Factor -1/2*d**3 + c - 1/4*d**s + 0*d**2 + 1/2*d.
-(d - 1)*(d + 1)**3/4
Suppose 2*u + 50 = 7*u. Let s be 8/u - (-110)/(-200). Find p, given that 0*p + 0 - s*p**2 = 0.
0
Let q(y) = -4*y**2 - 19*y - 41. Let o(h) = 2*h**2 + 10*h + 20. Let v(b) = 5*o(b) + 2*q(b). Let v(r) = 0. Calculate r.
-3
Suppose -5*n = -3*n - 4, 2*n - 4 = 5*s. Let v be 4/4 - (s + -1). Factor 5*r - 11*r + 5*r**3 - 2 - v + r**3 + 4*r**2.
2*(r - 1)*(r + 1)*(3*r + 2)
Let k(w) be the first derivative of -1/2*w**3 - 1/10*w**5 - w**2 + 1/2*w**4 + 2*w + 1. Factor k(q).
-(q - 2)**2*(q - 1)*(q + 1)/2
Let l(u) be the first derivative of -u**3 - 6*u**2/5 - 7. Factor l(g).
-3*g*(5*g + 4)/5
Let m(f) be the third derivative of 1/72*f**4 - 1/90*f**5 + 0 + 0*f**3 + 0*f - 1/1008*f**8 + 0*f**6 + 3*f**2 + 1/315*f**7. Find k, given that m(k) = 0.
-1, 0, 1
Let j(c) be the second derivative of 5*c**4/72 + 5*c**3/12 - 42*c. Find u such that j(u) = 0.
-3, 0
Let d be -1*1*10/(-45). Factor 0 + 2/9*c**3 - 4/9*c - d*c**2.
2*c*(c - 2)*(c + 1)/9
Let v be ((-2)/16)/(105/(-100)). Let o(p) be the second derivative of 4*p - 1/105*p**6 + 0*p**2 + v*p**4 + 1/147*p**7 - 3/70*p**5 - 2/21*p**3 + 0. Factor o(u).
2*u*(u - 1)**3*(u + 2)/7
Let d(x) = -5*x + 6 + 3*x - 2*x + 2*x**2. Let k(a) be the first derivative of -a - 1. Let p(y) = d(y) + 4*k(y). Factor p(o).
2*(o - 1)**2
Let k(q) = 4*q**3 + 2*q**2 + 4*q - 3. Let o(t) = 5*t**3 + 2*t**2 + 4*t - 2. Let i(z) = 6*k(z) - 5*o(z). Suppose i(s) = 0. What is s?
-2, 2
Let x(o) = -15*o**3 - 5*o**2 + 15*o - 35. Let y(c) = c**3 + c**2 - c + 1. Let w(g) = x(g) + 20*y(g). Solve w(j) = 0 for j.
-3, -1, 1
Let g(n) be the third derivative of n**7/420 - n**6/240 - n**5/40 + 5*n**4/48 - n**3/6 - 2*n**2. Solve g(w) = 0 for w.
-2, 1
Let h(z) = -94*z**3 - z**2 + 1. Let p be h(1). Let w be (-16 + 0)*(p - 1). Factor 510*j**3 + 1960*j**4 + w*j**3 - 347*j**2 + 200*j + 16 + 686*j**5 + 1287*j**2.
2*(j + 1)**2*(7*j + 2)**3
Let d be (-3*(-3)/(-9))/(-24). Let x(u) be the second derivative of -1/12*u**3 + d*u**4 + 0 + 2*u + 0*u**2. Factor x(y).
y*(y - 1)/2
Let x = 167 + -164. Factor -32/5 - 448/5*h**x - 624/5*h**2 - 256/5*h - 98/5*h**4.
-2*(h + 2)**2*(7*h + 2)**2/5
Let v(y) = 3*y**2 + 7*y. Let w(p) = p**2 - 2*p. Let x(l) = -l. Let t(h) = w(h) - 5*x(h). Let d(j) = -5*t(j) + 2*v(j). Suppose d(k) = 0. Calculate k.
0, 1
Let x(y) be the third derivative of 0*y**3 + 0*y - 1/80*y**5 - 5*y**2 + 0*y**4 + 0 + 1/160*y**6. Factor x(n).
3*n**2*(n - 1)/4
Let o(l) = 3*l**4 - l**3. Let q(j) = -j**4 + j**3. Let a(d) = o(d) + 5*q(d). Factor a(u).
-2*u**3*(u - 2)
Suppose -2*j + 56 = -4*j. Let f be (-7)/j - (-7)/4. Let -2/7 - 4/7*z + 2/7*z**f + 4/7*z**3 = 0. Calculate z.
-1, -1/2, 1
Let b = -47 + 49. Factor 2/7*t**3 + 0*t**b - 2/7*t + 0.
2*t*(t - 1)*(t + 1)/7
Let r(o) be the second derivative of o**7/210 - 2*o**5/25 - o**4/10 + 7*o**3/30 + 3*o**2/5 + 27*o. Find u such that r(u) = 0.
-2, -1, 1, 3
Let s(o) be the second derivative of 0 + 0*o**4 - 3/2*o**2 + 2*o + 0*o**3 - 1/150*o**5. Let f(g) be the first derivative of s(g). Let f(j) = 0. Calculate j.
0
Let y(u) be the first derivative of -1/5*u**4 + 0*u + 5 + 0*u**2 + 8/15*u**3. What is l in y(l) = 0?
0, 2
Let b(g) be the third derivative of g**6/480 + g**5/80 + g**4/32 + g**3/24 - 6*g**2. Find t such that b(t) = 0.
-1
Let u(d) be the third derivative of -d**9/12600 + d**8/8400 + d**4/4 + 4*d**2. Let k(m) be the second derivative of u(m). Factor k(g).
-2*g**3*(3*g - 2)/5
Let h(p) = -8*p**4 + 8*p**3 + 36*p**2 + 24*p + 12. Let a(y) = -y**5 - y**2 + y - 1. Let s(f) = 4*a(f) + h(f). Solve s(i) = 0 for i.
-1, 2
Let g(v) be the first derivative of 1/4*v + 1/4*v**3 - 1/2*v**2 - 2. Factor g(a).
(a - 1)*(3*a - 1)/4
Let g = 10 + -5. Let s(k) be the first derivative of 1/9*k**6 + 0*k**2 + 2 - 1/6*k**4 + 0*k**g + 0*k**3 + 0*k. Factor s(f).
2*f**3*(f - 1)*(f + 1)/3
Let j = -315 + 5357/17. Suppose 0*l**2 - 4/17 - j*l**3 + 6/17*l = 0. Calculate l.
-2, 1
Let x(v) = 19*v**2 - 7*v + 1. Suppose -d - 29 = 10. Let g(r) = -3*r**2 + r. Let a(f) = d*g(f) - 6*x(f). Let a(b) = 0. What is b?
-2, 1
Let s(z) be the first derivative of 0*z**3 + 2*z - 3 - 1/42*z**4 + 0*z**2 + 1/70*z**5. Let g(w) be the first derivative of s(w). Factor g(y).
2*y**2*(y - 1)/7
Let g = -128 - -257/2. Let p(m) be the first derivative of 0*m - 2 - 1/6*m**6 + 0*m**5 - g*m**2 + 1/2*m**4 + 0*m**3. Factor p(r).
-r*(r - 1)**2*(r + 1)**2
Let u(d) be the first derivative of -2*d**5/15 - 7*d**4/6 - 4*d**3 - 20*d**2/3 - 16*d/3 + 21. Solve u(o) = 0 for o.
-2, -1
Factor 0 - 4/5*j**2 + 0*j - 1/5*j**3.
-j**2*(j + 4)/5
Let c(z) be the third derivative of -z**5/150 + z**4/60 + 25*z**2. Factor c(i).
-2*i*(i - 1)/5
Let c = -2 - -5. Let u(i) = i**2 - 14*i + 13. Let g be u(13). What is o in -1/2*o**4 + 0*o + 0 + 1/2*o**c + g*o**2 = 0?
0, 1
Let k(h) = -2*h**4 + 20*h**3 - 3*h - 3. Let n(b) = -3*b**4 + 20*b**3 - 2*b - 2. Let v(i) = -2*k(i) + 3*n(i). Suppose v(o) = 0. What is o?
0, 4
Let p be 12/7 - 6/(-21). Suppose v + 0*v + 2*v - v**p - 5*v = 0. What is v?
-2, 0
Let m be (-10)/(-24) + ((-49)/21)/7. Let c(i) be the second derivative of i + m*i**4 + 0*i**2 + 1/3*i**3 + 0. Factor c(z).
z*(z + 2)
Factor -13*n**2 - 90*n**3 + 2*n + 48*n**5 + 6*n**5 + 16 + 38*n - 7*n**2.
2*(n - 1)**2*(3*n + 2)**3
Factor -3/4*o + 1/4*o**2 + 1/2.
(o - 2)*(o - 1)/4
Suppose -1 = -3*j - 3*s - 10, -j + 17 = -3*s. Factor 1 + 0*a**4 + j*a**2 + a**5 - 2*a**3 - 2 - a**4 - a + 2*a.
(a - 1)**3*(a + 1)**2
Let j(o) = -8*o + 10. Let h(b) = b**2 + 16*b - 21. Let s(f) = -2*h(f) - 5*j(f). Solve s(z) = 0 for z.
2
Let a(c) be the second derivative of -c**4/24 + c**2/4 + 8*c. Factor a(q).
-(q - 1)*(q + 1)/2
Let r(d) be the second derivative of -d**4/16 - d**3/8 + 3*d**2/4 + d. Suppose r(q) = 0. Calculate q.
-2, 1
Factor -5*z**3 - 33/2*z**2 - 20*z - 8 - 1/2*z**4.
-(z + 1)**2*(z + 4)**2/2
Let d = -51783/5 - -10273. Let n = 84 + d. Factor -1/5*z + 1/5*z**2 - n.
(z - 2)*(z + 1)/5
Let g(k) = 9*k**2 + 25*k - 184. Let j(l) = l**2 - l - 2. Let t(v) = -2*g(v) + 22*j(v). Factor t(x).
4*(x - 9)**2
Let o = 1/300 - -149/300. Solve 5/4*b + o - 7/4*b**2 = 0.
-2/7, 1
Let d(q) be the second derivative of q**7/8820 + q**4/3 + 4*q. Let o(b) be the third derivative of d(b). Suppose o(h) = 0. Calculate h.
0
Let u(g) be the second derivative of -2*g**6/15 - g**5/10 + g**4/3 + g**3/3 + 4*g. Solve u(m) = 0 for m.
-1, -1/2, 0, 1
Let q = 8 - 10. Let w be 5 + -3 + q/(-2). Factor 0 + 0*u**2 + 1/4*u**w - 1/4*u.
u*(u - 1)*(u + 1)/4
Let r(g) be the third derivative of 0 + g**2 + 0*g + 0*g**3 + 0*g**4 + 0*g**5 - 1/280*g**7 - 1/240*g**6 - 1/1344*g**8. Factor r(m).
-m**3*(m + 1)*(m + 2)/4
Factor 2*l**2 + l**2 - 12*l**4 + 15*l**3 - 6*l**3.
-3*l**2*(l - 1)*(4*l + 1)
Let j(w) be the third derivative of -w**5/10 + w**4/3 + 4*w**3/3 + 7*w**2. Suppose j(i) = 0. Calculate i.
-2/3, 2
Let p = -54 - -131. Let b be p/42 + 2/12. Factor 3/4 + 3/2*f + 3/4*f**b.
3*(f + 1)**2/4
Let n = -3/32 + 25/96. Let p(w) be the first derivative of 1/2*w - 1 + n*w**3 + 1/2*w**2. Suppose p(l) = 0. Calculate l.
-1
Let m(w) be the second derivative of 0*w**3 + 4/63*w**7 + 6*w - 11/30*w**5 - 8/45*w**6 + 0*w**2 + 0 - 1/6*w**4. Factor m(o).
2*o**2*(o - 3)*(2*o + 1)**2/3
Let h = 13 + -11. Factor 10 + 3*o**2 - 4*o**h + o - 9 + 0*o**2 - o**3.
-(o - 1)*(o + 1)**2
Factor 13/3*z**3 + 2*z**2 + 1/3*z + 4*z**4 + 4/3*z**5 + 0.
z*(z + 1)**2*(2*z + 1)**2/3
Let q(j) = j**2 - 10*j - 3. Let k be q(7). Let l(z) = -7*z**2 + 10*z - 7. Let w(i) = i**2 - i + 1. Let c(a) = k*w(a) - 3*l(a). Factor c(s).
-3*(s + 1)**2
Suppose 0*a + 6/7*a**3 - 2/7*a**5 - 4/7*a**2 + 0*a**4 + 0 = 0. What is a?
-2, 0, 1
Let j be (-3)/(-6)*(-1 + 1). Let s(g) be the second derivative of 1/30*g**4 + 4/5*g**2 + 4/15*g**3 + 2*g + j. What is o in s(o) = 0?
-2
Let j(g) = -g**5 + g**4 - g**3 + g**2 - g - 1. Let x(k) = 3*k**5 + k**4 - 3*k**3 - 5*k**2 + 12*k. Let h(b) = 4*j(b) + x(b). Find l such that h(l) = 0.
-1, 1, 2
Let n(j) = -2*j**2 + 0*j**2 - 2*j + 3*j + 3*j**2. Let y(a) = 6*a**2 + 2*a. Let o(m) = -4*n(m) + y(m). Det