a = p, 0 = -4*q - q + 3*a + 7. Factor -q*d**5 - 4*d**3 - 2 + d - 4*d**2 + 0 + 6*d**4 + 5*d.
-2*(d - 1)**4*(d + 1)
Let l(x) be the second derivative of -x**8/504 + x**6/90 - x**4/36 + 2*x**2 - 4*x. Let t(f) be the first derivative of l(f). Factor t(c).
-2*c*(c - 1)**2*(c + 1)**2/3
Let i = -13 - -15. Determine j so that 5*j**i - 7*j**2 + 5*j**2 - 12 = 0.
-2, 2
Let b(o) = 2*o + 24. Let a be b(-10). Let g(s) be the first derivative of 77*s**3 + 12*s - 1 - 147/4*s**a - 48*s**2. What is j in g(j) = 0?
2/7, 1
Let r(a) be the second derivative of -a**6/105 - a**5/70 + 5*a**4/42 - a**3/7 - 19*a - 3. Find w such that r(w) = 0.
-3, 0, 1
Let b(g) = -g + 4. Let o be b(4). Suppose 3*x**2 + x**3 + o*x**2 - 2*x**2 = 0. Calculate x.
-1, 0
Suppose -75 = 2*c - 5*c. Factor -c*p + 24*p - p**3 + 2*p**2 + 0*p**2.
-p*(p - 1)**2
Let a be (-13 + 1 + 0)*8/(-60). Let 2/5*q**2 + a*q + 8/5 = 0. Calculate q.
-2
Let a(b) be the third derivative of 0*b**3 + 0*b + 1/240*b**5 + 0 - 1/480*b**6 + 8*b**2 + 0*b**4. Factor a(j).
-j**2*(j - 1)/4
Suppose 2*v = -2*v + 5*w + 39, -5*w + 57 = 2*v. Suppose 0 = -m - 3*m + v. Solve 4*y**m + 2*y**5 - 4*y**2 - y - 3*y + 2*y = 0 for y.
-1, 0, 1
Let v(w) be the second derivative of -w**5 - 2*w**4 + 2*w**3 + 8*w**2 - 8*w. Factor v(p).
-4*(p + 1)**2*(5*p - 4)
Let u(q) be the first derivative of -5*q**8/336 - q**7/70 + q**6/60 - 2*q**2 + 4. Let r(x) be the second derivative of u(x). Factor r(w).
-w**3*(w + 1)*(5*w - 2)
Let j(w) = -2*w**4 + 10*w**3 - 17*w**2 - 8*w + 16. Let n(s) = s**4 - 5*s**3 + 9*s**2 + 4*s - 8. Let k(o) = -3*j(o) - 5*n(o). Find b such that k(b) = 0.
-1, 2
Suppose -36*p + 9*p**2 + 4 + 39*p - 23*p = 0. What is p?
2/9, 2
Suppose -5*q + 275 = -5*k, 3*k + 109 = -0*q + 2*q. Let i be ((-21)/q)/((-3)/2). Determine v so that -1/4*v**2 + 0 - 1/2*v + i*v**4 + 1/2*v**3 = 0.
-2, -1, 0, 1
Factor n**3 + 4*n**2 + 6*n - 20*n + 9*n.
n*(n - 1)*(n + 5)
Let g(n) be the third derivative of -7*n**6/120 - 23*n**5/40 - 3*n**4/4 + n**3/6 - n**2. Let i(v) be the first derivative of g(v). Factor i(q).
-3*(q + 3)*(7*q + 2)
Let c(g) = -g**5 + g**3 - g + 1. Let l(y) = -8*y**5 + y**4 + 8*y**3 - y**2 - 9*y + 9. Let x(h) = 18*c(h) - 2*l(h). Factor x(d).
-2*d**2*(d - 1)*(d + 1)**2
Let u = -152/3 - -52. What is j in -2*j - 2/3*j**2 - u = 0?
-2, -1
Suppose -3*k + k + 4 = 0. Let z(u) be the second derivative of -1/40*u**5 + 3*u + 1/12*u**3 + 0 + 1/24*u**4 - 1/4*u**k. Suppose z(p) = 0. What is p?
-1, 1
Let g(p) be the first derivative of 1/3*p**3 + 7 + 3/5*p - 1/20*p**4 - 7/10*p**2. Factor g(q).
-(q - 3)*(q - 1)**2/5
Let k be ((-3)/(-12))/(5/16). Factor -2/5*b**4 - 2/5*b**2 + 0*b + 0 + k*b**3.
-2*b**2*(b - 1)**2/5
Solve 2/3*o**5 + 2/3*o**2 - 2/3*o**4 + 0 - 2/3*o**3 + 0*o = 0 for o.
-1, 0, 1
Let y be 12930/(-54) + (-6)/(-9). Let f = y + 239. Find l, given that -f*l**4 + 0*l**3 + 0*l**2 + 0*l + 0 = 0.
0
Let y(u) be the first derivative of -u**7/420 + u**3 - 3. Let q(o) be the third derivative of y(o). Factor q(n).
-2*n**3
Let r(t) = 23*t**5 - 35*t**3 - 5*t**2. Let p(i) = 4*i**5 - 6*i**3 - i**2. Let k(a) = 34*p(a) - 6*r(a). Let k(d) = 0. Calculate d.
-2, 0, 1
Factor -6*u**2 + 2*u - u**3 + 0*u**3 + 5*u**2.
-u*(u - 1)*(u + 2)
Let f = 173/3 - 509/9. Factor f*h - 2/9 - 8/9*h**2.
-2*(h - 1)*(4*h - 1)/9
Let m(b) = 3*b**3 + 4*b**2 + b - 4. Let n(f) = -7*f**3 - 7*f**2 - 3*f + 7. Let v(z) = -15*m(z) - 6*n(z). Suppose v(o) = 0. Calculate o.
-6, -1, 1
Let s(v) be the third derivative of 5*v**2 + 1/40*v**5 + 0*v**3 + 1/8*v**4 + 0 + 0*v. Factor s(b).
3*b*(b + 2)/2
Let 4/5*j + 4/5 - 1/5*j**2 - 1/5*j**3 = 0. What is j?
-2, -1, 2
Let p(s) = 3*s**3 - 9*s**2 - 5*s + 5. Let h(t) = t**3 - t**2 - t + 1. Let a(g) = 5*h(g) - p(g). Let a(d) = 0. Calculate d.
-2, 0
Factor 0*s - 2/13*s**2 + 0.
-2*s**2/13
Suppose -3*v = -2*l - 8, 5*v = l + l + 12. Let k(m) be the third derivative of 0*m + 0 + 2*m**v - 1/30*m**5 + 1/6*m**4 - 1/3*m**3. Factor k(x).
-2*(x - 1)**2
Let k = 7369/24 + -307. Let b(d) be the first derivative of -k*d**4 - 1/6*d**2 + 0*d + 1 - 1/6*d**3. Determine w so that b(w) = 0.
-2, -1, 0
Suppose 0 + 0*o + 0*o**2 - 1/2*o**4 - 2*o**3 = 0. What is o?
-4, 0
Let i = 52 + -257/5. Factor -3*u**2 + i*u - 12/5*u**4 + 24/5*u**3 + 0.
-3*u*(u - 1)*(2*u - 1)**2/5
Suppose 4*p**2 - p**2 - 4*p**2 + 4*p**2 = 0. What is p?
0
Let v(m) be the second derivative of 3/160*m**5 + 7/1440*m**6 + 1/48*m**4 + 0*m**2 + 0 - 1/6*m**3 - 2*m. Let j(t) be the second derivative of v(t). Factor j(u).
(u + 1)*(7*u + 2)/4
Find r such that -6*r + 0*r - r**2 - 7*r - 16 + 5*r = 0.
-4
Let a(p) be the first derivative of 0*p - 1/2*p**4 - 1/2*p**3 + 1 + 1/4*p**2. Factor a(o).
-o*(o + 1)*(4*o - 1)/2
Let r(k) be the second derivative of k**7/70 - k**6/50 - 3*k**5/100 + k**4/20 + 5*k. Factor r(d).
3*d**2*(d - 1)**2*(d + 1)/5
Let l(m) be the first derivative of -m**4/6 - 2*m**3/3 - m**2 - 4*m - 1. Let i(q) be the first derivative of l(q). Suppose i(b) = 0. Calculate b.
-1
Let z be 1/(-4) - (-4 - 357/(-140)). What is u in -z*u**2 + 0*u - 2/5*u**3 + 0 = 0?
-3, 0
Suppose -4*m - v + 2*v + 11 = 0, 0 = -3*m - 2*v. Factor 21*k - 3*k - 8*k**m - 5 - 4 + 5.
-2*(k - 2)*(4*k - 1)
Suppose -2*j + 13 = 4*y - 3, -16 = 5*j - 4*y. Suppose -5*h + 1 + 14 = j. Factor 0*u**4 - h*u**4 + 2*u**2 - 4*u**3 + 5*u**4.
2*u**2*(u - 1)**2
Factor -4*k - 3*k**5 + 2*k**4 - 12*k**2 - 6*k**3 + 2*k**2 + 5*k**5.
2*k*(k - 2)*(k + 1)**3
Let i(z) = 70*z**3 - 128*z**2 + 78*z - 12. Let p(k) = 24*k**3 - 43*k**2 + 26*k - 4. Let w(h) = -3*i(h) + 8*p(h). Suppose w(l) = 0. Calculate l.
2/9, 1
Let a(y) = y**2 - 13*y - 30. Let v be a(15). Let f be (-3)/(6*(-1)/4). Determine k, given that 2/3*k - 2/3*k**3 + 0*k**f + v = 0.
-1, 0, 1
Factor 6*h - 4*h**4 - 19*h + 17*h - 4*h**3 - 8 + 12*h**2.
-4*(h - 1)**2*(h + 1)*(h + 2)
Factor 0 + 2/5*y + 2/5*y**2.
2*y*(y + 1)/5
What is z in 30*z**2 - 27/2*z**3 + 3 - 39/2*z = 0?
2/9, 1
Let l be 0*6/(-54)*3. Factor 2/3*h**2 + 0*h + l.
2*h**2/3
Let h = -2381/36 + 265/4. Let 4/9 + 0*q - h*q**2 = 0. Calculate q.
-2, 2
Let k(x) be the third derivative of x**6/900 - x**5/150 + x**4/90 + 21*x**2. Let k(a) = 0. What is a?
0, 1, 2
Let r(g) be the first derivative of -g**5/5 + g**4/2 - g**2 + g + 9. Suppose r(z) = 0. Calculate z.
-1, 1
Let a(s) = -s + 1. Let o(d) be the second derivative of 3*d**4/2 - 2*d**3 - 3*d**2 + 2*d. Let g(b) = 2*a(b) + o(b). Factor g(y).
2*(y - 1)*(9*y + 2)
Let b(j) = 7*j**3 - 8*j**2 + j. Let n(w) = -6*w**3 + 7*w**2 - w. Let s = -3 + 8. Let c(m) = s*b(m) + 6*n(m). Factor c(l).
-l*(l - 1)**2
Suppose 6*p**2 - 9/2*p**3 + 0 - 6*p**4 + 6*p - 3/2*p**5 = 0. Calculate p.
-2, -1, 0, 1
Let r(m) be the first derivative of m**8/840 + m**7/525 - 3*m**2/2 - 2. Let h(d) be the second derivative of r(d). Let h(g) = 0. What is g?
-1, 0
Factor 0*g + 4/7 - 3/7*g**2 + 1/7*g**3.
(g - 2)**2*(g + 1)/7
Let c(x) be the third derivative of -9/80*x**6 - 6*x**2 + 1/20*x**7 + 0 + 1/8*x**5 + 0*x + 0*x**3 - 1/16*x**4 - 1/112*x**8. Factor c(l).
-3*l*(l - 1)**3*(2*l - 1)/2
Suppose c - 40 = -3*c. Suppose c*n = 5*n + 10. Solve y**3 + 2*y**2 + 5*y**3 + 0*y**3 - 4*y**4 - 4*y**5 + 2*y**4 - n*y = 0.
-1, 0, 1/2, 1
Suppose -4*f + 17*u - 4 = 14*u, 0 = 5*f - 2*u - 2. Suppose 4/9 + 2*g**f + 22/9*g = 0. Calculate g.
-1, -2/9
Let f = 1 - -97/3. Factor 115/3*z**3 + f*z**4 - 44/3*z - 38/3*z**2 - 8/3 - 125/3*z**5.
-(z - 1)**2*(5*z + 2)**3/3
Let d(w) = -w**3 + w**2 - w + 1. Let s be (9/3 + -4)*10. Let g(p) = p**4 - 7*p**3 + 5*p**2 - 3*p + 4. Let o(l) = s*d(l) + 2*g(l). What is m in o(m) = 0?
-1, 1
Let n(h) be the third derivative of -h**5/180 - h**4/18 - 6*h**2. Factor n(l).
-l*(l + 4)/3
Solve 0*f**5 + 69*f**4 - 2*f**5 + 4*f**3 - 71*f**4 = 0 for f.
-2, 0, 1
Let h(c) be the third derivative of -c**8/20160 + c**6/720 - c**5/20 + 3*c**2. Let p(f) be the third derivative of h(f). Determine b, given that p(b) = 0.
-1, 1
Suppose 19*t = 23*t - 20. Let g(d) be the third derivative of -1/210*d**7 - 1/48*d**4 + 1/672*d**8 + 0*d**6 + 1/60*d**t + 0 + 0*d + d**2 + 0*d**3. Factor g(a).
a*(a - 1)**3*(a + 1)/2
Let c be -1*-2*((-44)/24 - -2). Suppose -3*q + 10 - 4 = 0. Solve 0*o + c*o**q + 0 = 0.
0
Let v(l) be the third derivative of l**5/90 - l**4/12 - 19*l**2. Factor v(w).
2*w*(w - 3)/3
Suppose -108 + 22*i**3 - 18*i**3 + 94*i - 30*i + 44*i - 36*i**2 = 0. What is i?
3
Let c(g) be the third derivati