 0*n + 0*n**4 - 3 + 0*n**6 - 1/3*n**3 - 1/840*n**7. Let y(r) be the third derivative of p(r). Factor y(q).
-q**3
Suppose 2*g - g + 6 = 0. Let w be (-21)/g - (-1)/2. Factor 0 + 1/2*c**w - 1/2*c**3 + 1/2*c**5 + 0*c - 1/2*c**2.
c**2*(c - 1)*(c + 1)**2/2
Let v be -2 + (-9)/(0 + -3). Let t be 0 - (-1 - v/(-2)). What is j in 1/2*j**2 + t*j**3 - 1/2 - 1/2*j = 0?
-1, 1
Suppose 3 = -3*u - 18. Let r = u - -22/3. Solve 0 - r*o - 2/3*o**2 = 0.
-1/2, 0
Let k(n) be the second derivative of 7*n - 6/5*n**5 + 2/15*n**6 + 8/3*n**4 + 0 - 18*n**2 + 4*n**3. Factor k(l).
4*(l - 3)**2*(l - 1)*(l + 1)
Let f(m) = m**3 + m**2 - m + 1. Let a be f(1). Suppose -2*z - 8 = -6*z. Factor -x**2 + x + a*x**z - 2*x.
x*(x - 1)
Suppose -r - 3*a - 6 = 0, r - 2*a - 4 = 5. Let n(g) be the first derivative of 3 - 7/3*g**r + 0*g - g**2 - 5/4*g**4. Factor n(d).
-d*(d + 1)*(5*d + 2)
Let b(h) be the second derivative of -h**7/56 - h**6/20 + h**4/8 + h**3/8 - h + 48. Determine u so that b(u) = 0.
-1, 0, 1
Let q(h) = -h**3 - 6*h**2 + 5*h - 10. Let a be q(-7). Suppose -4*x = -a*l - 36, l - 2 - 1 = -2*x. Solve 2 + 3*s - 5*s**3 - 2*s**x - 4*s + s**3 + 5*s = 0.
-1, 1
Let p(s) = 14*s**2 + 6. Let n(v) = -v**2 - 1. Let k(w) = 10*n(w) + p(w). Solve k(d) = 0.
-1, 1
Let s(i) be the first derivative of i**5/5 + 2*i**4 + 22*i**3/3 + 12*i**2 + 9*i - 13. Solve s(p) = 0.
-3, -1
Let g(v) be the first derivative of 0*v**2 + 1 - 3/4*v**4 + 0*v + v**3. Factor g(k).
-3*k**2*(k - 1)
Let j = 12 - 16. Let d(r) = 7*r**3 - 4*r**2 - 3*r. Let n(c) = c**3 - c**2. Let q(x) = j*n(x) + d(x). Factor q(m).
3*m*(m - 1)*(m + 1)
Let u be 8/10 - 20/150. Factor -2/9*l**3 - u*l**2 - 4/9*l + 0.
-2*l*(l + 1)*(l + 2)/9
Suppose 4*v - 5*y + y = 52, -v - 5*y = 11. Let n = v - 7. Factor 2/5*a - 1/5*a**n - 1/5.
-(a - 1)**2/5
Let a(o) be the second derivative of 7*o + 0*o**2 - 1/6*o**3 + 1/12*o**4 + 1/20*o**5 + 0 - 1/30*o**6. Factor a(j).
-j*(j - 1)**2*(j + 1)
Let y(f) be the second derivative of -5*f**5/4 - 65*f**4/12 + 65*f**3/3 - 20*f**2 - 36*f. Solve y(z) = 0.
-4, 2/5, 1
Let p(s) = -12*s**3 + 9*s**2 - 10*s + 13. Let u(x) = x**3 - x**2 + x - 1. Let y(t) = -2*p(t) - 22*u(t). What is a in y(a) = 0?
-2, -1, 1
Let d = -277/9 - -31. Factor 0*n**4 - 4/9*n**3 + d*n + 0*n**2 + 2/9*n**5 + 0.
2*n*(n - 1)**2*(n + 1)**2/9
Let k(t) = -t**2 - 6*t - 2. Let f be k(-4). Suppose -w + 19 = -4*w - 5*b, 0 = 4*w + 5*b + 17. Factor -w + 2*i**3 + i + 3*i**3 - f*i**3 + 2*i**2.
-(i - 2)*(i - 1)*(i + 1)
Let l(g) be the third derivative of g**6/30 - 2*g**5/5 + 64*g**3/3 + 53*g**2. Factor l(t).
4*(t - 4)**2*(t + 2)
Let -44/15*u + 38/5*u**2 + 0 - 76/15*u**3 + 2/5*u**4 = 0. Calculate u.
0, 2/3, 1, 11
Let p(g) be the third derivative of g**5/210 + g**4/42 - g**3/7 + 10*g**2. Solve p(f) = 0 for f.
-3, 1
Let q = 133 + -131. Factor 1/4*v**q - 1/4 + 0*v.
(v - 1)*(v + 1)/4
Let h = -4/77 + 328/385. Let -22/5*d - 4/5 - h*d**5 - 46/5*d**2 - 46/5*d**3 - 22/5*d**4 = 0. What is d?
-2, -1, -1/2
Let k be 2/2 + 2*1/(-4). Factor 1/4*f**5 + 0 - k*f**4 + 1/4*f**3 + 0*f**2 + 0*f.
f**3*(f - 1)**2/4
Suppose 0*w**2 + 4/3*w**4 + 0*w + 0 + 2/3*w**5 + 0*w**3 = 0. What is w?
-2, 0
Let h(b) = -b**3 - 4*b**2 + 2. Let q be h(-3). Let p = q + 9. Let -r + 3*r**p - 4 - 4 + 3 + 3 - r**4 + r**3 = 0. What is r?
-1, 1, 2
Let c(r) be the second derivative of -r**8/30240 + r**7/11340 + r**6/1620 - r**4/12 - 3*r. Let i(m) be the third derivative of c(m). What is a in i(a) = 0?
-1, 0, 2
Let j(d) be the first derivative of -d**3/9 - d**2/3 + 3. Let j(p) = 0. Calculate p.
-2, 0
Let d be 267*(0 - (-3)/9). Suppose -27*o - 278*o**3 - 50*o**5 + 190*o**4 + 8 - 37*o + 105*o**2 + d*o**2 = 0. What is o?
2/5, 1
Let y be (9 + -4)/(10/4). Let v(w) be the third derivative of -y*w**2 + 0 + 1/30*w**5 + 1/12*w**4 - 1/105*w**7 + 0*w - 1/60*w**6 + 0*w**3. Factor v(k).
-2*k*(k - 1)*(k + 1)**2
Let w(c) = 57*c**3 - 63*c**2 + 96*c - 33. Let a(l) = 7*l**3 - 8*l**2 + 12*l - 4. Let x(f) = -33*a(f) + 4*w(f). Determine h, given that x(h) = 0.
0, 2
Let v(c) be the second derivative of -c**5/70 + c**4/6 - 9*c. Factor v(q).
-2*q**2*(q - 7)/7
Let y(t) be the second derivative of 1/27*t**4 + 0*t**2 - 1/90*t**5 - 1/27*t**3 + 3*t + 0. Suppose y(b) = 0. What is b?
0, 1
Let t(z) = -21*z**2 - 13*z - 5. Let q be ((-4)/10)/((-5)/(-25)). Let y(g) = -21*g**2 - 13*g - 4. Let i(k) = q*t(k) + 3*y(k). Factor i(c).
-(3*c + 1)*(7*c + 2)
Suppose 13*n + 70 = 18*n. Suppose 0 = 4*t - g - n, -5*g + 2 + 24 = 4*t. Find l, given that -2/11*l**2 + 2/11*l**3 + 0 + 0*l + 4/11*l**t = 0.
-1, 0, 1/2
Let c(f) be the first derivative of -2*f**5/5 + f**4 - 2*f**3/3 - 1. Suppose c(d) = 0. Calculate d.
0, 1
Let k(t) = -8*t**3 + 24*t**2 - 32*t + 12. Let w(y) = -15*y**3 + 47*y**2 - 64*y + 25. Let r(m) = 7*k(m) - 4*w(m). Factor r(p).
4*(p - 2)**2*(p - 1)
Let p(a) be the second derivative of 4*a**4 - 3/4*a**5 - 5/2*a**6 - 2*a**3 + 0*a**2 + a + 0. Factor p(i).
-3*i*(i + 1)*(5*i - 2)**2
Factor -2*j**3 + 64*j - 33*j - 31*j.
-2*j**3
Let r = -14831/48 + 309. Let t(o) be the second derivative of 0*o**2 + 1/120*o**6 - r*o**4 + 0*o**5 + 0*o**3 + o + 0. Factor t(v).
v**2*(v - 1)*(v + 1)/4
Let d(f) be the first derivative of -5 - 1/18*f**3 + 0*f + 1/30*f**5 - 1/12*f**2 + 1/24*f**4. Factor d(b).
b*(b - 1)*(b + 1)**2/6
Let q(w) be the first derivative of -2 - 21/25*w**5 + 3/10*w**4 + 0*w**3 + 0*w**2 + 1/2*w**6 + 0*w. Suppose q(f) = 0. Calculate f.
0, 2/5, 1
What is s in 0*s - 2/5*s**3 + 0 - 2/5*s**2 = 0?
-1, 0
Let x(l) be the third derivative of l**9/15120 + l**8/1680 + l**7/630 + l**5/30 - 6*l**2. Let m(k) be the third derivative of x(k). Factor m(c).
4*c*(c + 1)*(c + 2)
Let b be 4/((-12)/(-7))*-3. Let j(y) = -y - 7. Let a be j(b). Factor -4/7*q**4 + a*q + 0*q**2 + 0 - 2/7*q**3 - 2/7*q**5.
-2*q**3*(q + 1)**2/7
Let i(m) be the second derivative of -m**7/840 + m**6/480 - m**2 + 2*m. Let k(r) be the first derivative of i(r). What is n in k(n) = 0?
0, 1
Factor -12*a - 1/5*a**3 + 72/5 + 14/5*a**2.
-(a - 6)**2*(a - 2)/5
Let d(j) = 11*j**5 - 5*j**4 - 9*j**3 + 7*j**2 - j. Let g(l) = -12*l**5 + 4*l**4 + 10*l**3 - 8*l**2 + 2*l. Let p(q) = -4*d(q) - 3*g(q). Factor p(s).
-2*s*(s - 1)**2*(2*s + 1)**2
Suppose -3*s = -34*u + 38*u + 4, -4*s - 8 = 4*u. Find g such that -g - 3*g**u - 9/4*g**3 + 1/2*g**4 + 0 + 3/4*g**5 = 0.
-1, -2/3, 0, 2
Let j(u) be the third derivative of u**5/240 + u**4/96 + 5*u**2. Factor j(m).
m*(m + 1)/4
Let p(d) be the third derivative of d**6/360 + d**5/180 + 12*d**2. Factor p(m).
m**2*(m + 1)/3
Let a(z) be the second derivative of -z**6/10 + 9*z**5/20 - z**4/2 + 14*z. Factor a(m).
-3*m**2*(m - 2)*(m - 1)
Let b(t) be the second derivative of 2/5*t**3 - 2/5*t**2 - 3*t + 1/25*t**5 - 1/5*t**4 + 0. Factor b(w).
4*(w - 1)**3/5
Suppose 29 - 129 = 5*s. Let r be s/(-7)*21/6. Factor -2*l + 6*l**2 - 10 + r.
2*l*(3*l - 1)
Suppose 8 = 4*l - 0. Find i such that -5*i**2 - l*i**2 + 3*i - 5*i + 3*i**2 = 0.
-1/2, 0
Let m(x) be the first derivative of x**8/840 - x**7/420 - x**6/180 + x**5/60 + 5*x**3/3 + 3. Let v(q) be the third derivative of m(q). Factor v(r).
2*r*(r - 1)**2*(r + 1)
Let x(c) be the first derivative of 5*c**3/3 + 50*c**2 + 500*c - 10. Suppose x(q) = 0. Calculate q.
-10
Suppose -8*w + 3*w**5 - 4*w**4 + 12*w**3 + 0*w**2 - 7*w**5 + 2*w**2 + 2*w**2 = 0. What is w?
-2, -1, 0, 1
Let h(t) be the first derivative of -t**4/6 + t**3/3 - t**2/6 - 38. Factor h(x).
-x*(x - 1)*(2*x - 1)/3
Let a = -34/9 - -341/90. Let d(f) be the third derivative of 2/9*f**3 + 0 + 0*f + 1/12*f**4 + a*f**5 + 2*f**2. Factor d(n).
2*(n + 1)*(n + 2)/3
Let h(f) be the second derivative of -1/4*f**4 + 0 - 1/2*f**3 - 8*f + 0*f**2. Factor h(u).
-3*u*(u + 1)
Let a(j) be the second derivative of 1/25*j**6 + 0 - 5*j + 0*j**4 + 1/25*j**5 + 0*j**3 + 1/105*j**7 + 0*j**2. Factor a(h).
2*h**3*(h + 1)*(h + 2)/5
Let w(d) be the first derivative of -d**6/360 + d**5/120 + d**4/12 + 2*d**3 + 5. Let n(b) be the third derivative of w(b). Factor n(a).
-(a - 2)*(a + 1)
Let c(s) = -s**5 - 6*s**4 - 2*s**3 + 8*s**2 + s + 2. Let k(y) = -3 - y**5 + y + 5*y**3 + 2 - y**2 - 3*y**3 - y**3. Let w(p) = c(p) + 2*k(p). Factor w(n).
-3*n*(n - 1)*(n + 1)**3
Find d such that 9 - 13 - 8 - 2*d**2 - 14*d = 0.
-6, -1
Let u(r) be the first derivative of -10*r**6/3 + 13*r**5 - 75*r**4/4 + 35*r**3/3 - 5*r**2/2 + 15. Factor u(n).
-5*n*(n - 1)**3*(4*n - 