, given that t*x**2 + x - x + 4*x**3 + 2*x**4 = 0.
-1, 0
Let n(l) = l**2 - 8*l + 2. Let j be n(9). Let o = j + -9. Find w such that 0*w + 0 - 1/2*w**o = 0.
0
Factor 10*m**2 + 379 - 369 + 2*m + 23*m.
5*(m + 2)*(2*m + 1)
Suppose -4*z + 2 = -3*z. Let s(o) = o + 16. Let u be s(-10). Let -4*q + 2 - 10*q**z - 2 - u*q**3 = 0. What is q?
-1, -2/3, 0
Let o(b) be the third derivative of -b**5/270 + b**4/54 + b**3/9 - 3*b**2. Suppose o(j) = 0. What is j?
-1, 3
Let r be (-10)/8*2*12/(-15). Let o(q) be the second derivative of 0*q**2 + 1/15*q**3 + 0 - 1/30*q**4 + r*q. Factor o(j).
-2*j*(j - 1)/5
Let x be 8/(-12)*(-30)/4. Let a = -2 + x. Factor -4 + 4 + u**2 + 2*u**a + u**4.
u**2*(u + 1)**2
Let s(w) be the second derivative of w**8/3360 + w**7/1260 - w**6/72 + w**5/20 - 7*w**4/12 - w. Let j(y) be the third derivative of s(y). Factor j(n).
2*(n - 1)**2*(n + 3)
Let u(d) be the third derivative of d**6/40 + 7*d**5/20 + 15*d**4/8 + 9*d**3/2 + 14*d**2. Find c such that u(c) = 0.
-3, -1
Let g(h) be the first derivative of -h**6/60 + h**5/20 - h**3/6 + h**2/4 + 2*h + 3. Let l(o) be the first derivative of g(o). Factor l(k).
-(k - 1)**3*(k + 1)/2
Let q(m) be the second derivative of m**6/135 + 2*m**5/45 + m**4/27 - 4*m**3/27 - m**2/3 + m. Determine n, given that q(n) = 0.
-3, -1, 1
Let j(g) be the second derivative of 0 - 3*g + 1/12*g**4 + 2*g**2 + 2/3*g**3. Factor j(i).
(i + 2)**2
Let r(i) be the second derivative of 2*i**7/21 - 2*i**6/15 - i**5/5 + i**4/3 + 10*i. Factor r(m).
4*m**2*(m - 1)**2*(m + 1)
Suppose -g + 4 - 3 = 0, -4*m + 34 = -2*g. Let w = m + -4. Factor -3*d**3 - 6*d**4 + 0*d**3 + 3*d**w + 6*d**3.
3*d**3*(d - 1)**2
Suppose -8 + 23 = -4*i - u, -2*u = 6. Let s be (i/12)/((-6)/32). Factor s*l**3 + 1/3 + 4/3*l + 2*l**2 + 1/3*l**4.
(l + 1)**4/3
Let n(d) be the second derivative of -1/10*d**5 + 0 + 1/6*d**4 - 1/30*d**6 - 1/2*d**2 + 1/6*d**3 + 1/42*d**7 + d. Suppose n(q) = 0. Calculate q.
-1, 1
Let 3/8*g**2 + 0 + 3/2*g**4 - 15/8*g**3 + 0*g = 0. Calculate g.
0, 1/4, 1
Let j = 19/6 + -17/6. Factor 1/3 + j*c**3 - 1/3*c**2 - 1/3*c.
(c - 1)**2*(c + 1)/3
Suppose 4*y + y + y**2 - 5*y - 3 - 2*y = 0. Calculate y.
-1, 3
Let g = 138 - 135. Let -3/7 + 3/7*p + 3/7*p**2 - 3/7*p**g = 0. Calculate p.
-1, 1
Let b be (5/7 + -1)/((-24)/42). Let a(v) be the second derivative of b*v**2 - 3*v + 0 - 1/6*v**4 + 0*v**3 + 0*v**5 + 1/30*v**6. Factor a(g).
(g - 1)**2*(g + 1)**2
Let n be 2/12 + (-11)/66. Suppose -1/2*o**4 - 1/4*o**2 + 0*o + 3/4*o**3 + n = 0. Calculate o.
0, 1/2, 1
Suppose 5*p - 5 = 0, -3*i - 5*p - 11 = 2. Let l = i - -8. Factor 3*g**2 - g**2 + 0*g**l.
2*g**2
Let w be (-14)/7 + (-36)/(-10). Let s be (-44)/110 - -2*1. Factor -2/5*l**2 - w + s*l.
-2*(l - 2)**2/5
Let f(j) be the first derivative of 6*j**5/5 + 3*j**4/4 - 5*j**3 + 3*j**2 - 2. Let f(w) = 0. What is w?
-2, 0, 1/2, 1
Let n be (7 - 3)/((-1)/(-1) - -1). Factor 1/4*k**n + 1/4 + 1/2*k.
(k + 1)**2/4
Let d(u) = 23*u + 25. Let j be d(-1). Factor 2/7*f - 2/7 - 2/7*f**3 + 2/7*f**j.
-2*(f - 1)**2*(f + 1)/7
Let h(v) be the third derivative of 1/2*v**3 - 1/20*v**5 + 3*v**2 - 1/40*v**6 + 1/8*v**4 + 0 + 0*v. Suppose h(c) = 0. What is c?
-1, 1
Factor -1/6*u**5 + 0 + 0*u**2 + 1/2*u**4 + 0*u - 1/3*u**3.
-u**3*(u - 2)*(u - 1)/6
Factor 1/4*t**2 - 1/4 + 1/4*t - 1/4*t**3.
-(t - 1)**2*(t + 1)/4
Suppose 3*q - 4 + 1 = 0, 0 = 4*h - 3*q - 97. Factor 25 - h + c**4 - c**2.
c**2*(c - 1)*(c + 1)
Let f(y) = -y**4 + y**3 + y**2. Let g(r) = 9*r**3 + 3*r**2 - 6*r - 3. Let a(k) = -3*f(k) + g(k). Suppose a(m) = 0. Calculate m.
-1, 1
Let n(j) be the first derivative of -j + 1/2*j**2 - 1/4*j**4 + 8 + 1/3*j**3. Let n(v) = 0. What is v?
-1, 1
Let u(x) be the first derivative of 2*x**6/3 + 4*x**5/5 - 62. Factor u(k).
4*k**4*(k + 1)
Let x(n) = -n**3 - 2*n**2 + 2*n + 4. Let c be (3 + 20/(-8))*-4. Let g be x(c). Factor -9/5*q**2 + g - 3/5*q**4 + 9/5*q**3 + 3/5*q.
-3*q*(q - 1)**3/5
Factor -19*a**2 + 7*a**3 + 20*a**2 - 8*a - 5*a**4 + 8*a**5 + 4 - 7*a**5.
(a - 2)**2*(a - 1)**2*(a + 1)
Let s(j) be the first derivative of j**6/48 - j**4/16 + j**2/16 + 9. Find t such that s(t) = 0.
-1, 0, 1
Let l = -7 + 9. Factor -8*n - 2 + n**3 + 2 + 9*n - 2*n**l.
n*(n - 1)**2
Suppose 4*r - 18 - 14 = 2*d, 0 = d + 4. Let o be r/15 + (-8)/(-5). Factor 1 + 1 - 5*z + o*z**2 + z.
2*(z - 1)**2
Let s(d) = -7*d**3 + 20*d + 2. Let w(o) = -15*o**3 + 40*o + 5. Let f(j) = -5*s(j) + 2*w(j). Factor f(v).
5*v*(v - 2)*(v + 2)
Suppose -6*a**3 + 5*a**3 - 2*a**3 + a**3 + 2*a = 0. Calculate a.
-1, 0, 1
Suppose 5*w + 5*j = w + 2, -w + 5 = -j. Let t = 0 + w. Factor -4 + t*k**3 - 3*k + 6 - 2.
3*k*(k - 1)*(k + 1)
Let n(u) be the first derivative of 5*u**4/4 + 5*u**3/3 - 5*u**2/2 - 5*u + 9. Let n(z) = 0. What is z?
-1, 1
Let r(s) = -s**4 + 8*s**3 - 30*s**2 + 28*s - 11. Let u(x) = x**3 + x**2 - x + 1. Let b(z) = r(z) + 3*u(z). Factor b(c).
-(c - 8)*(c - 1)**3
Suppose -27 = -4*h + 5*h. Let q be (-48)/h + (-4)/(-18). What is y in 2 + 3*y**q + y**2 - 6*y - 2*y**3 + 2*y**2 = 0?
1
Find n, given that 8*n**2 - 3*n**4 + 48*n - 6*n**4 + 6*n**3 - 54*n + 1 = 0.
-1, 1/3, 1
Let y be 0/(0 + (4 - 2)). Let b = 2 - y. Let 2*r + r - 2*r**b - r = 0. What is r?
0, 1
Let m(q) = -4*q**3 + 20*q**2 - 16*q + 4. Let r(k) = 4*k**3 - 19*k**2 + 15*k - 3. Let c(p) = -3*m(p) - 4*r(p). Factor c(w).
-4*w*(w - 3)*(w - 1)
Suppose 0 + 6/11*h + 6/11*h**5 - 24/11*h**4 - 24/11*h**2 + 36/11*h**3 = 0. What is h?
0, 1
Let y = 8 + 2. Let b be 10/(-2)*(-6)/y. Find c, given that 17*c**3 + 4*c**4 + b*c**4 - 5*c**4 - 4*c**2 - 15*c**3 = 0.
-2, 0, 1
Let y = -11/72 + 7/36. Let b(h) be the first derivative of 1/16*h**4 - 1/12*h**3 + 2 - y*h**6 + 0*h + 1/20*h**5 + 0*h**2. Factor b(q).
-q**2*(q - 1)**2*(q + 1)/4
Let -148*v**2 - 25*v**3 + 6 + 2 - 12*v + 37*v**3 + 140*v**4 = 0. What is v?
-1, -2/7, 1/5, 1
Let m(o) be the first derivative of -o**5/15 + o**4/12 + o**3/9 - o**2/6 - 8. Solve m(h) = 0 for h.
-1, 0, 1
Let 0*q + 0 + 4/3*q**2 = 0. What is q?
0
Suppose 4*m = 12, 3*d + m - 13 = -1. Solve -4*q**3 - 4*q**2 + 2*q**3 - 13*q**4 + 16*q**d + 3*q**4 = 0 for q.
0, 2/5, 1
Factor 4*v + 0*v**3 + 7*v**2 + 4 - v**3 - 8*v**2.
-(v - 2)*(v + 1)*(v + 2)
Let a(y) be the first derivative of 3*y**4/8 - y**3/2 - 15*y**2/4 - 9*y/2 + 6. Solve a(j) = 0 for j.
-1, 3
Let v(g) be the first derivative of -3 - 10/33*g**3 + 2/55*g**5 - 2/11*g**2 + 0*g + 1/33*g**6 - 3/22*g**4. Factor v(o).
2*o*(o - 2)*(o + 1)**3/11
Let o(s) be the third derivative of s**7/1260 + s**6/360 - s**4/72 - s**3/36 + 7*s**2. Factor o(g).
(g - 1)*(g + 1)**3/6
Let n(m) be the second derivative of -2*m**6/15 + 10*m. Find b such that n(b) = 0.
0
Suppose -4*h**3 - 22*h**5 + 8*h**4 + 24*h**5 + 10*h**3 = 0. Calculate h.
-3, -1, 0
Let f(x) be the third derivative of -x**9/3024 - x**8/560 - x**7/280 - x**6/360 - x**3/6 + x**2. Let g(k) be the first derivative of f(k). Factor g(h).
-h**2*(h + 1)**3
Let o = -20 - -20. Suppose 1/3*r**4 - 2/3*r**3 + 0*r + 1/3*r**2 + o = 0. Calculate r.
0, 1
Let a(w) be the first derivative of w**8/10080 - w**6/360 - w**5/90 - w**4/48 + 4*w**3/3 + 3. Let t(i) be the third derivative of a(i). Factor t(v).
(v - 3)*(v + 1)**3/6
Let r = -2 - -4. Factor -s**r - 2*s**3 - 2*s**2 + 0*s**2 + s**2 + 2*s**5 + 2*s**4.
2*s**2*(s - 1)*(s + 1)**2
Suppose 34*q - 36*q**3 + 2*q**5 + 12*q**4 - 2*q - 48*q**2 + 38*q**3 = 0. Calculate q.
-4, 0, 1
Suppose -2*u + 2*v = -14, -u - 4*v - 19 = -2*u. Suppose 2/7*o**2 - 2/7*o**4 - 2/7*o + 2/7*o**u + 0 = 0. What is o?
-1, 0, 1
Let q(l) be the second derivative of -l**4/16 - l**3/4 + 4*l. Factor q(x).
-3*x*(x + 2)/4
Let n(y) be the first derivative of 7/9*y**3 - 4/3*y + 2*y**2 - 5. Factor n(s).
(s + 2)*(7*s - 2)/3
Let x(u) be the second derivative of u**6/75 + u**5/10 + 3*u**4/10 + 7*u**3/15 + 2*u**2/5 - 4*u. Factor x(j).
2*(j + 1)**3*(j + 2)/5
Factor 2/5*o**3 + 2/5*o + 0 + 4/5*o**2.
2*o*(o + 1)**2/5
Let p(v) be the third derivative of -7*v**6/240 - v**5/24 + v**4/24 + 22*v**2. Let p(s) = 0. Calculate s.
-1, 0, 2/7
Factor -5 - 2*z**2 - 4*z**2 + 40*z - 75 + z**2.
-5*(z - 4)**2
Let z(w) be the first derivative of -w**7/420 - w**6/90 - w**5/60 - w**3 - 1. Let c(s) be the third derivative of z(s). Factor c(f).
-2*f*(f + 1)**2
Let u be (-1)/(-1) + (-21 - -21). Factor 3/2*p - 1/2*p**2 - u.
-(p - 2)*(p - 1)/2
Let t(h) = h**3 + 10*h**2 - h - 9. Let x be t(-10). Find v, 