t**w + 1/2*t + 0 = 0. What is t?
0, 1
Let m = 58/5 + -10. What is w in m*w**3 - 2/5*w**2 + 0*w + 0 = 0?
0, 1/4
Let q(m) be the first derivative of -m**4/2 - 4*m**3/3 - m**2 + 1. Factor q(w).
-2*w*(w + 1)**2
Let b be (-1)/(-2)*-2*-2. Determine m so that 3*m - 3*m**3 + m**2 - b*m**4 + 1 + 6*m - 6*m = 0.
-1, -1/2, 1
Let n(i) = 7*i**2 + 6*i + 6. Let r(s) = -s**2 - s - 1. Let k(w) = 5*n(w) + 30*r(w). Factor k(y).
5*y**2
Let o(j) be the second derivative of j**7/189 + j**6/135 - j**5/45 + 41*j. Factor o(l).
2*l**3*(l - 1)*(l + 2)/9
Let m(d) be the first derivative of -d**5/25 + d**4/10 + d**3/3 - 3*d**2/5 + 9. Suppose m(r) = 0. Calculate r.
-2, 0, 1, 3
Let d(l) be the second derivative of 1/72*l**4 + 1/36*l**3 - 3*l + 0*l**2 + 0. Factor d(v).
v*(v + 1)/6
Let k(w) be the third derivative of w**6/200 - 3*w**5/100 + 3*w**4/40 - w**3/10 - 2*w**2. Let k(z) = 0. Calculate z.
1
Let y = -131/3 - -44. Factor -1/3*z**2 - 1/2*z + 1/6*z**5 + y*z**3 - 1/6 + 1/2*z**4.
(z - 1)*(z + 1)**4/6
Factor 4*q**3 + 2*q**5 + 59*q**2 - 6*q**3 - 61*q**2 + 2*q**4.
2*q**2*(q - 1)*(q + 1)**2
Let p(x) be the second derivative of -x**7/2940 - x**6/1260 + x**3/6 - x. Let r(l) be the second derivative of p(l). Factor r(t).
-2*t**2*(t + 1)/7
Let p(j) be the second derivative of -j**5/4 - 5*j**4/3 + 5*j**3/6 + 10*j**2 - 5*j. Suppose p(o) = 0. Calculate o.
-4, -1, 1
Let g = 1 + 1. Let i = 0 + 3. Solve t**3 - 3*t**i + 2*t**2 - 2*t**g + 2*t**2 = 0.
0, 1
Factor -p**4 + 0 + 2/3*p**3 + p**2 - 2/3*p.
-p*(p - 1)*(p + 1)*(3*p - 2)/3
Let k(i) be the second derivative of 0 - 1/8*i**5 + 0*i**3 + 7/60*i**6 + 0*i**2 + i - 1/12*i**4. Factor k(s).
s**2*(s - 1)*(7*s + 2)/2
Let z(x) be the first derivative of -3/2*x**2 - 7 + x**3 - 6*x. Factor z(d).
3*(d - 2)*(d + 1)
Let -29*c**2 + 2*c + 36*c**2 - 4 + 10*c = 0. What is c?
-2, 2/7
Let j = -3 - -10. Solve -5*h - 3*h - h**2 + j*h = 0.
-1, 0
Let c = 72/1235 + -76477/11115. Let t = -33/5 - c. Let 0 + t*o + 8/3*o**3 + 16/9*o**4 + 4/3*o**2 = 0. Calculate o.
-1/2, 0
Let s(y) be the third derivative of -4*y**7/525 + 11*y**5/150 - 3*y**4/20 + 2*y**3/15 + y**2. Find k such that s(k) = 0.
-2, 1/2, 1
Let o(v) = -v**3 - 5*v**2 + 4. Let u be o(-5). Suppose 12 = u*y + 2*y. Factor 0 - 2/9*g**5 + 0*g**4 + 0*g + 2/9*g**3 + 0*g**y.
-2*g**3*(g - 1)*(g + 1)/9
Suppose 0 = 4*h - 2*h - 4, -3*o - 2*h = -16. Factor -o*l**2 - 4 - 2*l**2 + l**2 + 4*l**2 + 4*l.
-(l - 2)**2
Let r(t) be the third derivative of -t**7/42 + t**5/6 - 5*t**3/6 - 11*t**2. Factor r(m).
-5*(m - 1)**2*(m + 1)**2
Let k = 3 + 13. Let b = k - 14. Factor -2/3*g + 0 - b*g**3 - 2*g**2 - 2/3*g**4.
-2*g*(g + 1)**3/3
Suppose -8 = 2*y - 4*y. Solve y*j - 2*j**2 + 0*j - j**2 + j**2 = 0 for j.
0, 2
Let k(x) = x**2 + 10*x + 3. Let b be k(-9). Let h be 14/12*b/(-4). Find l, given that 1/4*l + 0 + h*l**2 + 9/4*l**4 + 15/4*l**3 = 0.
-1, -1/3, 0
Let q(p) be the second derivative of -p**5/90 - p**4/27 + 7*p**3/27 - 4*p**2/9 - 6*p. Let q(l) = 0. Calculate l.
-4, 1
Let m(v) be the first derivative of -5/7*v**2 - 4 + 8/7*v + 2/21*v**3. Factor m(a).
2*(a - 4)*(a - 1)/7
Suppose -2*v - 4 = s - 1, 3*s = -5*v - 9. Let t(c) be the third derivative of -c**2 + 1/24*c**4 + v + 1/60*c**5 + 0*c + 0*c**3. Determine q so that t(q) = 0.
-1, 0
Let i = -6 + 7. Let g = i + 0. Factor -2*h**2 + 2*h + 2*h + 4*h**2 + 3 - g.
2*(h + 1)**2
Let -5*n**5 - 6*n - 20*n**4 + 12*n - 30*n**3 - 20*n**2 - 11*n = 0. Calculate n.
-1, 0
Let f(p) be the second derivative of 5*p**4/12 + 5*p**3/3 + 5*p**2/2 - 5*p. Let f(s) = 0. What is s?
-1
Let d = 3 - 1. Let -8/9*t**3 - 2/9 - d*t**2 - 4/3*t = 0. Calculate t.
-1, -1/4
Let g(q) = q**2 + 4*q - 2. Let y be g(-5). Suppose f**4 + 3*f - y*f - 3*f**4 = 0. What is f?
0
Let j(n) = n**3 - 5*n**2 - 7*n - 4. Let d(w) = -w**3 - w**2 - w. Let k(c) = -6*d(c) - 2*j(c). Factor k(t).
4*(t + 1)**2*(t + 2)
Factor 18/5*x**2 + 4*x - 6/5 - 8/5*x**3.
-2*(x - 3)*(x + 1)*(4*x - 1)/5
Let x(c) be the first derivative of 4*c**5/5 - 4*c**3/3 + 25. Let x(l) = 0. What is l?
-1, 0, 1
Let h be 36/54 + (-2)/6. Let 0 + 1/3*f**2 + 2/3*f - h*f**3 = 0. What is f?
-1, 0, 2
Let x(q) be the third derivative of q**8/168 + 2*q**7/105 - q**6/60 - q**5/15 - 6*q**2. What is z in x(z) = 0?
-2, -1, 0, 1
Factor -1/2*v**2 + 0 - v + 1/2*v**3.
v*(v - 2)*(v + 1)/2
Let u be (-470)/12*(-4)/(-5). Let m = u + 32. Factor m*k - 2/3*k**3 + 2/3*k**2 - 2/3.
-2*(k - 1)**2*(k + 1)/3
Let t(u) be the first derivative of 2/3*u**2 - 1 - 2/9*u**3 + 0*u. Factor t(j).
-2*j*(j - 2)/3
Let u(k) be the first derivative of -2*k**3/21 + 8*k**2/7 - 32*k/7 - 25. Suppose u(p) = 0. Calculate p.
4
Let v be 261/6 - 6/(-4). Let b be 48/v + (-6)/15. Factor b - 7/3*z - 4/3*z**2.
-(z + 2)*(4*z - 1)/3
Let d(y) be the second derivative of -1/135*y**6 - 2/27*y**3 - 2/45*y**5 - 5/54*y**4 + 0 + 0*y**2 + 2*y. What is x in d(x) = 0?
-2, -1, 0
Factor 0 + 1/4*s**2 - 1/4*s.
s*(s - 1)/4
Let a = 1240 + -6167/5. Factor -6/5*v + a*v**2 + 0.
3*v*(11*v - 2)/5
Factor 8 - 5 + 768*q**4 + 768*q**3 + 288*q**2 + 52*q - 4*q.
3*(4*q + 1)**4
Let f(d) be the third derivative of d**6/720 - d**4/48 - d**3/18 + 5*d**2. Suppose f(n) = 0. Calculate n.
-1, 2
Let v(c) be the third derivative of -c**8/168 + c**7/70 + c**6/120 - c**5/20 + c**4/24 - 5*c**2. Determine j so that v(j) = 0.
-1, 0, 1/2, 1
Solve -2/9*a**4 + 0 - 2/9*a**3 + 0*a + 4/9*a**2 = 0 for a.
-2, 0, 1
Let c(n) = -n**2 + 13*n - 9. Let k be c(6). Let w = -31 + k. Factor j**w + 0 - 1/2*j - 1/2*j**3.
-j*(j - 1)**2/2
Suppose -c + 2 = -1. Suppose 2*h + c*z = 0, -5*h = -2*h - z. Factor h - 1/2*p + 1/2*p**2.
p*(p - 1)/2
Let u(h) be the third derivative of 0*h + 8*h**2 - 1/660*h**6 + 2/33*h**3 + 0 + 1/44*h**4 + 0*h**5. Solve u(j) = 0 for j.
-1, 2
Let c be -119*-1*5/100. Let g = c + -26/5. Factor g*z**2 + 0*z**3 + 0 - 3/4*z**4 + 0*z.
-3*z**2*(z - 1)*(z + 1)/4
Let t(b) be the first derivative of 7*b**7/40 + 7*b**6/5 + 39*b**5/10 + 4*b**4 + 2*b**3 - b**2 - 3. Let x(l) be the second derivative of t(l). Factor x(j).
3*(j + 2)**2*(7*j + 2)**2/4
Let j(q) be the second derivative of -2*q**6/15 + 4*q**5/5 + 11*q. Let j(v) = 0. Calculate v.
0, 4
Let y = 2324/4245 - 4/283. Factor y + 16/15*w - 2/3*w**2.
-2*(w - 2)*(5*w + 2)/15
Let y(p) = -9*p**5 + p**4 - 2*p**3 - p**2 - 3*p. Let m(a) = 5*a**5 - a**4 + a**3 + a**2 + 2*a. Let b(h) = -7*m(h) - 4*y(h). What is k in b(k) = 0?
-2, -1, 0, 1
Suppose -237*w + 238*w - 2 = 0. Factor -2/7*c**3 + 0 - 8/7*c + 8/7*c**w.
-2*c*(c - 2)**2/7
Let z be 1/((-12)/(-39)) + (-6)/3. Let d(o) = 2*o**3 + o**2 - o + 1. Let n be d(1). Determine a so that -1/4*a**4 - a**n - z*a**2 - 1/2*a + 0 = 0.
-2, -1, 0
Let x(v) = 4*v**3 - 4*v**2 + v + 2. Let t be x(1). Factor 8/5*k**2 + 12/5*k**t + 2/5*k**5 + 0 + 8/5*k**4 + 2/5*k.
2*k*(k + 1)**4/5
Let i(z) be the first derivative of z**6/18 - 2*z**5/5 + 2*z**4/3 + z**3/3 + 4. Let k(b) be the third derivative of i(b). Factor k(d).
4*(d - 2)*(5*d - 2)
Let q(w) be the first derivative of -w**4/2 + 16*w**3/3 - 16*w**2 - 4. Find d, given that q(d) = 0.
0, 4
Let m(x) = -6*x**3 + 4*x**2 + 4. Let n(t) = 17*t**3 - 10 - 3 - 5*t**2 + 2 - 6*t**2. Let k(c) = -11*m(c) - 4*n(c). Let k(f) = 0. Calculate f.
0
Let p = -4205/7 + 601. Factor 8/7*a**2 + 10/7*a + 4/7 + p*a**3.
2*(a + 1)**2*(a + 2)/7
Let a(m) be the second derivative of -m**6/60 + m**4/4 - 2*m**3/3 + 5*m**2/2 + 6*m. Let c(o) be the first derivative of a(o). Factor c(g).
-2*(g - 1)**2*(g + 2)
Let f(d) = 9*d**3 - 39*d**2 - 120*d - 72. Let l(w) = -w**3 + 5*w**2 + 15*w + 9. Let n(y) = -6*f(y) - 51*l(y). Factor n(x).
-3*(x + 1)*(x + 3)**2
Let y be (5/(-90))/((-2)/6). Let u(l) be the third derivative of y*l**4 + 0*l + 2*l**2 + 0 - 1/30*l**5 - 1/3*l**3. Factor u(q).
-2*(q - 1)**2
Let v(z) be the first derivative of -1/12*z**3 - 1/2*z - 1 - 3/8*z**2. Let v(s) = 0. What is s?
-2, -1
Let m(y) be the second derivative of 3/2*y**2 + 0 + 3/2*y**5 + 5/2*y**3 + 1/14*y**7 + 5*y + 5/2*y**4 + 1/2*y**6. Solve m(s) = 0 for s.
-1
Suppose 33 + 132 = 5*u. Suppose -4*a + u = s, 2 = 3*a - s - 21. Determine l, given that -98/5*l**5 - 8/5*l + 6/5*l**3 - 28*l**4 + 0 + a*l**2 = 0.
-1, 0, 2/7
Let y = 6 - 1. Suppose t**3 - 4*t**5 + t**2 - t**4 + 3*t**y + 0*t**3 = 0. What is t?
-1, 0, 1
Let r(c) be the first derivative of 2*c**2 + 4 - 1/4*c**4 - 4*c + 1/3*c**3. Factor r(m).
-(m - 2)*(m - 1)*(m + 2)
Suppose -69 = 3*q - 3