2 + 2*t**3 = 0. What is t?
-2, -1, 1
Let p be (-12)/(-15) + (-71)/90. Let a(f) be the third derivative of 1/945*f**7 + 0 - 1/108*f**4 + 0*f**3 + p*f**5 - 2*f**2 - 1/180*f**6 + 0*f. Solve a(s) = 0.
0, 1
Let q(s) be the third derivative of 7*s**5/12 + 5*s**4/4 - 5*s**3/6 + 16*s**2. Factor q(l).
5*(l + 1)*(7*l - 1)
Suppose -2*f - k - k = -10, -5*f = 3*k - 31. Suppose 10 - 2 + f*l + 2*l**2 + 0*l = 0. Calculate l.
-2
Let a(p) be the third derivative of -p**7/42 - p**6/15 - p**5/60 + p**4/12 - 4*p**2. Factor a(o).
-o*(o + 1)**2*(5*o - 2)
Let q(z) be the first derivative of -1/2*z**4 + 0*z**5 + 0*z**3 + 0*z + 0*z**2 + 1/3*z**6 - 2. Factor q(g).
2*g**3*(g - 1)*(g + 1)
Let x = 1/31 + 26/155. Factor 1/5*a**2 + 0 - x*a.
a*(a - 1)/5
Let b(y) be the third derivative of 0*y**3 - y**2 + 1/240*y**6 + 1/48*y**4 + 0*y + 1/60*y**5 + 0. Factor b(q).
q*(q + 1)**2/2
What is p in -35/2*p**2 - 5/4*p**5 + 25/4*p**4 + 45/4 + 15/4*p - 5/2*p**3 = 0?
-1, 1, 3
Find s such that -3/2*s**4 - 9*s**2 + 6*s**3 - 3/2 + 6*s = 0.
1
Let f(z) be the third derivative of 1/3*z**3 + 0 - z**2 + 1/30*z**5 + 1/6*z**4 + 0*z. Factor f(c).
2*(c + 1)**2
Let q(o) = -o**3 + o**2 - o - 1. Suppose 2*c = -0*c + 14. Let i(w) = -c*w**3 + 4*w**2 - 4*w + 2*w**3 - w - 6. Let v(p) = -i(p) + 6*q(p). Factor v(h).
-h*(h - 1)**2
Let l be (-4)/(-4)*(9 + 0). Solve 9*r**4 + 6*r**3 - l*r + 0*r + 0*r**5 - 3 + 3*r**5 - 6*r**2 = 0.
-1, 1
Let d(w) be the second derivative of -2*w**7/147 - 4*w**6/105 + 2*w**5/35 + 4*w**4/21 - 2*w**3/21 - 4*w**2/7 - 15*w. Solve d(l) = 0.
-2, -1, 1
Suppose 0 = 131*t - 147*t + 32. Suppose 1/2*z**t - z + 1/2 = 0. Calculate z.
1
Let n be (-1)/1 + (-18)/(-6) + -2. Factor n*i - 2/7*i**5 + 0 + 2/7*i**2 - 2/7*i**4 + 2/7*i**3.
-2*i**2*(i - 1)*(i + 1)**2/7
Let v(m) = -m**2 - 6*m + 1. Let n be v(-5). Let y(s) = s**2 + 1. Let g(f) = 4*f**2 - 2*f**2 + 7 + 3*f**2. Let i(b) = n*y(b) - g(b). Factor i(h).
(h - 1)*(h + 1)
Let u(w) be the first derivative of -w**7/420 + w**5/15 - 2*w**3/3 + 5. Let g(d) be the third derivative of u(d). Factor g(c).
-2*c*(c - 2)*(c + 2)
Suppose 2*t - 1 - 3 = 0. Factor -5*u + t*u + 2*u + u**3.
u*(u - 1)*(u + 1)
Let s(d) be the third derivative of -d**5/360 - d**4/48 - 44*d**2. Factor s(q).
-q*(q + 3)/6
Let h(u) be the third derivative of -u**5/15 - 7*u**4/36 - u**3/9 + u**2. Solve h(y) = 0 for y.
-1, -1/6
Suppose -2 = 2*w - 6. Let f(k) be the first derivative of -32/5*k**5 - k**w - 1 + 2/3*k**3 + 8*k**4 + 0*k. Let f(d) = 0. What is d?
-1/4, 0, 1/4, 1
Let s(v) = 22*v**2 + 35*v - 13. Let u(g) = -g**2 + g + 1. Let j(b) = s(b) + u(b). Factor j(o).
3*(o + 2)*(7*o - 2)
Let w(n) = 2 - 3 - 6 + 3. Let m(c) = -c**2 - c - 3. Let p(g) = 4*m(g) - 3*w(g). Factor p(i).
-4*i*(i + 1)
Let j(g) be the second derivative of 2*g**6/15 - 9*g**5/20 + g**4/2 - g**3/6 - 9*g. Let j(y) = 0. Calculate y.
0, 1/4, 1
Suppose 11 = 4*o - 5. Let 0*f**2 + f**4 + f**2 - 3*f**o - 4*f**3 - 3*f**2 = 0. Calculate f.
-1, 0
Let z(k) = 8*k**2 + 8*k - 13. Let m(j) = 15*j**2 + 15*j - 25. Let c(u) = -3*m(u) + 5*z(u). Factor c(i).
-5*(i - 1)*(i + 2)
Let u be 4/(-6) + 22/24. Let f be 0/(396/(-231) + (-4)/14). Let 1/4*j - u*j**3 + f + 0*j**2 = 0. Calculate j.
-1, 0, 1
Let u(b) = 7*b**2 + 4*b - 11. Let k(r) = 11*r**2 + 6*r - 17. Let n(f) = -f**2 - 7*f. Let d be n(-8). Let z(i) = d*u(i) + 5*k(i). Solve z(g) = 0.
-3, 1
Let o(h) be the second derivative of -h**5/150 + h**3/15 - h**2 + 2*h. Let v(q) be the first derivative of o(q). Find s, given that v(s) = 0.
-1, 1
Let n(a) be the first derivative of -a**4/4 - 2*a**3 + 2*a + 2. Let q be n(-6). Factor 3*z**3 + z**q + 5 - z - 2*z**3 - 6.
(z - 1)*(z + 1)**2
Let j(t) be the third derivative of 0*t + 0*t**3 - 4*t**2 - 1/48*t**4 + 1/60*t**5 + 0. Suppose j(b) = 0. What is b?
0, 1/2
Let s(p) be the first derivative of 1/2*p**6 + 4 - 9/2*p**2 - 8/3*p**3 - 2*p + 3/2*p**4 + 2*p**5. Solve s(v) = 0.
-2, -1, -1/3, 1
Let j(x) = 10*x**4 - 50*x**3 + 44*x**2 - 12*x + 4. Let m(n) = -n**4 - n**3 + n**2 - n + 1. Let q(t) = j(t) - 4*m(t). Find v such that q(v) = 0.
0, 2/7, 1, 2
Let t be (6/(-14))/1*-7. Factor 6*w + 3 - w + 7*w + 12*w**2 + t*w.
3*(w + 1)*(4*w + 1)
Let p(t) be the first derivative of 20*t**4 + 8*t**3/3 - 11*t**2/2 - 2*t - 1. Let p(j) = 0. What is j?
-1/4, 2/5
Suppose 0 = 7*v - 173 + 173. Factor 2/5*c**2 + 0*c + v + 2/5*c**4 - 4/5*c**3.
2*c**2*(c - 1)**2/5
Let -9*d**2 + 9*d**2 - d**2 - 30 - 19 + 14*d = 0. Calculate d.
7
Let y(r) be the first derivative of r**6/21 + 8*r**5/35 + 5*r**4/14 + 4*r**3/21 - 10. Solve y(k) = 0 for k.
-2, -1, 0
Let y(h) = 9*h**2 - h. Let x be y(-1). Suppose -4*q - 7 + 0 = -5*o, 4*o - q = x. Factor 5*k**o - 4*k**4 - 4*k**3 - 2*k**2 + 5*k**3.
-2*k**2*(k - 1)*(2*k - 1)
Let v be (-2 + (-16)/(-9))/((-88)/30). Let h(i) be the second derivative of 1/165*i**6 + 0 + 4*i + 2/33*i**3 + v*i**4 + 2/55*i**5 + 0*i**2. Solve h(f) = 0.
-2, -1, 0
Let d(c) be the first derivative of -9/8*c**2 - 7/20*c**5 - 4 + 1/2*c + 9/16*c**4 + 5/12*c**3. Suppose d(f) = 0. What is f?
-1, 2/7, 1
Suppose 35*t**3 - 15*t**2 - 9 - 71*t**2 + 41*t**2 - 60*t + 29 = 0. Calculate t.
-1, 2/7, 2
Factor 8*i**3 - 3*i + 5*i**2 - 2*i - 5*i**4 - 7*i**3 + 4*i**3.
-5*i*(i - 1)**2*(i + 1)
Let k(d) = -d**2 + 3*d + 3. Let b be k(3). Let -v + 0*v - 5*v**2 - 3 - 4*v**2 - b*v**3 - 8*v = 0. Calculate v.
-1
Factor 0 + 0*z**2 + 2/5*z**3 + 0*z.
2*z**3/5
Let r(n) be the third derivative of n**5/300 + n**2. Factor r(t).
t**2/5
Let p = -4 + 7. Determine b so that 2*b**2 - 4*b + p + 3 - 4 = 0.
1
Let c(l) be the third derivative of l**6/480 + l**5/60 + 5*l**4/96 + l**3/12 - 3*l**2. Suppose c(b) = 0. What is b?
-2, -1
Let u(b) be the first derivative of -b**4/16 + b**3/8 - b**2/16 + 24. What is t in u(t) = 0?
0, 1/2, 1
Let v(o) be the first derivative of -o**3/5 + 3*o**2/2 - 12*o/5 + 13. Determine g so that v(g) = 0.
1, 4
Let n = 2/23 - -9/161. Let j(w) be the second derivative of -1/21*w**6 - 5/21*w**4 - 1/147*w**7 - 5/21*w**3 - n*w**2 - 1/7*w**5 - w + 0. Factor j(k).
-2*(k + 1)**5/7
Suppose -3*h - 72 = -2*p - 74, -5*h - p + 12 = 0. Let 99/5*j**h + 0 + 12/5*j**5 + 51/5*j**3 - 63/5*j**4 - 27/5*j = 0. Calculate j.
-1, 0, 1/4, 3
Let h(a) = a**3 + 4*a**2 + 6*a - 6. Let d(r) = -r**2 - r + 1. Let i(f) = -6*d(f) - h(f). Let i(g) = 0. Calculate g.
0, 2
Let h(g) be the first derivative of 13/4*g**2 + 7/2*g**3 + 1 + g. Factor h(o).
(3*o + 1)*(7*o + 2)/2
Let t(a) be the second derivative of 1/360*a**6 - 1/36*a**4 + 0 - 1/360*a**5 + a - 1/2*a**3 + 0*a**2. Let l(g) be the second derivative of t(g). Factor l(c).
(c - 1)*(3*c + 2)/3
Solve -4/9*c + 2/9*c**3 + 2/9*c**2 + 0 = 0 for c.
-2, 0, 1
Suppose -26 = -4*t + 2. Let a = -3 + t. Solve -3*v**3 + 2*v**2 - 5*v**2 - 4*v**3 + a*v**4 + 5*v**2 + v = 0 for v.
-1/4, 0, 1
Let y(h) be the second derivative of -h**6/120 + h**4/8 + 2*h**3/3 + 5*h. Let f(l) be the second derivative of y(l). Factor f(x).
-3*(x - 1)*(x + 1)
Factor -174 + 162 - 3*p - 5*p + 4*p**2 + 0*p**2.
4*(p - 3)*(p + 1)
Let r(n) be the third derivative of 1/6*n**4 + 0*n + 0 + 0*n**3 - 1/30*n**5 + 2*n**2. Suppose r(w) = 0. What is w?
0, 2
Let s(p) = -2*p + 64. Let q be s(30). Determine t so that 2/7*t**q + 2/7*t**5 + 2/7 + 2/7*t - 4/7*t**2 - 4/7*t**3 = 0.
-1, 1
Factor -15*h + 18*h**2 - 9*h**3 + 9/2 + 3/2*h**4.
3*(h - 3)*(h - 1)**3/2
Let j(t) be the second derivative of t**7/56 - t**6/40 - 3*t**5/80 + t**4/16 + 8*t. Let j(i) = 0. Calculate i.
-1, 0, 1
Suppose 4*y + 2 = -q, 8*y = 3*y - 2*q - 4. Suppose 5*i - 4*b - 44 = 0, y = 3*i + i + 5*b - 27. Factor -5*r**5 + 2*r**2 + 9*r - 2*r**4 - i*r + 4*r**5.
-r*(r - 1)*(r + 1)**3
Factor -2/5*g**2 + 0 - 2/5*g.
-2*g*(g + 1)/5
Let h = 76/45 + -22/15. Factor -2/9 + h*i + 2/3*i**3 + 10/9*i**2.
2*(i + 1)**2*(3*i - 1)/9
Let h(c) be the third derivative of -c**8/1344 - c**7/840 + c**6/96 - c**5/80 - 5*c**2. Solve h(v) = 0 for v.
-3, 0, 1
Let q be (-2)/3 + 112/(-37). Let a = 36/37 - q. Factor 4/3 - 4/3*b**2 - a*b + 14/3*b**3.
2*(b - 1)*(b + 1)*(7*b - 2)/3
Let o(r) = r**3 - 4*r**2 - 9*r - 18. Let p be o(6). Determine w, given that -3/5*w**2 + 3/5 + p*w = 0.
-1, 1
Let t(f) be the first derivative of -f**3/4 - 9*f**2/2 - 33*f/4 + 54. Solve t(w) = 0 for w.
-11, -1
Suppose -5*p = 42 - 12. Let b = p - -6. Factor 4/7*h**3 + 0 + 2/7*h**4 + b*h + 2/7*h**2.
2*h**2*(h + 1)**2/7
Let r(v) = -v**3 + 5*v**2 + v - 4.