2
Let h be (-1398)/(-210)*(-30)/48. Let a = -31/8 - h. Factor -4/7*y**3 + a*y**5 + 0*y**4 + 0*y**2 + 2/7*y + 0.
2*y*(y - 1)**2*(y + 1)**2/7
Let v = 1155 - 1153. Let t(m) be the second derivative of 0 + 2*m - 1/9*m**3 + 0*m**v + 0*m**4 + 1/30*m**5. Determine s, given that t(s) = 0.
-1, 0, 1
What is d in -4*d**4 - d**4 - 66*d**3 + 141*d**3 + 170*d**2 - 240*d**3 = 0?
-34, 0, 1
Let w(r) = -r**2 - 14*r + 21. Let z be w(-12). Let b = z + -403/9. Factor 4/9*j - b + 2/3*j**2.
2*(j + 1)*(3*j - 1)/9
Factor -12/7*h**2 + 0 - 9/7*h**3 + 0*h + 3/7*h**4.
3*h**2*(h - 4)*(h + 1)/7
Let k(d) be the second derivative of d**7/42 + d**6/10 + 3*d**5/20 + d**4/12 + 5*d + 1. Factor k(h).
h**2*(h + 1)**3
Let y(c) be the first derivative of c**4/3 - 2*c**2 + 8*c/3 - 458. Suppose y(j) = 0. What is j?
-2, 1
Let h be 0*(9/(-18) + 1). Let z(w) be the second derivative of 0*w**2 - 1/36*w**4 - 1/90*w**6 + h*w**3 + 0 + 6*w - 1/30*w**5. Factor z(i).
-i**2*(i + 1)**2/3
Let a = 1/17765 - -1421/3553. Suppose 2*b - 8/5 - a*b**2 = 0. What is b?
1, 4
Let p(d) be the first derivative of -d**3/3 + 4*d**2 - 12*d - 13. Find a such that p(a) = 0.
2, 6
Let s(u) = -7*u**2 - 3*u + 5. Let a(j) = 13*j**2 + 5*j - 9. Let b(x) = 6*a(x) + 13*s(x). Let t(r) = 7*r**2 + 5*r - 6. Let l(y) = 6*b(y) + 11*t(y). Factor l(d).
-d*(d - 1)
Factor 29*c + 46*c**3 + c**5 + 39*c**2 - 2*c - 2*c + 21*c**2 + 12*c**4.
c*(c + 1)**2*(c + 5)**2
Let p = 146 - 139. Let a(q) be the third derivative of -1/36*q**6 + 0 - 4*q**2 + 0*q**3 + 1/90*q**5 + 0*q + 4/315*q**p + 0*q**4. Factor a(j).
2*j**2*(j - 1)*(4*j - 1)/3
Factor 2/5*d**3 + 49296/5*d - 126*d**2 + 49928/5.
2*(d - 158)**2*(d + 1)/5
Let l be (-16)/1 + 3 + (9 - -4). Factor -1/2*z**5 + l*z + z**2 + 3/2*z**3 + 0 + 0*z**4.
-z**2*(z - 2)*(z + 1)**2/2
Let r(c) be the first derivative of -c**5/30 - 7*c**4/4 - 41*c**3/18 - 506. Let r(h) = 0. Calculate h.
-41, -1, 0
Let k(x) be the first derivative of -49*x**6/72 - 77*x**5/60 - 2*x**4/3 - x**3/9 + 91. Factor k(p).
-p**2*(p + 1)*(7*p + 2)**2/12
Let z(a) = 4. Let r(m) = m**2 + m - 2. Let x(h) = 3*r(h) - 3*z(h). Solve x(k) = 0.
-3, 2
Let z(q) = 2*q**3 - 6*q**2 + 8*q + 4. Let b(p) = 5*p**3 - 19*p**2 + 25*p + 11. Let o(g) = -4*b(g) + 11*z(g). Factor o(r).
2*r*(r - 1)*(r + 6)
Factor 0 + b - 1/5*b**2.
-b*(b - 5)/5
Let c(r) be the first derivative of r**8/280 + 2*r**7/175 - 3*r**2/2 + 2. Let v(g) be the second derivative of c(g). Factor v(j).
6*j**4*(j + 2)/5
Let r = 38 - 8. Suppose r = 6*z + 9*z. Factor -1/4*o - 1/4*o**3 + 0 - 1/2*o**z.
-o*(o + 1)**2/4
Let r(z) = z**2 - 8*z - 4. Let i(j) = -j**2 - 9*j + 9. Let x be i(-9). Let s be r(x). Solve 6 - 3*f + 2*f**2 - s*f**2 + 5*f**2 - 5*f**2 = 0.
-2, 1
Let i(h) be the second derivative of 0*h**4 + 5*h - 1/90*h**6 + 0 + 0*h**3 - 1/30*h**5 + 0*h**2. Factor i(k).
-k**3*(k + 2)/3
Let i(t) be the first derivative of 1/3*t**3 - 4 + 1/2*t**2 - 2*t. Factor i(j).
(j - 1)*(j + 2)
Let z(x) be the first derivative of 9 - 2/5*x**5 + 0*x - 4/3*x**3 + 5/4*x**4 + 1/2*x**2. Factor z(b).
-b*(b - 1)**2*(2*b - 1)
Let b(k) be the first derivative of k**6/240 - k**5/120 - k**4/12 + k**3/3 + 3*k**2 - 15. Let w(s) be the second derivative of b(s). Factor w(q).
(q - 2)*(q - 1)*(q + 2)/2
Let g(z) be the second derivative of -z**6/30 + 3*z**5/20 - 2*z**3/3 - 4*z - 6. What is f in g(f) = 0?
-1, 0, 2
Let d be 289/24 + -6 - 6. Let g(l) be the third derivative of 0*l - 1/120*l**5 + 4*l**2 + d*l**4 - 1/12*l**3 + 0. Factor g(j).
-(j - 1)**2/2
Let y = -7088 - -21265/3. Determine p so that -y*p**2 + 5/3 + 4/3*p = 0.
-1, 5
Suppose 3*p = 4*p + 5*k + 23, 0 = 4*p + 2*k + 2. Suppose 0 = 4*q + 4*c + 4, -p*q + 4 = -3*c - 9. Let q*i**2 - i + i**2 - 4*i**2 + 2*i**2 = 0. Calculate i.
0, 1
Let l(i) be the third derivative of -i**9/15120 - i**8/960 - i**7/168 - i**6/80 + 31*i**4/24 - 16*i**2. Let b(z) be the second derivative of l(z). Factor b(y).
-y*(y + 1)*(y + 3)**2
Let y(o) be the second derivative of -25*o**7/56 + 3*o**6 - 627*o**5/80 + 83*o**4/8 - 15*o**3/2 + 3*o**2 - 83*o. Suppose y(p) = 0. Calculate p.
2/5, 1, 2
Let x = -40/93 - -34/31. Factor x*u - 2/9*u**2 + 0.
-2*u*(u - 3)/9
Solve -361*y + 16*y**2 - 368*y + 709*y - 4*y**3 + 8 = 0 for y.
1, 2
Let j be (5 + -5)*1/(-2 - 1). Let 1/4*q**3 + j*q + 0*q**2 + 1/4*q**5 - 1/2*q**4 + 0 = 0. Calculate q.
0, 1
Let q = -46 + 51. Let z(y) be the first derivative of 0*y**2 - 2/5*y**q + 4/3*y**3 - 2*y + 0*y**4 - 4. Factor z(g).
-2*(g - 1)**2*(g + 1)**2
Let v(f) be the third derivative of f**7/350 + 17*f**6/600 + 31*f**5/300 + 23*f**4/120 + f**3/5 + 212*f**2. Factor v(d).
(d + 1)**2*(d + 3)*(3*d + 2)/5
Let v(i) be the second derivative of -i**9/22680 + i**8/10080 - 11*i**4/4 - 3*i. Let l(t) be the third derivative of v(t). Factor l(r).
-2*r**3*(r - 1)/3
Let p be (2 - 4) + 6 + 2. Suppose 0 = -5*x + p + 4. Factor -4*q - 2*q - 34*q**2 + 31*q**x.
-3*q*(q + 2)
Solve 2/13*a**3 + 0*a + 0 + 28/13*a**2 = 0 for a.
-14, 0
Let s(l) = -4*l**2 - 10*l + 9. Let b(i) = -7*i**2 - 9*i + 10. Let m(g) = 3*b(g) - 4*s(g). Solve m(f) = 0.
3/5, 2
Let g(r) be the first derivative of r**6/3 - 32*r**5/5 + 12*r**4 + 640*r**3/3 + 400*r**2 + 715. Let g(w) = 0. Calculate w.
-2, 0, 10
Let v = -6670/3 - -2224. Factor 6*k**3 - 10*k**2 - v + 14/3*k.
2*(k - 1)*(3*k - 1)**2/3
Let m be (-508)/(-328) + (-10)/205. Factor 2 - m*w - 1/2*w**2.
-(w - 1)*(w + 4)/2
Let s be 22527/84 + (-2)/(-8) + 1. Let l = 270 - s. Suppose -2/7*w**5 - 2/7 - 2/7*w**4 + 4/7*w**3 + l*w**2 - 2/7*w = 0. What is w?
-1, 1
Let o(g) be the first derivative of 3*g**8/3920 - g**7/490 + g**6/840 + 14*g**3/3 - 31. Let m(q) be the third derivative of o(q). Solve m(s) = 0 for s.
0, 1/3, 1
Let p = -595/18 - -67/2. Let b = -380 + 3424/9. Factor -p*o - 2/9 + b*o**3 + 2/9*o**4 + 0*o**2.
2*(o - 1)*(o + 1)**3/9
Let c(z) be the first derivative of 1 + 1/12*z**4 + 4*z + 1/3*z**3 + 1/2*z**2. Let a(o) be the first derivative of c(o). What is u in a(u) = 0?
-1
Let a = 37287/5 - 7457. Solve 2/5*s**2 + a*s - 4/5 = 0 for s.
-2, 1
Let g(r) be the third derivative of -r**7/210 + 3*r**6/40 - 7*r**5/15 + 3*r**4/2 - 8*r**3/3 + 9*r**2 - r. Suppose g(i) = 0. Calculate i.
1, 2, 4
Factor -1154*r**2 + 576*r**2 - 50*r + 581*r**2 + 362*r.
3*r*(r + 104)
Let f(x) be the third derivative of x**7/1050 + x**6/24 + 23*x**5/150 + 462*x**2 + 2*x. Determine t, given that f(t) = 0.
-23, -2, 0
Let h(q) be the second derivative of -q**6/45 - q**5/30 + 16*q**4/9 + 20*q**3/3 + 593*q. What is r in h(r) = 0?
-5, -2, 0, 6
Let g be -8 + 354/30 - 3. Determine w, given that -1/5*w**3 + 4/5 - g*w**2 + 1/5*w = 0.
-4, -1, 1
Factor -116*g**2 + 118*g**2 + 35*g - 7*g + 48.
2*(g + 2)*(g + 12)
Let p = 10 + -7. Let b = -103404 - -103407. Factor 243/4*x**b + p - 24*x + 135/4*x**2.
3*(x + 1)*(9*x - 2)**2/4
Let t be (-1)/((-2)/32*(-1 + 8)). Let d(k) = -59*k - 291. Let n be d(-5). Let 0*u - 12/7*u**n + t*u**2 + 0*u**3 + 4/7*u**5 + 0 = 0. What is u?
-1, 0, 2
Let d(q) = -4*q**5 + 8*q**4 + 24*q**3 - 28*q**2 - 4. Let v(l) = l**4 - l**2 + 1. Let f(u) = -d(u) - 4*v(u). Determine y, given that f(y) = 0.
-2, 0, 1, 4
Suppose 23 = -3*o + 11. Let s be 39/(-12) - -3 - 7/o. Find j such that 3/2*j**4 - 1/2*j**3 + 1/2*j - s*j**2 + 0 = 0.
-1, 0, 1/3, 1
Let w(m) be the second derivative of -m**4 + 0*m**2 + 3/14*m**7 + 0*m**3 + 0 - 11/10*m**6 + 9/5*m**5 + 31*m. Determine k, given that w(k) = 0.
0, 2/3, 1, 2
Suppose 0 = 8*t - 34 - 14. Let o(w) be the third derivative of 1/3*w**4 + 3*w**2 + 0*w + 1/60*w**t + 0*w**3 + 2/15*w**5 + 0. Factor o(i).
2*i*(i + 2)**2
Let w(u) = -u**4 - u**3 + 2*u**2 - 1. Let l(o) = -24*o**4 + 294*o**3 - 1334*o**2 + 800*o - 134. Let g(c) = -l(c) + 6*w(c). Suppose g(a) = 0. Calculate a.
1/3, 8
Let n(y) = y**4 - y. Let j(r) = 2*r**5 + 18*r**4 + 12*r**3 - 4*r. Let o(t) = j(t) - 4*n(t). Let o(u) = 0. What is u?
-6, -1, 0
Let l(c) be the third derivative of -1/9*c**4 + 0 + 0*c - 8/9*c**3 - 28*c**2 + 1/15*c**5 + 1/36*c**6 + 1/315*c**7. Let l(g) = 0. Calculate g.
-2, 1
Let i(b) = 10*b**2 + 16*b - 9. Let a(w) = -23*w**2 - 33*w + 21. Let t(s) = 3*a(s) + 7*i(s). Find p such that t(p) = 0.
-13, 0
Let h(j) be the second derivative of j**6/60 - 11*j**5/20 + 5*j**4 + 11*j**3/6 - 121*j**2/4 + 107*j. Let h(b) = 0. Calculate b.
-1, 1, 11
Let r(s) = 3*s**3 - s + 1. Let n = -274 - -275. Let o be r(n). Find q such that 3/2*q**2 - q + 0 - 