-1, 2
Let f be (-2)/(-23) - 4512/(-47564). Find t such that 6/11*t**4 - 14/11*t**2 + 8/11 - f*t**3 + 2/11*t**5 + 0*t = 0.
-2, -1, 1
Let z be (-52)/9 - (34/(-9))/(-17) - -6. Let 0*b + z*b**3 + 1/4*b**4 + 0 + 1/4*b**5 + 0*b**2 = 0. What is b?
-1, 0
Let f = 23281/2 + -11629. Find t such that -1/2*t**5 + 4*t - f*t**2 + 8 - 7/2*t**3 + 7/2*t**4 = 0.
-1, 1, 4
Let b(s) = s**2 + s - 17. Let v be b(6). Let w = v + -20. Factor k**3 - k**2 - 1/2 - 3/2*k + 3/2*k**4 + 1/2*k**w.
(k - 1)*(k + 1)**4/2
Let m(p) be the third derivative of -p**5/240 + p**4/96 + 42*p**2 - p. Determine w, given that m(w) = 0.
0, 1
Let b(i) be the third derivative of -1/60*i**5 + 0 + 1/480*i**6 + 0*i + 0*i**3 + 1/24*i**4 + 12*i**2. Factor b(r).
r*(r - 2)**2/4
Suppose -16/9 + 14/9*o**2 - 2/9*o = 0. Calculate o.
-1, 8/7
Suppose 33*a - 152 = -20. Let z(b) = -b**2 - 5*b - 4. Let v be z(-3). Factor 6*g**3 + 18*g + a + 15*g**2 + 12*g**v - 7*g**2.
2*(g + 1)*(g + 2)*(3*g + 1)
Suppose -6*g - 839 + 857 = 0. Let h(m) = m**2 - 6*m - 3. Let p be h(7). Factor 20/9*w**g + 14/9*w**p - 6*w + 2/9*w**5 + 6 - 4*w**2.
2*(w - 1)**2*(w + 3)**3/9
Suppose 2*y + 3*d + 3 - 1 = 0, -y - 6 = 4*d. Let j be -6 - (24/(-9))/((-14)/(-35)). Factor j + 2/3*x**y + 4/3*x.
2*(x + 1)**2/3
Let w be (21/(-6))/(1/2). Let q = w + 12. Determine b, given that -q*b**3 + 3*b + 6*b**3 + 3*b**2 + 0*b**2 + 1 = 0.
-1
Let q(y) be the third derivative of -5/6*y**3 - 1/75*y**5 - 1/900*y**6 + 0 + 5*y**2 + 0*y - 1/15*y**4. Let p(f) be the first derivative of q(f). Factor p(n).
-2*(n + 2)**2/5
Let y(a) be the third derivative of 0 + 71/540*a**6 + 0*a - 7/270*a**5 + 0*a**3 + 4/315*a**7 - 35*a**2 - 1/18*a**4. Solve y(p) = 0.
-6, -1/4, 0, 1/3
Suppose 0 = p + 3*p - 56. Factor -4*b**2 + p*b**2 + 0*b**2 - 2*b**3 - 8*b.
-2*b*(b - 4)*(b - 1)
Let a(q) be the third derivative of q**10/113400 + q**9/11340 + q**8/3780 - q**5/6 - 2*q**2 + 7. Let k(r) be the third derivative of a(r). Factor k(c).
4*c**2*(c + 2)**2/3
Let q(d) be the third derivative of 3*d**5/80 - 83*d**4/96 + 3*d**3/4 - d**2 - 7. Factor q(w).
(w - 9)*(9*w - 2)/4
Let q(j) = -j**2 + 6*j + 18. Let w be q(6). Factor -9*i**3 - w*i**2 - 12 + 0*i**3 + 12*i**3 + 27*i.
3*(i - 4)*(i - 1)**2
Let w(z) = -4*z**3 + 7*z**2 - 3*z. Let f = -4 - -5. Let b(l) = -l**3 + l**2. Let t(x) = f*w(x) - 3*b(x). Factor t(h).
-h*(h - 3)*(h - 1)
Let o(x) be the second derivative of 1/50*x**5 + 0 + 14*x + 1/30*x**4 - 2/15*x**3 + 0*x**2. Factor o(b).
2*b*(b - 1)*(b + 2)/5
What is c in 0 + 2/13*c**4 + 6/13*c**2 - 2/13*c - 6/13*c**3 = 0?
0, 1
Let a(r) = -r**2 + 3*r - 6. Let q be 0/((-1)/(-3 + 2)). Suppose -3*y + 8 + 4 = q. Let s(n) = -n**2. Let u(h) = y*s(h) - a(h). Factor u(k).
-3*(k - 1)*(k + 2)
Let c(p) be the second derivative of -1/70*p**5 + 1/21*p**3 + 0*p**4 + 7*p + 0*p**2 + 0. Factor c(n).
-2*n*(n - 1)*(n + 1)/7
Suppose -10*u - 857 + 877 = 0. Let a(d) be the first derivative of 8 + 0*d - 1/6*d**3 + 1/3*d**u - 1/24*d**4. Let a(r) = 0. What is r?
-4, 0, 1
Let x(u) be the first derivative of 6*u**5/35 + 2*u**4/7 - 2*u**3/21 - 2*u**2/7 - 51. Determine l so that x(l) = 0.
-1, 0, 2/3
Let w(c) be the first derivative of -9/8*c**3 - 3/8*c**5 - 10 - 3/8*c**2 + 0*c - 9/8*c**4. Factor w(m).
-3*m*(m + 1)**2*(5*m + 2)/8
Suppose 0 + 20/7*k**2 - 9/7*k**5 + 2/7*k**3 - 3*k**4 + 8/7*k = 0. Calculate k.
-2, -2/3, 0, 1
Let s be (-1428)/(-224) + -9 + (-3)/(2/(-2)). Factor 21/8*g + 3 - s*g**2.
-3*(g - 8)*(g + 1)/8
Let k(f) = f**2 + 9*f + 10. Let z be k(7). Suppose -120 = u - z. Factor -25/3 - 10/3*a - 1/3*a**u.
-(a + 5)**2/3
Suppose 2*q - 2 = -0*q. Let i be 52/16 + (q + 0)*-3. Factor 0 - i*d**3 + 1/4*d**2 + 0*d.
-d**2*(d - 1)/4
Let o(s) = 2*s**3 + 0 + 7*s**2 - 3*s**3 + 9 - 7*s. Let f be o(6). Find q such that -2*q - 2 + 2*q**2 + 0*q - 2*q**f + 4*q = 0.
-1, 1
Let u(w) be the first derivative of -2*w**6/13 - 38*w**5/65 - 11*w**4/13 - 22*w**3/39 - 2*w**2/13 + 69. What is p in u(p) = 0?
-1, -2/3, -1/2, 0
Let j = -3362 - -3364. Find f such that -2/3*f**j + 1/3 - 1/3*f = 0.
-1, 1/2
Suppose -14/3 - 2/3*b**2 + 29/3*b - 1/3*b**5 + 16/3*b**4 - 28/3*b**3 = 0. Calculate b.
-1, 1, 14
Let u(p) = -3*p**3 - 21*p**2 - 18*p + 2. Let z(h) = -39*h**3 - 273*h**2 - 234*h + 27. Let x(v) = -27*u(v) + 2*z(v). Factor x(f).
3*f*(f + 1)*(f + 6)
Let k = 2018/3 + -672. Let u(i) be the first derivative of 1/9*i**3 - 10 + k*i - 1/2*i**2. Factor u(y).
(y - 2)*(y - 1)/3
Let p(f) = f**2 + 14*f - 171. Let i be p(-22). What is d in 4/13 + 16/13*d**4 + 10/13*d**i - 20/13*d**2 - 2/13*d - 8/13*d**3 = 0?
-1, 2/5, 1
Let s(p) = -p**5 - p**4 - p. Let i be 1 - (1 + (1 - 6)). Let o(m) = 6*m**5 + 8*m**4 + m**3 - 3*m**2 + 3*m. Let l(g) = i*s(g) + o(g). Let l(t) = 0. Calculate t.
-2, -1, 0, 1
Let m = -6 - -5. Let r(n) = -5*n**4 - 82*n**3 + 37*n**2 + 54*n. Let k(w) = -w**4 + w**3 - w**2. Let i(b) = m*r(b) - 4*k(b). Let i(o) = 0. What is o?
-9, -2/3, 0, 1
Let b be 27/(-18) + 26/4. Let x = 504 - 502. Let -5/3*t**3 + 0*t - t**b + 0 + 7/3*t**4 + 1/3*t**x = 0. Calculate t.
0, 1/3, 1
Let k(n) be the first derivative of -6/5*n**2 + 0*n**3 + 8/5*n - 25 + 1/5*n**4. Find i such that k(i) = 0.
-2, 1
Let i(o) = -3*o - 14. Let j(d) = 2*d + 14. Let l(x) = -3*i(x) - 4*j(x). Let h be l(16). Suppose 2*s**2 - h + 3*s + 2 - 7*s = 0. What is s?
0, 2
Let h(u) = 6*u**4 - 30*u**3 + 59*u**2 - 42*u + 17. Let w(k) = 21*k**4 - 105*k**3 + 207*k**2 - 147*k + 60. Let m(d) = 18*h(d) - 5*w(d). Let m(g) = 0. What is g?
1, 2
Factor -8/15*x + 8/15 + 2/15*x**2.
2*(x - 2)**2/15
Let c(g) be the first derivative of -5*g**6/6 - 2*g**5 - 15. Find h, given that c(h) = 0.
-2, 0
Let r = -2460 - -2464. Suppose 2*t - 2*q = 4*t - 10, -3*t + 9 = q. Solve -2/5*g**3 + 0*g**t + 0 - 2/5*g**r + 0*g = 0.
-1, 0
Let q = 17257 + -17254. Factor -12/7*v**q + 0 - 4/7*v**4 - 8/7*v + 4/7*v**5 + 20/7*v**2.
4*v*(v - 1)**3*(v + 2)/7
Let n(j) = -3*j**2 + 6. Let y be n(-4). Let g be (27/y)/((-6)/7). Solve 9*z**2 + 0 - 9/2*z**3 + g*z**4 - 6*z = 0 for z.
0, 2
Suppose 1310 = 7*w - 1329. Factor -24 - 264*r**2 + w*r**2 - 860*r**2 + 324*r - 711*r**2 + 2187*r**3.
3*(9*r - 2)**3
Let n = 270 - 260. Let v(t) be the second derivative of 0*t**2 + 0 + 0*t**3 + 1/6*t**4 + n*t. Factor v(d).
2*d**2
Let o(g) = -12*g**3 + g**2 + 2. Let c(r) = 50*r**3 - 5*r**2 - 9. Let s(n) = -2*c(n) - 9*o(n). What is a in s(a) = 0?
-1/8, 0
Let t(i) be the second derivative of i**4/42 - 11*i**3/7 - 108*i**2/7 + 765*i. Factor t(d).
2*(d - 36)*(d + 3)/7
Let i = 93632/3 + -31210. Determine c, given that 0 - 22/3*c + i*c**2 = 0.
0, 11
Suppose 5*g = -3*u - 222, 3*g + 125 + 17 = -4*u. Let t be (g/(-630))/(1/2). Solve 0*q**2 + 0*q + 0 + 2/15*q**3 - t*q**4 = 0.
0, 1
Let k(h) be the second derivative of h**7/294 - h**6/30 + 4*h**5/35 - h**4/7 + 105*h. Solve k(c) = 0 for c.
0, 2, 3
Let l(x) = -3*x**2 - 8*x - 22. Let r(z) = 13*z**2 + 30*z + 89. Let p(j) = -9*l(j) - 2*r(j). Solve p(k) = 0 for k.
-10, -2
Find g such that -4*g**4 + 22 + 198*g + 12*g**2 + 47*g**2 + 3*g**4 + 10 + 12*g**3 - 120*g = 0.
-2, -1, 16
Let g(n) be the second derivative of -n**5/40 - n**4/8 - n**3/6 - 2*n + 17. Factor g(o).
-o*(o + 1)*(o + 2)/2
Let h(f) = f**2 + 11*f. Let d be h(-11). Find u such that 4 + 20*u + d*u**5 + 40*u**3 + 40*u**2 + 20*u**4 - 7*u**5 + 11*u**5 = 0.
-1
Let n(i) = i**3 + 10*i**2 - 16*i - 52. Let o be n(-11). Factor 0*d + 2/7*d**4 + 2/7*d**2 + 0 + 4/7*d**o.
2*d**2*(d + 1)**2/7
Suppose -3*o - 27 = -3*f - 3, 0 = -3*f + o + 24. Factor -15*q**2 - f + 20*q + 20*q**3 - 16*q**3 + 9*q**2 - 10*q**2.
4*(q - 2)*(q - 1)**2
Let w(x) be the second derivative of x**6/165 + 3*x**5/55 - 25*x**4/66 + 6*x**3/11 - 45*x. Determine d so that w(d) = 0.
-9, 0, 1, 2
Suppose -24/7*q**2 - 18/7*q**4 + 128/7 - 576/7*q + 16*q**3 = 0. What is q?
-2, 2/9, 4
Let r = 56 - 4. Let j = r - 49. Factor 0 - 3/5*k - 3/5*k**4 - 9/5*k**j - 9/5*k**2.
-3*k*(k + 1)**3/5
Suppose -5*t = 25, 3*y + 19 = 6*y - 2*t. Factor 3*z**3 + 3 - 575*z + 566*z + y.
3*(z - 1)**2*(z + 2)
Let s(m) = 4*m**3 - m**2 + m. Let x(o) = -22*o**3 + 9*o**2 - 6*o. Let h(z) = -6*s(z) - x(z). Factor h(g).
-g**2*(2*g + 3)
Let i(y) be the third derivative of -y**5/90 + 2*y**4/9 + y**3 - 75*y**2. Find z such that i(z) = 0.
-1, 9
Suppose 4*q - 7 = -5*z, -5*z + 3*q - 4*q + 13 = 0. Let o(w) be the first derivative of -w**z - 1/2*w**2 + 2*w - 2. Let o(c) = 0. Calculate c.
-1, 2/3
Let y