(q - 2)*(q - 1)*(q + 1)
Let n = 517 + -7753/15. Let l(u) be the second derivative of -4/75*u**6 + 0*u**2 + 8*u + 0 - 1/15*u**3 - 1/105*u**7 - n*u**4 - 3/25*u**5. Factor l(q).
-2*q*(q + 1)**4/5
Let c(n) be the third derivative of -n**6/420 - n**5/105 + n**4/84 + 2*n**3/21 + 352*n**2. Factor c(h).
-2*(h - 1)*(h + 1)*(h + 2)/7
Let f(x) = 8*x**2 + 33*x + 25. Let c(s) = -7*s**2 - 32*s - 25. Let g(l) = 7*c(l) + 6*f(l). Factor g(y).
-(y + 1)*(y + 25)
Factor -3*b**2 + 138*b + 4*b + 326*b - 18252.
-3*(b - 78)**2
Let j(d) be the third derivative of -3*d**8/448 - d**7/56 + d**6/40 + d**5/20 - d**2 - 54*d. Suppose j(o) = 0. Calculate o.
-2, -2/3, 0, 1
Let y(b) = -b**3 - b**2 + b - 1. Let m(i) = 3*i**3 - 25*i**2 + 49*i - 33. Let w(f) = -m(f) + y(f). Factor w(p).
-4*(p - 2)**3
Let a(f) be the third derivative of -25/48*f**3 - 5/96*f**4 - 8*f**2 + 0*f - 1/480*f**5 + 0. Suppose a(r) = 0. What is r?
-5
Let c be 120/16 - (-6)/(-4). Suppose 0 = 2*h - c. Factor -12 + 8*a**h - 4*a + 0 - 3*a**3 + 12*a**2 - a**3.
4*(a - 1)*(a + 1)*(a + 3)
Solve 0 + 4/11*r**4 - 2/11*r**5 + 78/11*r**3 - 800/11*r - 80/11*r**2 = 0 for r.
-4, 0, 5
Let f(k) = 45*k + 2344. Let b be f(-52). Factor 0*o**2 + 0 + 0*o + 1/5*o**b + 0*o**3 - 1/5*o**5.
-o**4*(o - 1)/5
Let n = -29 - -29. Let y = n - -3. Factor -p**2 - 2*p**3 + 2*p**5 - y*p**2 + 2*p**4 + 2*p**2.
2*p**2*(p - 1)*(p + 1)**2
Find z, given that -z**2 - 1573*z + 1582*z + 4*z**2 = 0.
-3, 0
Let s(j) = 0 + 0*j**2 + 12*j**3 - 3*j**2 - 6 + 2*j + 4*j - 3*j**4. Let k(n) = -9*n**4 + 35*n**3 - 9*n**2 + 17*n - 17. Let c(y) = 6*k(y) - 17*s(y). Factor c(w).
-3*w**2*(w - 1)**2
Let n be 90/(-27)*6/(-5). Determine y so that 44*y**2 + 428*y**3 - 8*y**5 - 484*y**3 + 34*y**n + 2 - 13*y - 3*y = 0.
1/4, 1
Let n(t) be the third derivative of 1/330*t**5 + 1/660*t**6 - 2*t**2 + 0*t**3 - 1/1155*t**7 - 14 - 1/132*t**4 + 0*t. Factor n(b).
-2*b*(b - 1)**2*(b + 1)/11
Factor -2/7*s**3 - 4/7*s**2 + 6/7*s**4 + 0*s + 0.
2*s**2*(s - 1)*(3*s + 2)/7
Factor 0*y**3 + 8/9*y**2 + 2/9*y**5 - 2/3*y**4 + 0 + 0*y.
2*y**2*(y - 2)**2*(y + 1)/9
Let j(u) be the third derivative of -u**9/20160 + u**8/2240 + u**7/420 + 11*u**5/15 - 8*u**2. Let i(f) be the third derivative of j(f). Factor i(q).
-3*q*(q - 4)*(q + 1)
Let q(g) be the second derivative of g**7/14 - 8*g**6/5 + 153*g**5/20 - 8*g**4 - 26*g**3 + 72*g**2 + g - 1. Determine i, given that q(i) = 0.
-1, 1, 2, 12
Suppose v + 2*z = -0*z - 103, -3*v - 317 = -2*z. Let p be 6/8 + (v/(-44))/7. Solve -10/11*l**4 - 2/11 + 12/11*l**5 + 4/11*l + p*l**2 - 16/11*l**3 = 0.
-1, -1/2, 1/3, 1
Suppose -2*y**2 + 0 - 2/7*y**4 - 20/7*y**3 + 36/7*y = 0. What is y?
-9, -2, 0, 1
Let l be 14/(-35) + (-34)/(-10). Suppose 3*j + 3 - 30 = -l*z, 2*j - 38 = -4*z. Determine u so that -7*u**4 + 4*u + 3*u**4 + z*u**2 + 6*u**4 + 8*u**3 = 0.
-2, -1, 0
Let a(m) be the third derivative of -m**5/240 + m**4/96 + 5*m**3/4 + 171*m**2. Let a(v) = 0. What is v?
-5, 6
Determine a so that -28/9*a - 10/9*a**2 + 2/3 = 0.
-3, 1/5
Suppose 25 = 3*n + 13. Suppose -24*r + 61 + n*r**2 + 39 - 80 = 0. Calculate r.
1, 5
Let t be 7/4 + (-19)/(-76). Factor -9*v**2 - 6*v - 7*v**t + v**2.
-3*v*(5*v + 2)
Let t(o) be the third derivative of o**7/195 + 2*o**6/39 + 12*o**5/65 + 8*o**4/39 - 16*o**3/39 + 50*o**2. Factor t(w).
2*(w + 2)**3*(7*w - 2)/13
Let t(g) = -4 - 387*g - 12 - 3*g**2 + 404*g. Let v be t(4). Factor 4/3*s + 0*s**2 - 2/3 - 4/3*s**3 + 2/3*s**v.
2*(s - 1)**3*(s + 1)/3
Let n(f) be the first derivative of 4*f**3/15 + 26*f**2/5 + 88*f/5 - 352. Factor n(i).
4*(i + 2)*(i + 11)/5
Let h be 2/(-7) + (-82)/7. Let n be (12/8)/(h/(-16)). Let -l**2 + 69*l**3 + l - 68*l**3 - l**n = 0. What is l?
0, 1
Let s(i) be the third derivative of -2*i**2 + 0 - 1/60*i**4 + 0*i - 1/300*i**5 + 0*i**3. Solve s(k) = 0 for k.
-2, 0
Suppose 0 = -x + 3, -4*w + 7 = 3*x - 10. Solve -2*f - 4/3*f**w - 2/9*f**3 - 8/9 = 0 for f.
-4, -1
Suppose 162/17*n - 22/17*n**4 - 180/17*n**2 - 54/17 + 92/17*n**3 + 2/17*n**5 = 0. What is n?
1, 3
Let z(t) = t**4 + t**3 - t**2 + t - 1. Let a(d) = -8*d**4 - d**3 + 2*d**2 - 7*d + 7. Let r(k) = 4*a(k) + 28*z(k). Factor r(g).
-4*g**2*(g - 5)*(g - 1)
Let u(g) be the first derivative of 35*g**6/2 - 519*g**5/5 + 1056*g**4/5 - 856*g**3/5 + 312*g**2/5 - 48*g/5 + 143. What is d in u(d) = 0?
1/7, 2/5, 2
Suppose -5*z + 10 = -2*v - 3*v, 0 = -5*v. Suppose 7 + 3*n**z - 4*n - 11 - 4*n**2 = 0. What is n?
-2
Let z(a) be the third derivative of -a**5/20 + 15*a**4/4 - 225*a**3/2 - 45*a**2 + 2. Factor z(q).
-3*(q - 15)**2
Let n(x) be the first derivative of 4*x**5/15 - 2*x**4 + 20*x**3/9 + 8*x**2 - 491. Factor n(s).
4*s*(s - 4)*(s - 3)*(s + 1)/3
Let l be (144/(-560))/((-14)/(-20) - 1). Factor -l + 18/7*p**2 - 3/7*p.
3*(2*p + 1)*(3*p - 2)/7
Let p = 16348 - 16348. Let p + 1/5*r**2 + 1/5*r**3 + 0*r = 0. What is r?
-1, 0
Let r be 9/((-9)/(-3)) - 3. Suppose 5*c = -117 + 127. Factor 0 + 1/2*z**3 + r*z - 1/2*z**4 + 1/2*z**c - 1/2*z**5.
-z**2*(z - 1)*(z + 1)**2/2
Let d(n) be the first derivative of -5*n**7/42 + n**5/4 + 3*n + 6. Let u(g) be the first derivative of d(g). Factor u(b).
-5*b**3*(b - 1)*(b + 1)
Let u(q) be the third derivative of -2*q**6/15 - 151*q**5/15 + 19*q**4/3 - 29*q**2 + 3*q. Find l, given that u(l) = 0.
-38, 0, 1/4
Let p be 17/((-476)/(-96)) + (-4)/(-7). Factor 1/4*v**p - v**3 + 7/2*v - 2 - 3/4*v**2.
(v - 4)*(v - 1)**2*(v + 2)/4
Factor -1484 - 368*k**3 + 1172*k + 16*k + 364*k**3 - 180*k**2 - 352.
-4*(k - 3)**2*(k + 51)
Factor -128/13*y**3 - 770/13*y**2 - 18/13 - 1164/13*y.
-2*(y + 3)**2*(64*y + 1)/13
Let v = -6 + 10. Let t be 104/(-13)*(-3)/v + -2. Factor 0*w + 3/2*w**2 - 3*w**3 + 0 + 3/2*w**t.
3*w**2*(w - 1)**2/2
Let c(g) be the second derivative of 0 + 0*g**2 + 1/50*g**5 - 1/15*g**3 + 0*g**4 - 7*g. Find p, given that c(p) = 0.
-1, 0, 1
Let c(z) be the second derivative of 0 + 3/140*z**5 + 5/28*z**4 - 40*z + 0*z**2 - 3/7*z**3. Factor c(q).
3*q*(q - 1)*(q + 6)/7
Let m be 28/(-13) - (20/(-26))/5. Let o(x) = -30*x**2 - 2*x + 2. Let j(i) = -i**2 + i + 1. Let s(h) = m*j(h) + o(h). Factor s(y).
-4*y*(7*y + 1)
Let x = 4228 + -4225. Determine h so that -2/9*h**2 + 2/9*h**4 - 4/9*h + 4/9*h**x + 0 = 0.
-2, -1, 0, 1
Suppose -4*b + 10 = -0*b - s, -3*b - 3*s = 0. Find r such that -2*r**2 - 3*r**2 - 12*r - b - 13 - 8*r = 0.
-3, -1
Let n(z) be the first derivative of 1/4*z + 1/8*z**4 + 1/20*z**5 - 1 - 1/6*z**3 - 1/24*z**6 - 1/8*z**2. Determine c, given that n(c) = 0.
-1, 1
Let y be (2/(-3))/((-60)/270). Let z(h) be the first derivative of -2/25*h**5 - 2/15*h**3 + y + 0*h + 0*h**2 - 1/5*h**4. Let z(k) = 0. Calculate k.
-1, 0
Let o(c) = -9*c**5 - 21*c**4 - 8*c**3 + 6*c**2. Let a(v) = -v**5 - v**4 + v**2. Let s(l) = -6*a(l) + 3*o(l). Solve s(h) = 0 for h.
-2, -1, 0, 2/7
Let k(v) = v**3 - 3*v**2 + v - 5. Let a be k(3). Let g be (-1 + a - 7/(-2))/2. What is j in -g*j**2 - 9/4 + 3/2*j = 0?
3
Let -40*m - 1/2*m**2 - 800 = 0. What is m?
-40
Let g(p) be the second derivative of 5*p**4/12 + 110*p**3 + 10890*p**2 + 83*p - 2. Factor g(d).
5*(d + 66)**2
Let z(y) be the first derivative of y**6/1080 - y**4/72 + 13*y**3/3 - 8. Let a(k) be the third derivative of z(k). Factor a(c).
(c - 1)*(c + 1)/3
Let x(t) be the third derivative of 0 + 1/200*t**6 + 1/20*t**5 + 16*t**2 - 4/5*t**3 + 0*t + 1/20*t**4. Factor x(b).
3*(b - 1)*(b + 2)*(b + 4)/5
Let k(s) = -s**5 - 14*s**4 - 7*s**3 - 2. Let q(v) = -v**5 - v**4 + v**3 + 1. Let n(j) = -3*k(j) - 6*q(j). Factor n(l).
3*l**3*(l + 5)*(3*l + 1)
Let n(i) = 7*i**5 - 8*i**4 + 8*i**2 - i. Let b(q) = -8*q**5 + 8*q**4 - 8*q**2. Let l(y) = -3*b(y) - 4*n(y). Determine a, given that l(a) = 0.
-1, 0, 1
Let l(x) = -9*x**2 - 51*x - 18. Let j(d) = 2*d**2 + 2*d. Let b(s) = -2*j(s) - l(s). Solve b(h) = 0 for h.
-9, -2/5
Let d(v) be the second derivative of v**4/42 + v**3 + 7*v - 1. Suppose d(a) = 0. What is a?
-21, 0
Let y(x) = -2*x**3 - 8*x**2 + 2. Let l be -8*((-42)/(-12))/7. Let c be y(l). Determine h, given that 0 + 2/3*h**3 - 2/9*h**c - 4/9*h = 0.
-2/3, 0, 1
Suppose -6*w - 73*w**2 + 2*w**4 + 32*w**2 + 0*w + 31*w**2 - 2*w**3 = 0. Calculate w.
-1, 0, 3
Let b = 19 + -15. Let m be (1 - b) + 148/20 - 2. Determine v so that -3/5*v**4 + 12/5*v**3 + m*v - 3/5 - 18/5*v**2 = 0.
1
Let y(r) = 7*r**4 + 46*r**3 - 102*r**2 - 41*r + 90. Let w(d) = 4*d**4 + 23*d**3 - 51*d**2 - 20*d + 44. Let k(j) = 5*w(j) - 3