*z + 3*s - 2*s = 50. Factor 25*l + 7*l**2 - 4*l**2 - 10 + z*l**2 - 15*l**3.
-5*(l - 2)*(l + 1)*(3*l - 1)
Suppose -23*a = 12*a - 19*a. Factor -4/3*k + a - 4/3*k**2.
-4*k*(k + 1)/3
Let q be (-11*2 - -3)/(-3)*6. What is n in -105*n**2 + 75*n + 41*n**4 + 33*n**3 + q*n**4 - 82*n**4 = 0?
0, 1, 5
Let k(d) = 4*d**3 + 2*d - 4. Let z(a) = 9*a**3 - a**2 + 6*a - 9. Let g(n) = 5*k(n) - 2*z(n). Factor g(p).
2*(p - 1)*(p + 1)**2
Let g = -41 - -46. Factor -10*i**2 + g*i**3 - 15*i**2 + 2 + 4*i + 43 + 11*i.
5*(i - 3)**2*(i + 1)
Suppose 0 = 2*r - 3*r - 4*f + 25, -5 = -f. Let j(a) be the second derivative of 3/16*a**4 + 1/8*a**2 + 4*a - 1/20*a**r + 0 - 1/4*a**3. Factor j(p).
-(p - 1)**2*(4*p - 1)/4
Let i(s) = -s**3 + s**2 - s + 1. Let a(g) = 4*g**4 - 20*g**3 - 16*g**2 + 84*g - 52. Let n(y) = -a(y) - 4*i(y). Determine t so that n(t) = 0.
-2, 1, 6
Let w(p) be the first derivative of 7*p**5/40 - 47*p**4/32 - 7*p**3/12 - 41. What is n in w(n) = 0?
-2/7, 0, 7
Let v be 17 - 1/((-4)/12). Factor 4*o**2 - 2*o**4 - 2 - 4*o**3 - v*o**5 - 13*o**5 + 2*o + 35*o**5.
2*(o - 1)**3*(o + 1)**2
Let q be -2 + (-4)/(-2) + 3. Let x(w) be the first derivative of 0*w + 0*w**2 - w**6 - 9/5*w**5 + 0*w**4 + w**q + 1. Determine t so that x(t) = 0.
-1, 0, 1/2
Let v(r) = r**2 - 9. Let n be v(-3). Let l(c) be the second derivative of -1/9*c**4 + 0*c**3 + 0*c**2 - 2/15*c**6 + 2/63*c**7 + 9*c + n + 1/5*c**5. Factor l(f).
4*f**2*(f - 1)**3/3
Suppose -6*o - 16 = -8*o. Let x be (54/(-72))/((-18)/o). Factor -x - 1/3*d + 1/3*d**2 + 1/3*d**3.
(d - 1)*(d + 1)**2/3
Let i be (-3 - -64)*-7*2/(-6). Let a = -140 + i. Find c such that -5*c - 1/3*c**3 + a*c**2 + 3 = 0.
1, 3
Let c(k) = 0*k**3 + 0*k + 2*k**5 + k + 3*k**5 + 4*k**4 - 6*k**3. Let m(b) = -5*b**5 - 3*b**4 + 7*b**3 - 2*b. Let r(s) = -3*c(s) - 4*m(s). Solve r(w) = 0.
-1, 0, 1
Let l(p) be the third derivative of -p**5/120 + 19*p**4/48 - p**2 - 257. Solve l(r) = 0 for r.
0, 19
Factor 4/9*v**4 + 0 + 0*v**2 + 0*v + 20/9*v**3.
4*v**3*(v + 5)/9
Let v(z) be the first derivative of 2*z**5/15 - z**4/4 - 11*z**3/9 + z**2 + 18. Factor v(h).
h*(h - 3)*(h + 2)*(2*h - 1)/3
Let l(t) = t + 2. Let z be l(-10). Let p be 22/z*(-1)/(-3)*-16. Factor -20/3*x**2 - p*x - 8/3.
-4*(x + 2)*(5*x + 1)/3
Let y(k) = k**2 - 2*k + 1. Let o(j) = -3*j**2 - 21. Let t(l) = o(l) + 6*y(l). Factor t(r).
3*(r - 5)*(r + 1)
Let v(d) = -d**2 - 1331*d - 110191. Let r(t) = -2*t**2 - 1330*t - 110202. Let s(p) = -3*r(p) + 2*v(p). Determine u so that s(u) = 0.
-166
Let a(j) = 25*j**4 + 20*j**3 - 65*j**2 + 34*j - 7. Let k(f) = -8*f**4 - 7*f**3 + 22*f**2 - 11*f + 2. Let z(b) = 2*a(b) + 7*k(b). Factor z(l).
-3*l*(l - 1)*(l + 3)*(2*l - 1)
Let h(j) be the first derivative of j**6/3 + 8*j**5/5 - 10*j**4 + 20*j**3/3 + 19*j**2 - 28*j + 7. What is p in h(p) = 0?
-7, -1, 1, 2
Let j(k) be the second derivative of -k**6/15 - 21*k**5/20 - 11*k**4/3 - 11*k**3/2 - 4*k**2 + 126*k. Suppose j(o) = 0. What is o?
-8, -1, -1/2
Let n(p) be the second derivative of 0 + 3/40*p**5 - 1/4*p**3 - 8*p - 1/8*p**4 + 3/4*p**2. Factor n(r).
3*(r - 1)**2*(r + 1)/2
Let k(f) be the first derivative of -f**5/25 + f**4/10 + 4*f**3/15 - f**2/5 - 3*f/5 + 20. Factor k(l).
-(l - 3)*(l - 1)*(l + 1)**2/5
Let w = 8 - 2. Suppose 3*k - k = -3*y - 6, -k + 3*y + w = 0. Solve -2*u**2 + k*u**2 - 3*u**4 + 5*u**2 = 0.
-1, 0, 1
Suppose 4*r + r = -v - 15, r = 3*v - 35. Factor u**2 + 0*u**2 - 9*u**2 + v*u - 7*u**2 - 25*u**3.
-5*u*(u + 1)*(5*u - 2)
Let q(t) = -2*t**2 + 8*t + 3. Let o be q(4). Suppose o*b = 39 + 42. Factor 24*z**4 + 6*z + 2*z**2 - b*z**4 + z**2 - 6*z**3.
-3*z*(z - 1)*(z + 1)*(z + 2)
Let l = 18 + -13. Factor p**3 - 9*p**4 - l*p**4 + 20*p**4 - 2*p**2 - 5*p**4.
p**2*(p - 1)*(p + 2)
Let f = -1/54 - -11/108. Let x(n) be the second derivative of -1/3*n**3 + f*n**4 + 2*n + 0 - 3/2*n**2. Factor x(i).
(i - 3)*(i + 1)
Suppose -20 + 0 = -4*o. Let r be 6/(-1 - 1) + o. Find f such that 7*f**4 - r*f**4 - 4*f**4 - 3*f**2 + 2*f**4 = 0.
-1, 0, 1
Let d = -42 - -46. Suppose 3*k**3 - 3*k**3 + 8*k**2 + 0*k**3 + d*k**3 = 0. Calculate k.
-2, 0
Let b be ((-198)/264)/(15/16) + (-2)/(-2). Factor 6/5*d**3 - 16/5 - 24/5*d - 1/5*d**4 - b*d**2.
-(d - 4)**2*(d + 1)**2/5
Factor 72119*d - 36 + 4*d**2 - 72119*d.
4*(d - 3)*(d + 3)
Suppose -4*l - 5*c = -5*l - 13, 2*l + c - 7 = 0. Let w(m) be the second derivative of -3*m + 0 + 1/6*m**l + 1/36*m**4 + 1/9*m**3. Factor w(f).
(f + 1)**2/3
Let a = -162548/3 - -54184. Factor 0*l + 4/3 - a*l**2.
-4*(l - 1)*(l + 1)/3
Let c(y) = -33 + 22 + 2*y**3 + y**2 - 4*y + 14. Let o(w) = 9*w**3 + 5*w**2 - 17*w + 13. Let a(u) = -26*c(u) + 6*o(u). Factor a(s).
2*s*(s + 1)**2
Let f(y) be the first derivative of y**4/4 + y**3 + y**2 + 242. Solve f(c) = 0 for c.
-2, -1, 0
Let x be (-4)/((-40)/22) - (-3)/(-15). Factor k**x + 0*k**2 + 386 + 96*k + 382 + 2*k**2.
3*(k + 16)**2
Suppose 5*h - 3*h = -k, 28 = 4*h - 5*k. Factor 2/9*b**h + 8/9*b + 2/3.
2*(b + 1)*(b + 3)/9
Suppose -187 = 2*y - 193. Let r(f) be the first derivative of -6*f + 3/2*f**2 + f**y - 8. Let r(d) = 0. Calculate d.
-2, 1
Let x(i) be the first derivative of -33*i**5/5 - 39*i**4/4 + 9*i**3 + 39*i**2/2 + 6*i + 213. Find o such that x(o) = 0.
-1, -2/11, 1
Let v = -70 + 70. Let n(o) be the second derivative of -7/33*o**3 + v + 2/11*o**2 + 1/22*o**4 - 6*o. Factor n(a).
2*(a - 2)*(3*a - 1)/11
Suppose 0 = 3*d - 6 - 18. Suppose 0 = 3*i + i - d. Suppose p**2 - 3*p + 0*p**2 + 0*p**i - 1 + 3 = 0. Calculate p.
1, 2
Let b = -1196 + 17942/15. Let x(z) be the second derivative of 0*z**3 + 0 + 0*z**2 + z**4 - 2/5*z**5 - b*z**6 + 11*z. Find a such that x(a) = 0.
-3, 0, 1
Let c be -2 + 1 - 3/((-9)/156). Let f = 53 - c. Factor 1/4*r**f - 1/2 - 1/4*r.
(r - 2)*(r + 1)/4
Suppose 0 = -m + 5*m. Let n(g) = g**2 - 35*g + 304. Let d be n(16). Suppose m*w + 1/4*w**2 + d = 0. Calculate w.
0
Let 140*u**2 + 50/3*u**3 + 144 + 264*u = 0. What is u?
-6, -6/5
Let f(o) be the first derivative of 4*o**3/9 - 17*o**2/3 - 6*o + 200. Factor f(h).
2*(h - 9)*(2*h + 1)/3
Let p be (2/10)/(93/372). Let t(j) be the first derivative of 11 + 4/15*j**3 - p*j + 0*j**2. Determine n, given that t(n) = 0.
-1, 1
Let k(p) be the third derivative of -p**8/50400 + p**7/2520 + p**6/300 + 8*p**5/15 + 4*p**2. Let v(u) be the third derivative of k(u). Factor v(c).
-2*(c - 6)*(c + 1)/5
Let y(v) be the third derivative of -v**7/42 + v**6/12 + v**5/12 - 5*v**4/12 + 66*v**2. Determine z so that y(z) = 0.
-1, 0, 1, 2
Let h = -23 + 23. Suppose -4*o + 0*o + 8 = h. Let 1 + 1 - 2*r**2 - 2 - 2*r + o + 2*r**3 = 0. Calculate r.
-1, 1
Let j = 512 - 2559/5. Let z(w) be the second derivative of 0 + 1/14*w**7 - w**2 + 1/2*w**4 - 2/15*w**6 - j*w**5 + w + 1/6*w**3. Factor z(q).
(q - 1)**3*(q + 1)*(3*q + 2)
Let y(a) be the first derivative of -49/60*a**5 - 3/2*a**2 - 2/3*a**3 + 7/6*a**4 + 0*a + 6. Let f(o) be the second derivative of y(o). Factor f(t).
-(7*t - 2)**2
Let z be 27/6 + (1 + -3 - 2). Suppose 2*l = -5*o - 7, -l + 2*l = -3*o - 5. Factor 1/2*h - z*h**3 + 0*h**2 + 1/4*h**l - 1/4.
(h - 1)**3*(h + 1)/4
Factor -24/5*i - 3/5*i**2 - 21/5.
-3*(i + 1)*(i + 7)/5
Let z be (533/(-455) + (-2)/(-2))/((-14)/140). Find q such that 4/7*q**2 - z*q**3 - 8/7 + 4/7*q**4 + 12/7*q = 0.
-1, 1, 2
Let u = -1136835092/1545 + 735816. Let n = u - 2/309. Factor 4/5*z + n + 2/5*z**2.
2*(z + 1)**2/5
Let l = -145859/195 + 748. Let t(v) be the third derivative of 4*v**2 - 1/780*v**6 - 1/156*v**4 + 0 + 0*v**3 + l*v**5 + 0*v. Factor t(p).
-2*p*(p - 1)**2/13
Determine a, given that 3/7*a**2 - 12/7 + 9/7*a = 0.
-4, 1
Let o = -83 + 169/2. Let g(l) be the first derivative of -3 - 3*l**3 - 9/4*l**4 - o*l**2 + 0*l - 3/5*l**5. Determine q, given that g(q) = 0.
-1, 0
Let f = -4520/3 + 1508. Let 0*v - f*v**2 + 0 = 0. Calculate v.
0
Let r = -6844/3 - -6848/3. Let 8/3*j + 4/3*j**5 + r*j**4 - 4*j**3 - 4/3*j**2 + 0 = 0. Calculate j.
-2, -1, 0, 1
Let y = -1738 - -1742. Solve -4/5 - 4/5*h**2 + 2/5*h**5 + 8/5*h**3 + 8/5*h**y - 2*h = 0.
-2, -1, 1
Let c(k) be the second derivative of k**6/6 + 21*k**5/2 + 200*k**4 + 2000*k**3/3 - 350*k. Factor c(x).
5*x*(x + 2)*(x + 20)**2
Suppose 1631*d = 1618*d. Factor -2/9*y**3 + d*y + 0 + 2/9*y**2.
-2*y**2*(y - 1)/9
Let a(w) be the third derivative of -1/30*w**5 - 2*w**2 + 0*w + 0*w**3 + 1/6*w**4 + 0. Factor a(b).
-2*b*(b - 2)
Let -n**3 + 19/3*n**2 + 4/3*n - 4 - 7/3*n**4 