 8*c - 1. Let a(l) = 5*f(l) + 4*k(l). Let x be a(-3). Factor i**2 + 0*i**x + 2*i**2 - 21*i**3 + 9*i**3.
-3*i**2*(4*i - 1)
Let j(k) be the third derivative of k**9/15120 + k**8/4200 + k**7/4200 + 19*k**3/3 - 17*k**2. Let a(s) be the first derivative of j(s). What is w in a(w) = 0?
-1, 0
Let v(z) be the first derivative of -z**3/3 + 3*z**2/2 + 10*z - 86. Factor v(p).
-(p - 5)*(p + 2)
Find q such that -41*q**2 + 52 + 5*q**3 + 66*q**2 + 38 - 15*q - 45*q**2 = 0.
-2, 3
Solve 68*d**2 + 43*d**3 + 36*d**3 - 83*d**3 - 8*d**2 - 252*d + 196 = 0 for d.
1, 7
Let y = 14044 - 14041. Factor 0*a**2 - 8/7*a**4 + 0 + 0*a + 2/7*a**y.
-2*a**3*(4*a - 1)/7
Let k be ((-24)/63 - -1) + 144/(-432). Solve -5/7*f**2 + 3/7*f + k = 0.
-2/5, 1
Let k(w) be the first derivative of -w**4/84 - 2*w**3/21 + 3*w - 31. Let v(l) be the first derivative of k(l). Suppose v(y) = 0. Calculate y.
-4, 0
Let c(t) = -7*t**3 + 4*t**2 + 2*t. Let i = -60 + 66. Let j(p) = -20*p**3 + 12*p**2 + 5*p. Let s(g) = i*j(g) - 17*c(g). Solve s(k) = 0.
0, 2
Let u(n) = -2*n**4 - 7*n**3 - 5*n**2 - 5*n. Let s(z) = -z**3 - z**2 + z. Let h(t) = 5*s(t) + u(t). Suppose h(g) = 0. What is g?
-5, -1, 0
Let t(m) = -m**3 - 4*m**2 + 3*m - 7. Let z be t(-5). Factor 3 + 61*x**3 + 6*x**2 - 63*x**3 - z.
-2*x**2*(x - 3)
Let h(z) be the second derivative of z**4/36 + z**3/9 - 35*z + 1. Let h(r) = 0. What is r?
-2, 0
Suppose -5*y - 6 + 16 = 0. Let f(l) = -l**2 + 5*l + 2. Let a be f(5). Factor 2 - 16*n + 16*n - a*n**y.
-2*(n - 1)*(n + 1)
Let v(m) be the second derivative of -m**5/50 - m**4/30 + 8*m**3/15 + 12*m**2/5 + 16*m - 2. Find d such that v(d) = 0.
-2, 3
Let z be ((-55)/15)/(1/(-3)). Let j = z - 3. Factor -g**3 + 4*g**3 + 10*g - 10 - g**3 + 6 - j*g**2.
2*(g - 2)*(g - 1)**2
Let d = 618 - 5560/9. Factor -4/9 - 2/9*v + d*v**2.
2*(v - 2)*(v + 1)/9
Let b(q) be the second derivative of q**6/10 - 69*q**5/20 - 49*q**4/4 - 25*q**3/2 + 18*q + 1. Factor b(h).
3*h*(h - 25)*(h + 1)**2
Let b = 157 - 162. Let w be b*(-3 - 129/(-45)). Factor 32/3 - 16/3*u**3 + 16*u**2 - 64/3*u + w*u**4.
2*(u - 2)**4/3
Let s = 17653/6 - 2942. Factor 1/6*j**3 + 0 - 1/2*j**4 + s*j**5 + 1/2*j**2 - 1/3*j.
j*(j - 2)*(j - 1)**2*(j + 1)/6
Let j(s) be the second derivative of 1/30*s**4 - 18*s + 0 - 6/5*s**2 + 1/15*s**3. Factor j(f).
2*(f - 2)*(f + 3)/5
Suppose -h = -2*v - 6, -12 = 5*h + 5*v + 3. Determine k so that -1/2*k**4 + 0 + 0*k + k**3 + h*k**2 = 0.
0, 2
Let g(w) be the first derivative of w**4/7 - 76*w**3/21 - 128*w**2/7 - 176*w/7 - 224. Factor g(s).
4*(s - 22)*(s + 1)*(s + 2)/7
Let a(u) be the first derivative of 1/1080*u**6 + 4 - 4/3*u**3 + 0*u**2 + 0*u - 1/180*u**5 + 1/72*u**4. Let y(c) be the third derivative of a(c). Factor y(x).
(x - 1)**2/3
Solve 330 + 2*i - 661 + 323 + 9*i**3 - 5*i**2 - 24*i = 0.
-1, -4/9, 2
Let i(p) = -5*p**2 - 8*p + 11. Let w(k) = -2*k**2 + k + 1. Let v(f) = -3*i(f) + 15*w(f). Suppose v(g) = 0. What is g?
3/5, 2
Suppose 4*t = -o + 13, 8 = 2*o - t + 3*t. Let x be 0/((1 + -2)*o). Factor -3/2*v**2 - 1/2*v - v**3 + x.
-v*(v + 1)*(2*v + 1)/2
Factor 226 - 5*m - 464 - 10*m + 17*m**2 + 236.
(m - 1)*(17*m + 2)
Suppose -4*b = -2*a + 4, -b + 3*b = -2. Let f = -405 - -405. Factor -1/3*q**2 + a*q + f.
-q**2/3
Let a(w) = 2*w**3 + 93*w**2 - 265*w + 163. Let z(c) = -5*c**3 - 185*c**2 + 530*c - 325. Let b(j) = -15*a(j) - 7*z(j). Find u, given that b(u) = 0.
1, 2, 17
Let c(u) be the second derivative of -u**6/75 - 8*u**5/25 - u - 14. Let c(q) = 0. Calculate q.
-16, 0
Let l(h) be the second derivative of h**5/140 + 23*h**4/28 + 529*h**3/14 + 12167*h**2/14 - 94*h. Factor l(f).
(f + 23)**3/7
Let w = 6/62729 + 56895149/564561. Let o = 101 - w. Suppose 2/9*n**4 + 0 + 2/9*n**5 + 0*n - 2/9*n**3 - o*n**2 = 0. Calculate n.
-1, 0, 1
Find o such that -622*o**3 + 8 - 63*o**2 + 21*o**4 + 4 - 24*o + 616*o**3 = 0.
-1, 2/7, 2
Let i(h) = 6*h**2. Let n(j) = -13*j**2 - 6*j - 8. Let k(f) = 4*i(f) + 2*n(f). Factor k(l).
-2*(l + 2)*(l + 4)
Solve -5*r + 10*r + 23 + 9*r**2 - 4*r**2 - 3*r**2 + 42*r = 0.
-23, -1/2
Let d = 5 + -3. Let s be 8/12 - d/3. What is b in s*b**2 - 10*b**2 + 6*b - 12*b + 4 = 0?
-1, 2/5
Let v(k) be the second derivative of k**3/6 - 2*k**2 - 6*k. Let c be v(6). Find d such that 0*d - d**c - 4*d + 4 + d**3 + 0*d + 0*d = 0.
-2, 1, 2
Let q be (-14)/42 - 13/6*-2. Factor -12*x**q + 6*x - 3*x - 21*x**3 + 0*x - 6*x**2.
-3*x*(x + 1)**2*(4*x - 1)
Let f(b) = b**3 + 5*b**2 + b + 9. Let u(h) = 4*h**3 + 16*h**2 + 2*h + 30. Let d(i) = 10*f(i) - 3*u(i). Factor d(k).
-2*k*(k - 2)*(k + 1)
Solve -3*j**2 + 0*j**2 + 38*j - 3*j**2 + 4*j + 3*j**4 + 27 + 12*j**3 - 78*j = 0.
-3, 1
Suppose n = i + 4*n - 9, -2*i + 16 = 5*n. Let w(d) = -3*d**3 + d**2 - 7*d + 2. Let y be w(0). Factor 1/2*z + 1/2*z**i + 0 + z**y.
z*(z + 1)**2/2
Factor 0 - 2/7*j**2 + 2/7*j**4 + 2/7*j - 2/7*j**3.
2*j*(j - 1)**2*(j + 1)/7
Let a be ((-1)/2)/((-4)/96). Suppose o = -o + a. Factor -7*v + 6*v**2 - o - 8*v + 12.
3*(v - 2)*(2*v - 1)
Suppose 5*x - 2*v - 11 = 0, -x + 0*v + 7 = 2*v. Factor 16 + 4*w - 69*w**2 + 17*w**2 + 20*w**x + 12*w.
4*(w - 2)*(w - 1)*(5*w + 2)
Let u(f) = 3*f**3 - 3*f**2 + 8*f + 2. Let y(s) = s**3 + 2*s**2 + s + 1. Let x(h) = -2*u(h) + 4*y(h). Let x(z) = 0. Calculate z.
0, 1, 6
Let s = 128992 - 128992. Let c = 257 + -1273/5. Solve -c + 3/5*y**3 + s*y + 9/5*y**2 = 0 for y.
-2, 1
Let v be ((-8)/20)/((-6)/10). Let u = -999 - -999. Let u + v*l**2 + 2*l = 0. What is l?
-3, 0
Factor -612*k - 2/17*k**4 - 330*k**2 + 0 - 208/17*k**3.
-2*k*(k + 2)*(k + 51)**2/17
Let y(w) be the first derivative of 12*w**5/35 - 11*w**4/7 + 16*w**3/7 - 8*w**2/7 + 121. Find d such that y(d) = 0.
0, 2/3, 1, 2
Suppose 4*k = 48 - 24. Factor 0*y + k*y - 2*y**2 - 2 + 3*y - 5*y.
-2*(y - 1)**2
Let k be (6/(-45))/(17/(-510)). Let j(h) be the first derivative of 6/5*h**5 - 2*h**3 + 0*h**k + 2 - 1/2*h**6 + 3/2*h**2 + 0*h. Factor j(n).
-3*n*(n - 1)**3*(n + 1)
Let z(o) be the second derivative of 1/9*o**3 + 0 + 0*o**4 - 1/90*o**5 + 2/9*o**2 - 4*o. Solve z(n) = 0.
-1, 2
Let s = 826/3 - 274. Determine f so that -4*f + s*f**3 + 8/3 + 0*f**2 = 0.
-2, 1
Suppose 2*u + v = 3, -12*u = -7*u + 3*v - 7. Let j(x) be the third derivative of -u*x**2 + 1/240*x**5 + 0*x**3 + 0 + 0*x + 1/96*x**4. Factor j(o).
o*(o + 1)/4
Let u(a) be the first derivative of 2*a**3/27 - 35*a**2/9 - 148*a/9 - 234. Solve u(o) = 0 for o.
-2, 37
Let p(h) be the first derivative of h**9/9072 - h**7/2520 - 10*h**3/3 + 18. Let w(m) be the third derivative of p(m). Suppose w(x) = 0. Calculate x.
-1, 0, 1
Let l = -4785 - -14357/3. Factor -2*s + 4/3 + 0*s**2 + l*s**3.
2*(s - 1)**2*(s + 2)/3
Determine j, given that 0 - 1/5*j**2 + 11/5*j = 0.
0, 11
Factor -90774/11*w - 738/11*w**2 - 3721734/11 - 2/11*w**3.
-2*(w + 123)**3/11
Let q(b) = 5*b + 1. Let j be q(1). Let z(x) = x - 4. Let c be z(j). Determine g, given that -c*g**2 + 7*g - 3*g + 4*g**2 = 0.
-2, 0
Let s(j) be the first derivative of -16/3*j**3 - 4/5*j**5 + 2*j - 2 - 3/2*j**2 - 15/4*j**4. Determine y so that s(y) = 0.
-2, -1, 1/4
Let n(q) = -q**2 + 7*q - 12. Let h be 3/4*16/4. Let j be n(h). Factor j - 1/3*s**2 - 1/3*s.
-s*(s + 1)/3
Let l(z) be the second derivative of -z**6/105 + z**5/10 + 4*z**4/21 + 69*z. Suppose l(p) = 0. Calculate p.
-1, 0, 8
Let m(o) = 10*o**3 - 345*o**2 + 690*o - 330. Let j(u) = 9*u**3 - 346*u**2 + 689*u - 332. Let a(d) = -5*j(d) + 4*m(d). Solve a(v) = 0.
1, 68
Let u(k) = -24*k**2 + 905*k + 11. Let x(n) = 9*n**2 - 301*n - 4. Let p(r) = 4*u(r) + 11*x(r). Factor p(g).
3*g*(g + 103)
Let l = 2/855 + 2533/13680. Let i(u) be the first derivative of 1/4*u**3 + 2 - 3/4*u + l*u**4 - 3/8*u**2. Factor i(v).
3*(v - 1)*(v + 1)**2/4
Suppose y + q = 7, -8 - 19 = -y - 5*q. What is v in -1/3 + 2/9*v + 1/9*v**y = 0?
-3, 1
Let k(l) be the first derivative of 2*l**5/35 - 3*l**4/28 - 80*l**3/21 - 183*l**2/14 - 72*l/7 - 199. Factor k(x).
(x - 8)*(x + 3)**2*(2*x + 1)/7
Let i(m) = -4*m**3 + 11*m**2 - m. Let v(j) = -20*j**3 + 54*j**2 - 6*j. Let z = -65 + 51. Let w(h) = z*i(h) + 3*v(h). Let w(q) = 0. Calculate q.
0, 1
Let m = -819 - -828. Let h = -33/14 + 27/7. Factor -h*t**2 - 27/2 + m*t.
-3*(t - 3)**2/2
Factor -13*t**2 - 10*t - 12 - 22*t**2 + 33*t**2.
-2*(t + 2)*(t + 3)
Let f(d) be the third derivative of 2*d**8/105 + 136*d**7/525 + 361*d**6/300 + 3*d**5/2 - 63*d**4/20 + 9*d**3/5 - 10*d**2 - d. Factor f(i).
2*(i + 3)*