r - 14 - 12, -2*r = 4*f - 6. Suppose -r*j + 9 = -1. Determine a so that 108*a - j*a**2 - 108*a = 0.
0
Let l(o) be the first derivative of -o**4/12 - 77*o**3/9 - 481*o**2/2 + 507*o + 645. Suppose l(h) = 0. Calculate h.
-39, 1
Let b(i) be the third derivative of 0*i**3 + 2*i**2 + 1/24*i**4 + 0*i - 1/120*i**6 + 0*i**5 + 0. Determine x, given that b(x) = 0.
-1, 0, 1
Let 4 - 25*r**2 - 164*r**3 + 5*r + 1 + 179*r**3 + 0 = 0. What is r?
-1/3, 1
Let r(w) = -6*w**3 + 10*w**2 + 26*w + 18. Let h(a) = a**3 - a**2 + a - 1. Suppose -4*c = 2*x - 12, 5*c = 4*c + x. Let z(q) = c*h(q) + r(q). Factor z(f).
-4*(f - 4)*(f + 1)**2
Let r(f) be the second derivative of -f**5/50 + 11*f**4/15 - 121*f**3/15 - 37*f - 1. Determine q, given that r(q) = 0.
0, 11
Suppose 0 = -8*i + 9*i - 5. Suppose -5*c = -20 - 5. Let -7*y**i + 2*y - 4*y**3 + 8*y**5 + y**c = 0. Calculate y.
-1, 0, 1
Let n(m) be the first derivative of m**6/2 - 3*m**5/5 - 21*m**4/2 - 26*m**3 - 57*m**2/2 - 15*m - 178. Let n(s) = 0. What is s?
-1, 5
Let w be ((-14)/(-35))/(2/80). Factor -52*t**2 - 9*t - 21*t**3 + 6 + 0 + w*t**2.
-3*(t + 1)**2*(7*t - 2)
Let l(m) be the second derivative of -m**3 + 3/4*m**4 + 0*m**2 - 3/20*m**5 + 13*m + 0. Determine v, given that l(v) = 0.
0, 1, 2
Let d(h) be the third derivative of -h**8/47040 - h**7/2352 - h**6/280 + 31*h**5/60 + 31*h**2. Let r(z) be the third derivative of d(z). What is l in r(l) = 0?
-3, -2
Let w(c) be the third derivative of -c**6/200 - c**5/100 + c**4/20 - 5*c**2 + 16*c. Determine o so that w(o) = 0.
-2, 0, 1
Solve 1/6*j**3 + 75 + 55/2*j - 14/3*j**2 = 0.
-2, 15
Suppose 3*u + 8 + 16 = 3*x, 4*x - 14 = -5*u. Let z(y) be the first derivative of -6/5*y + x - 2/45*y**3 + 2/5*y**2. Find f, given that z(f) = 0.
3
Let w(k) be the first derivative of -1/9*k**2 - 5 + 2/27*k**3 - 4/9*k. Factor w(g).
2*(g - 2)*(g + 1)/9
Factor -8*n**3 + 1/3*n**4 + 338/3*n + 39*n**2 + 0.
n*(n - 13)**2*(n + 2)/3
Factor -4 + 7/2*c**3 + c**2 - 14*c.
(c - 2)*(c + 2)*(7*c + 2)/2
Factor -22*h + 17 + 10*h**2 - 1 + 6*h - 6*h**2 + 0*h**2.
4*(h - 2)**2
Find g, given that 4/7*g**4 + 4/7*g**2 + 2*g - 8/7 + 2/7*g**5 - 16/7*g**3 = 0.
-4, -1, 1
Let 27*i**3 + 14*i**2 + 230*i + 43*i**2 - 15*i**4 - 18*i**2 - 314*i - 3*i**5 + 36 = 0. What is i?
-6, -2, 1
Suppose 3*k - 266 = -74. Find c, given that 12 + 4*c**2 - 31*c - k - 17*c = 0.
-1, 13
Let f = -17744/3 + 5861. Let w = f + 54. Factor 1/6*o**2 + w + 1/2*o.
(o + 1)*(o + 2)/6
Let c be 0*-1*4*10/(-120). Solve 6*a**2 + 3/4*a**3 + 21/4*a + c = 0.
-7, -1, 0
Let b(a) be the third derivative of 0*a - 1/60*a**4 + 1/1200*a**6 + 0 - 10*a**2 - 2/15*a**3 + 1/300*a**5. Let b(v) = 0. What is v?
-2, 2
Let h(i) be the third derivative of 0 + 0*i**4 - 11*i**2 - 1/180*i**6 + 0*i - 4/9*i**3 + 1/30*i**5. Factor h(v).
-2*(v - 2)**2*(v + 1)/3
Let b(f) = -11*f**3 + 10*f**2 - 5*f + 3. Let u(m) = -43*m**3 + 40*m**2 - 23*m + 13. Let z(g) = -26*b(g) + 6*u(g). Factor z(i).
4*i*(i - 1)*(7*i + 2)
Let z = -61 - -49. Let k be 1 - 12/45*z. Determine d, given that 0 - 6/5*d**3 + 0*d - 12/5*d**5 - 3/5*d**2 + k*d**4 = 0.
-1/4, 0, 1
Let p(n) be the third derivative of -36*n**2 + 5/42*n**7 + 1/4*n**5 - 5/336*n**8 + 0 + 0*n**4 - 7/24*n**6 + 0*n**3 + 0*n. Factor p(j).
-5*j**2*(j - 3)*(j - 1)**2
Determine b so that 88 - 357 + 6*b**3 - 10*b + 167 - 239*b - 87*b**2 = 0.
-2, -1/2, 17
Let c(d) be the second derivative of -d**5/20 + 3*d**4/8 + 9*d**2 - d. Let o(h) be the first derivative of c(h). Solve o(z) = 0 for z.
0, 3
Factor 14792 - 221*u + 18*u**2 - 9*u**2 - 7*u**2 - 123*u.
2*(u - 86)**2
Let i = -50 - -32. Let p be (-4 - 84/i)*9/12. Factor -5/4*y**2 - 11/4*y**3 + p*y - y**4 + 0.
-y*(y + 1)*(y + 2)*(4*y - 1)/4
Let p(g) be the first derivative of 1/360*g**5 + 0*g - 1/36*g**4 + 1/9*g**3 + 6 - 3*g**2. Let d(x) be the second derivative of p(x). Factor d(s).
(s - 2)**2/6
Let u(m) be the first derivative of -32/3*m**3 + 0*m + 15 + 1/3*m**6 + 14/5*m**5 + 0*m**2 + 4*m**4. Factor u(a).
2*a**2*(a - 1)*(a + 4)**2
Let h = 65 + -91. Let j = 26 + h. Factor j - 3*l**2 - 3/2*l - 3/2*l**3.
-3*l*(l + 1)**2/2
Let b(r) be the second derivative of r**6/15 + 4*r**5/5 + 4*r**4 + 32*r**3/3 + 16*r**2 - 33*r. Let b(a) = 0. What is a?
-2
Let p(q) be the first derivative of 2*q**5/25 - q**4/10 - 2*q**3/5 + q**2/5 + 4*q/5 + 11. Factor p(x).
2*(x - 2)*(x - 1)*(x + 1)**2/5
Let z = 5 + -8. Let g = z - -6. Factor -6*j - 9*j**3 - 9*j**2 + 0*j**g + 6*j**3.
-3*j*(j + 1)*(j + 2)
Let y(t) = t**3 - 9*t**2 + t - 6. Let r be y(9). Suppose -4*x = 3*g, r*x - 10 = x + g. Find l such that 0 + 1 - l + x*l + l**2 = 0.
-1
Suppose -3*p + 4*p - i + 8 = 0, -i - 22 = 5*p. Let n(f) = 4*f + 20. Let u be n(p). Determine j, given that u*j**2 + 1/11*j**4 + 0*j + 0 + 0*j**3 = 0.
0
Let r be 2/(-5) - (-138)/120. Let t be ((-6)/88)/((-249)/913). Factor -t*x**3 + 5/4*x + 1/2 - 1/4*x**4 + r*x**2.
-(x - 2)*(x + 1)**3/4
Let t(x) be the first derivative of -x**4/14 + 2*x**3/3 - 2*x**2 + 16*x/7 + 76. Factor t(g).
-2*(g - 4)*(g - 2)*(g - 1)/7
Let o = -2443 + 2443. Let x(i) be the second derivative of 0 - 1/135*i**6 - 1/9*i**2 + 0*i**5 + o*i**3 + 1/27*i**4 - 4*i. Find c, given that x(c) = 0.
-1, 1
Let f(k) = 2*k**4 + k**3 - 3*k**2 - 6*k - 9. Let s(h) = -h**4 - h**3 + h**2 + 3*h + 4. Let n(q) = 4*f(q) + 10*s(q). What is o in n(o) = 0?
-2, -1, 1
Let v(o) = 3 - o + 2*o + 16 - 5. Let x be v(-12). Factor 99*j**x - 7*j**3 + 73*j**3 + 60*j + 12 + 60*j**4 - 45*j**4.
3*(j + 1)**2*(j + 2)*(5*j + 2)
Factor -45*o**2 + 315*o**3 + 47*o**5 - 42*o**5 - 36*o**4 - 360*o**2 + 121*o**4.
5*o**2*(o - 1)*(o + 9)**2
Let l be -135*((-591)/(-117) + -5). Let k = -398/65 - l. Find z, given that 0 + 4/5*z**2 + k*z = 0.
-1, 0
Factor 529*a + 0 - 21/2*a**3 - 345/4*a**2 - 1/4*a**4.
-a*(a - 4)*(a + 23)**2/4
Let l be (-5)/10 + 0 - (-5)/2. Find g, given that -3*g + g**2 + 6*g + 10*g**l - 12*g**2 = 0.
0, 3
Suppose -7 - 8 = -5*c. Determine o so that 12*o - 11*o**2 + 20*o**2 - 12 - 5*o**4 + 2*o**4 - 6*o**c = 0.
-2, 1
Suppose -j - 6*k + 11*k = 12, 5*k - 21 = -2*j. Let l(y) be the second derivative of 3*y**2 + 8*y + y**4 - 5/2*y**j - 3/20*y**5 + 0. Find v such that l(v) = 0.
1, 2
Let m be -1 + 3*8/6. Let -13*l**2 + 3*l - 27*l**m - 23*l**4 - 7*l**5 - 5*l + 0*l**4 = 0. Calculate l.
-1, -2/7, 0
Let c(m) be the third derivative of -m**8/3360 - m**7/700 + 3*m**6/400 - m**5/120 + 5*m**2 - m. Find n, given that c(n) = 0.
-5, 0, 1
Let h(k) be the second derivative of 6/5*k**2 + 19/20*k**4 + 5*k - 2*k**3 + 1/10*k**7 - 23/50*k**6 + 0 + 39/100*k**5. Let h(g) = 0. Calculate g.
-1, 2/7, 1, 2
Let i = -10439 - -10441. Factor -1/2*z**i - 5/2*z - 2.
-(z + 1)*(z + 4)/2
Let u be (2/6 + 14/3)/1. Let f(x) be the third derivative of -x**2 + 1/24*x**3 + 0*x + 1/24*x**4 + 1/60*x**u + 0. Find j, given that f(j) = 0.
-1/2
Let q(j) be the third derivative of j**5/60 + j**4/6 + 5*j**3/6 - j**2. Let w be q(-6). Find i, given that -16*i - 2*i**2 - i**3 + w*i + 2*i**3 = 0.
0, 1
Let n(j) = 2*j**2 + 3*j + 3. Let h be n(-1). Factor 3*u**3 - 3*u - 5*u**2 + 0*u**4 + 4*u**2 + 3*u**4 - 2*u**h.
3*u*(u - 1)*(u + 1)**2
Let i(x) = -10*x**2 + 10*x + 16. Let l(a) = -12*a**2 + 10*a + 17. Let y(t) = 5*i(t) - 4*l(t). Suppose y(q) = 0. Calculate q.
-1, 6
Let k(c) = 6 - 8*c + 12*c - 7*c**4 + 2*c + c**3. Let q(s) = 13*s**4 - 2*s**3 - 11*s - 11. Suppose 0*x + 24 = 4*x. Let l(a) = x*q(a) + 11*k(a). Factor l(p).
p**3*(p - 1)
Let z(q) be the second derivative of q**7/70 - 3*q**6/20 + 3*q**5/5 - 5*q**4/4 + 3*q**3/2 + q**2/2 + 6*q. Let o(l) be the first derivative of z(l). Factor o(p).
3*(p - 3)*(p - 1)**3
Let w be 1/(-2) - (-59455)/286. Let a = 208 - w. Determine g so that 8/13 - a*g**2 + 30/13*g = 0.
-1/4, 4
Let f = 47 + -47. Solve 7*i + 1 + i**2 - 19 + f + 10 = 0.
-8, 1
Let m(k) be the first derivative of -1/4*k**2 + 0*k - 10 + 1/3*k**3 - 1/8*k**4. Factor m(t).
-t*(t - 1)**2/2
Suppose 2*t + 3 = 9. Let r = -5885 + 11773/2. Factor t*l + r*l**2 - 9/2.
3*(l - 1)*(l + 3)/2
Let -34/7*x**3 + 0 + 6/7*x**2 + 0*x = 0. What is x?
0, 3/17
Let m = 2/147163 - -882964/1030141. Factor 2/7*y**3 - 2/7*y - m*y**2 + 4/7 + 2/7*y**4.
2*(y - 1)**2*(y + 1)*(y + 2)/7
Suppose -2 = 11*n - 12*n. Let t(b) be the second derivative of 0*b**3 + 0 - 1/42*b**4 - 5*b - 1/70*b**5 + 0*b**n. Determine x, given that t(x) = 0.
-1, 0
Let t(m) be the third derivative of -7*m**8/192 + m**7/15 +