/4
Let b(n) be the second derivative of -n**8/2100 + n**6/225 - n**4/30 - 13*n**3/6 + 9*n. Let p(f) be the second derivative of b(f). Factor p(x).
-4*(x - 1)**2*(x + 1)**2/5
Suppose -76 = -2*n - 64. Let i be (6/4)/((-1)/(-4)). Factor -n*d**2 + 5 - i - 8*d - 1.
-2*(d + 1)*(3*d + 1)
Suppose 6 - 5*y**3 - 53/3*y + 17*y**2 - 1/3*y**4 = 0. Calculate y.
-18, 1
Let o(u) = -26*u + 1. Let d be o(-1). Let x = 30 - d. Suppose -9*r**4 + 21/2*r**2 + 21/4*r**5 - 3/2 - 9/4*r - 3*r**x = 0. Calculate r.
-1, -2/7, 1
Let s(w) be the first derivative of -2*w**3/33 - 46*w**2/11 - 1058*w/11 + 145. Factor s(a).
-2*(a + 23)**2/11
Let m(s) be the third derivative of 1/12*s**5 + 0*s + 5/8*s**4 + 1/42*s**7 - 5/3*s**3 - 1/8*s**6 + 3*s**2 + 0. Solve m(j) = 0.
-1, 1, 2
Let h = 702/5 - 140. Let v = -476 + 476. Factor v - h*l**3 + 2/5*l**4 - 2/5*l**2 + 2/5*l.
2*l*(l - 1)**2*(l + 1)/5
Let a(w) = -11*w**4 + 3*w**3 + 19*w**2 - 21*w + 1. Let x(g) = 21*g**4 - 5*g**3 - 39*g**2 + 41*g - 3. Let r(k) = 5*a(k) + 3*x(k). Factor r(q).
2*(q - 1)*(q + 2)*(2*q - 1)**2
Let p(s) be the first derivative of 5/6*s**3 + 5/8*s**4 - 5/4*s**2 + 0*s - 1/2*s**5 + 11. Factor p(t).
-5*t*(t - 1)**2*(t + 1)/2
Let b = -606 - -609. Let k(w) be the second derivative of -1/75*w**6 - 1/105*w**7 + 1/10*w**5 + 1/30*w**4 + 0 - 8/15*w**b + 4/5*w**2 - 7*w. Factor k(a).
-2*(a - 1)**3*(a + 2)**2/5
Let h(q) = -q**2 + 24*q - 9. Let t be h(7). Find u, given that -t*u**2 + 2*u**4 + 7*u**4 + 116*u**2 - 21*u**3 = 0.
0, 1/3, 2
Let m be 16/3 + (4 - -2 - 11). Let n(q) be the second derivative of 0*q**2 + 0 + 1/6*q**4 - m*q**3 - 9*q. Factor n(f).
2*f*(f - 1)
Let d(t) be the third derivative of -t**5/120 + 23*t**4/12 - 529*t**3/3 - 29*t**2 - 5. Factor d(p).
-(p - 46)**2/2
Suppose 16*m**2 - 217*m**3 + 112*m + 106*m**3 + 107*m**3 + 128 = 0. What is m?
-2, 8
Let l(z) be the second derivative of 0 + 8*z + 1/12*z**3 - 1/168*z**7 + 0*z**2 - 1/80*z**5 + 1/16*z**4 - 1/40*z**6. Determine x so that l(x) = 0.
-2, -1, 0, 1
Let q be 6*296/640 - 21/(-35). Determine v so that -179/8*v**3 + 15*v**4 - 1/2*v - 1 + 49/4*v**2 - q*v**5 = 0.
-2/9, 2/3, 1, 2
Let k = -17 + 21. Factor -17*y**4 + 35*y**4 - 21*y**k + 3*y**2.
-3*y**2*(y - 1)*(y + 1)
Factor -3/2*i**4 + 1/2*i**5 + 3/2*i**2 + 0*i - 1/2*i**3 + 0.
i**2*(i - 3)*(i - 1)*(i + 1)/2
Suppose 13 = 5*m - 7. Suppose -5*l**2 + 506 - 5*l**m + 10*l**3 - 506 = 0. What is l?
0, 1
Let m(b) be the second derivative of -30*b + 4*b**2 + 0 + 5/3*b**3 + 1/6*b**4. Determine u so that m(u) = 0.
-4, -1
Let h be 2041*(1 - 30/27). Let g = h + 227. Find w such that -2/9 + 0*w**2 + 4/9*w**3 + g*w**4 - 4/9*w = 0.
-1, 1
Let z(v) = 4*v**4 - 6*v**3 + 3*v**2 + 22*v - 3. Let j(c) = 5*c**4 - 4*c**3 + c**2 + 22*c - 4. Let u(w) = 3*j(w) - 4*z(w). Factor u(o).
-o*(o - 11)*(o - 2)*(o + 1)
Determine f so that f**4 - 9*f**2 - 5*f**2 + 2*f + 0*f**2 + 3*f**2 - 9*f**3 + 10 + 7*f = 0.
-1, 1, 10
Suppose 3*r - 16 = -4*m + 2*r, 2*r - 17 = -3*m. Factor m*c**2 - 375 - 12*c + 391 - c**2.
2*(c - 4)*(c - 2)
Let g = -14314/45 + 1606/5. Let l = -11229 - -101077/9. Factor -40/9*i + l + g*i**2 - 2/3*i**3.
-2*(i - 2)**2*(3*i - 2)/9
Let -12*d - 18*d**2 + 14*d**2 - 21*d**4 + 25*d**4 + 12*d**3 = 0. Calculate d.
-3, -1, 0, 1
Let o be 6/(-7)*(-14)/3. Let f(j) = -2*j**3 - 12*j**2 - 6*j - 4. Let h(s) = 2*s**3 + 11*s**2 + 7*s + 4. Let d(n) = o*h(n) + 3*f(n). Factor d(k).
2*(k + 1)**2*(k + 2)
Let v = -32 + 37. Factor 58*x**3 - 36*x**2 - 12*x**4 - 2*x**4 + 9*x**v + 8*x - 25*x**4.
x*(x - 2)*(x - 1)*(3*x - 2)**2
Suppose 0 = 62*w - 53*w - 36. What is d in -1/2*d**2 - w - 9/2*d = 0?
-8, -1
Factor c**2 + 8*c - 5216 + 5234 + 4*c + c**2.
2*(c + 3)**2
Let c(f) be the second derivative of -f**5/80 + 7*f**4/48 - 5*f**3/8 + 9*f**2/8 - 48*f. Determine t so that c(t) = 0.
1, 3
Let b(r) be the first derivative of -3/2*r - 3/2*r**2 - 3/32*r**4 + 44 - 5/8*r**3. Suppose b(y) = 0. Calculate y.
-2, -1
Let z(h) be the third derivative of -h**8/896 - 3*h**7/560 - 3*h**6/320 - h**5/160 - 15*h**2 + 2*h. Determine j, given that z(j) = 0.
-1, 0
Let l(r) = -27*r**3 - 89*r**2 + 27*r - 51. Let o(t) = -9*t**3 - 30*t**2 + 9*t - 18. Let x(a) = -6*l(a) + 17*o(a). Factor x(u).
3*u*(u + 3)*(3*u - 1)
Let x(o) be the first derivative of 3*o**5/5 + o**4/2 - 11*o**3/9 - 2*o**2/3 + 4*o/3 - 31. Factor x(b).
(b + 1)**2*(3*b - 2)**2/3
Suppose 21/4*t**3 - 39/8*t**2 + 0*t + 0 - 3/8*t**4 = 0. Calculate t.
0, 1, 13
Let u be 1 - (-10 - 1)/(-1). Let h be ((-15)/25 - -1)/((-6)/u). Factor 8/9*k + h + 2/9*k**2.
2*(k + 1)*(k + 3)/9
Let a be (-722)/(-152) + -3 + (-26)/(-8). Let j(f) be the first derivative of -2/5*f**a - f - 1/2*f**2 + 1/4*f**4 - 9 + f**3. Let j(d) = 0. What is d?
-1, -1/2, 1
Let g(n) be the second derivative of -3/10*n**5 - 5/6*n**4 + 0 + 4*n**2 + n**3 + 1/15*n**6 - 13*n. Factor g(i).
2*(i - 4)*(i - 1)*(i + 1)**2
Let t(u) be the second derivative of -1/2*u**3 - 1/14*u**7 + 0 - 9*u + 3/10*u**5 - 1/5*u**6 - 3*u**2 + u**4. Suppose t(o) = 0. What is o?
-2, -1, 1
Suppose -4*i**5 + 26 - 12*i**4 + 8*i**2 + 17 + 12*i - 8*i**3 - 39 = 0. What is i?
-1, 1
Suppose 3*n = -4*a + 5, -3*a + 15 = -2*n - 10. Let q(d) = -2*d**2. Let x(z) = 3*z**2 + z. Let u(s) = a*q(s) + 4*x(s). Factor u(b).
2*b*(b + 2)
Let t(f) = 2*f**2 + 8*f - 6. Let v(m) be the second derivative of -m**4/6 - 7*m**3/6 + 3*m**2 - 6*m. Let a(w) = -3*t(w) - 4*v(w). Factor a(c).
2*(c - 1)*(c + 3)
Suppose 0 = -0*j - 2*j + o + 17, 4*o = 4*j - 36. Suppose 3*u - j*u + 45 = -4*s, 15 = -3*s. Factor 2*x + 9*x**3 + x**5 - x**2 + u*x**4 + 9*x**2 - x**2.
x*(x + 1)**3*(x + 2)
Let o = 891 + -886. Let i(f) be the first derivative of -2/33*f**3 - o + 4/11*f - 1/11*f**2. Factor i(z).
-2*(z - 1)*(z + 2)/11
Let m(l) be the second derivative of 0*l**6 - 3/50*l**5 - 1/15*l**4 + 0 + 0*l**2 + 3*l + 0*l**3 + 1/105*l**7. Find b such that m(b) = 0.
-1, 0, 2
Suppose 16/19*x**2 - 4/19 - 10/19*x**3 - 2/19*x = 0. Calculate x.
-2/5, 1
Let y be 0 + (-4)/5 - 24/(-5). Factor 3*p**2 + 16*p + y + 8 + 0 + p**2.
4*(p + 1)*(p + 3)
Let y(b) be the second derivative of -b**7/98 + 13*b**6/70 + 87*b**5/140 + 15*b**4/28 + 106*b. Let y(n) = 0. What is n?
-1, 0, 15
Let k(n) be the third derivative of n**6/360 - n**5/40 + n**4/12 - 7*n**3/6 + 2*n**2. Let h(c) be the first derivative of k(c). Factor h(q).
(q - 2)*(q - 1)
Let t(d) = -d**2 - 2*d - 1. Let h(f) = 2*f**2 - 126*f - 4353. Let n(c) = -4*h(c) - 12*t(c). Solve n(l) = 0.
-66
Let p(q) be the third derivative of -q**6/160 + 21*q**5/80 + q**4/32 - 21*q**3/8 + 66*q**2 - 2. Factor p(i).
-3*(i - 21)*(i - 1)*(i + 1)/4
Let r = 153/47 - 624/235. Suppose -12/5*u - r*u**2 - 12/5 = 0. What is u?
-2
Suppose 2*z - 8 = -0*z. Let -z*i**2 + 5*i - 9*i + 8*i = 0. What is i?
0, 1
Let i(r) be the second derivative of -r**6/24 + 5*r**4/12 - 141*r. Factor i(w).
-5*w**2*(w - 2)*(w + 2)/4
Let o(i) be the first derivative of -15*i**4/28 - 6*i**3/7 - 3*i**2/14 - 372. Factor o(j).
-3*j*(j + 1)*(5*j + 1)/7
Let s(y) be the first derivative of 0*y + 1/30*y**4 + 2/75*y**5 - 2/45*y**3 - 1/15*y**2 + 9. Find k, given that s(k) = 0.
-1, 0, 1
Let b = 31 - 36. Let q(t) = -8*t**3 - 4*t**2 + 4*t + 6. Let i(c) = -7*c**3 - 4*c**2 + 3*c + 5. Let d(m) = b*q(m) + 6*i(m). Factor d(y).
-2*y*(y + 1)**2
Let f = -206 + 3297/16. Let u(l) be the third derivative of 0*l**4 - 1/10*l**5 + 0*l + 0*l**3 + 3/40*l**6 + 5*l**2 + 0 + f*l**8 + 6/35*l**7. Factor u(t).
3*t**2*(t + 1)**2*(7*t - 2)
Let b(f) be the second derivative of 5*f**7/42 + f**6 - 40*f**4/3 - 3*f + 10. Factor b(s).
5*s**2*(s - 2)*(s + 4)**2
Let k(b) = b**3 + 4*b**2 - 3*b - 5. Let w be k(-4). Factor 10 + 2*s**3 + 3*s**3 - s - w*s - 7*s.
5*(s - 1)**2*(s + 2)
Let f(r) be the first derivative of -4*r**5 - 5*r**4/4 + 55*r**3/3 - 15*r**2 - 571. Factor f(u).
-5*u*(u - 1)*(u + 2)*(4*u - 3)
Let -51868672 + 2*r**3 + 281085*r + 354299*r - 109688*r - 1776*r**2 = 0. Calculate r.
296
Let k = -95 - -63. Let d be (-16)/(-30)*(-24)/k + 0. Factor 0 + 0*m - d*m**2.
-2*m**2/5
Factor -5/2*m**3 + 75 + 185/2*m + 31/2*m**2 - 1/2*m**4.
-(m - 6)*(m + 1)*(m + 5)**2/2
Let g(u) be the second derivative of u**4/48 - u**3/4 - 2*u**2 - 31*u + 3. Factor g(j).
(j - 8)*(j + 2)/4
Let h be 49*6/270 + -1. Let i = 14/45 + h. Suppose -2/5*j + i*j**2 - 2/5 + 2/5*j**3 = 0. What is j?
-1, 1
Let l(t) = -6*t**5 - 68*t**4 - 24*t**3 + 85*t**2 + 33*t - 17. Let r(u) = -2*