 + 1)*(u + 4)**2
Let k(i) = -81*i**3 + 2001*i**2 + 91149*i + 1366899. Let g(b) = -17*b**3 + 400*b**2 + 18230*b + 273380. Let f(s) = 24*g(s) - 5*k(s). Factor f(t).
-3*(t + 45)**3
Let x(d) be the third derivative of -d**8/1008 - 2*d**7/315 - d**6/90 + d**5/90 + 5*d**4/72 + d**3/9 + 15*d**2 - 4. Factor x(r).
-(r - 1)*(r + 1)**3*(r + 2)/3
Let i(v) = -17*v - 148. Let p be i(-9). Factor -2/7 + 4/7*m**3 + 6/7*m**4 - 6/7*m + 2/7*m**p - 4/7*m**2.
2*(m - 1)*(m + 1)**4/7
Let q be 2*15/30*(1 - 1). Let a(b) be the second derivative of 1/30*b**4 + 3*b - 2/5*b**2 - 1/15*b**3 + q. What is z in a(z) = 0?
-1, 2
Let u(g) be the second derivative of g**4/96 - 25*g**3/24 + 625*g**2/16 - g + 3. Solve u(k) = 0 for k.
25
Let o = 881 - 877. Let m(y) be the second derivative of 1/24*y**4 - 1/4*y**2 - 1/80*y**5 + o*y + 0 + 1/24*y**3. Factor m(u).
-(u - 2)*(u - 1)*(u + 1)/4
Let s(a) = -a**2 + 6*a - 2. Let c be s(5). Let j be c/2*16/(-36) - -1. Factor 2/3*h + 1 - j*h**2.
-(h - 3)*(h + 1)/3
Let z(m) = 10*m**2 - 5*m + 6. Let a be z(6). Let j be (-2)/7 - a/(-147). Determine r, given that 0*r**2 + 9*r**2 - 4*r**2 - 7*r**j = 0.
0
Let w = -4562/5 + 50222/55. Factor 6/11 - w*a + 2/11*a**2.
2*(a - 3)*(a - 1)/11
Factor 4/7*x**2 + 0 - 2/7*x**3 + 6/7*x.
-2*x*(x - 3)*(x + 1)/7
Determine z so that -4*z + 14*z + 929*z**2 + 8 - 926*z**2 = 0.
-2, -4/3
Let y(c) be the second derivative of 0*c**3 + 18*c - 3/100*c**5 + 0 + 1/150*c**6 + 1/30*c**4 + 0*c**2. Factor y(g).
g**2*(g - 2)*(g - 1)/5
Suppose 46 = 39*o - 32. Factor 1/4*i**o + 3/2*i + 0.
i*(i + 6)/4
Suppose -5*g - 21 = -w + 2*w, -2*g = -4*w + 26. Let h(k) be the first derivative of -k**3 + 9/8*k**2 + w + 3/4*k. Solve h(r) = 0 for r.
-1/4, 1
Let q(t) be the second derivative of 1/105*t**5 + 0*t**3 + 1/84*t**4 - 3*t + 1/420*t**6 + t**2 + 0. Let r(d) be the first derivative of q(d). Solve r(m) = 0.
-1, 0
Let h(g) be the first derivative of 1 - 1/36*g**4 + 0*g**2 + 3*g - 1/18*g**3. Let l(i) be the first derivative of h(i). Factor l(u).
-u*(u + 1)/3
Let r(d) be the second derivative of d**7/42 + 2*d**6/15 - d**5/10 - 2*d**4/3 + d**3/6 + 2*d**2 + 181*d. What is v in r(v) = 0?
-4, -1, 1
Let r = 486 - 483. Let 1/3*d**5 + 1/6*d**r + 1/2*d**4 + 0 + 0*d**2 + 0*d = 0. Calculate d.
-1, -1/2, 0
Factor -1/3*n**4 - 286/3*n**2 - 361/3 + 228*n - 12*n**3.
-(n - 1)**2*(n + 19)**2/3
Let 33/4*t**3 - 213/4*t + 63/2 + 3/4*t**4 + 51/4*t**2 = 0. What is t?
-7, -6, 1
Let q(f) be the third derivative of f**7/42 + f**6/12 - 5*f**4/12 - 5*f**3/6 - 6*f**2 + 4*f. Find d such that q(d) = 0.
-1, 1
Let b(m) be the first derivative of 9 + 30*m**2 + 15/2*m**4 - 20*m - 65/3*m**3 - m**5. Let b(d) = 0. Calculate d.
1, 2
Let o be 11194/1760 - (4 + -4 - -1). Let z = o + 7/176. Factor 21/5*c + 3/5*c**4 + z*c**2 + 6/5 + 3*c**3.
3*(c + 1)**3*(c + 2)/5
Let a(t) = 5*t**4 + 5*t**3 - 4*t**2 - 3*t - 3. Let v(p) = p**4 + p**3 - p - 1. Let j = 6 - 3. Let o(l) = j*v(l) - a(l). Solve o(s) = 0.
-2, 0, 1
Let h = -854 - -857. Let d(y) be the second derivative of 0*y**2 + 0 + 1/18*y**h - 7/72*y**4 - 7*y. Factor d(f).
-f*(7*f - 2)/6
Let g(t) be the second derivative of t**7/14 + t**6/10 - 27*t**5/20 - 13*t**4/4 + 4*t**3 + 18*t**2 - 464*t. Determine p, given that g(p) = 0.
-2, -1, 1, 3
Let t(k) be the first derivative of k**8/1680 + k**7/120 + k**6/20 + k**5/6 + k**4/3 + 8*k**3/3 - 13. Let l(i) be the third derivative of t(i). Factor l(d).
(d + 1)*(d + 2)**3
Let x(c) be the second derivative of -3/4*c**4 + 0 + 12*c**2 - 10*c - 5*c**3. Solve x(h) = 0.
-4, 2/3
Suppose 120*b - 125*b + 15 = 0. Solve -61*y - 3*y**b - 88*y**2 - 1 - 7 + 63*y**3 + y = 0 for y.
-1/3, -1/5, 2
Suppose 3*v + 16 = -4*o, 5*v - 3*o - 6 = 6. Let f(m) be the second derivative of 0 + 0*m**2 + v*m**3 - 1/3*m**4 + 2*m - 1/10*m**5. Determine u so that f(u) = 0.
-2, 0
Factor 14/9*m**2 - 2/9*m**3 + 0 + 4*m.
-2*m*(m - 9)*(m + 2)/9
Let u be 288/(-7)*(1 + (-36)/(-16)). Let t = u + 134. Find n, given that 0 + 1/7*n**2 + t*n = 0.
-2, 0
Suppose -3*m = -46 - 359. Let v = m + -1213/9. Factor -v*o**2 + 2/9*o**5 - 2/3*o**4 + 0 + 0*o + 2/3*o**3.
2*o**2*(o - 1)**3/9
Let q be (-96)/8*4/3*-1. Suppose -58*s = -54*s - q. Solve -8/3*m**s + 2*m**2 - 14/3*m + 16/3*m**3 + 4/3 = 0.
-1, 1/2, 2
Let y(k) be the first derivative of 35*k**4/4 - 85*k**3/3 + 65*k**2/2 - 15*k + 131. Find r such that y(r) = 0.
3/7, 1
Let f be 325/(-10) + ((-4)/4 - -2). Let a = f - -35. Suppose a*x**4 + 27/2*x**2 + 13/2*x + 1 + 23/2*x**3 = 0. Calculate x.
-1, -2/7
Let l(z) = -z - 2. Let d be l(-1). Let f be (3 + 1)*(-1)/d. Factor 1/4*k**f - 1/4 - 1/2*k**3 + 0*k**2 + 1/2*k.
(k - 1)**3*(k + 1)/4
Let f(v) be the second derivative of v**7/525 + v**6/300 - v**5/50 - v**4/12 - 2*v**3/15 - 5*v**2 + 5*v. Let k(y) be the first derivative of f(y). Factor k(z).
2*(z - 2)*(z + 1)**3/5
Suppose -4*h = -u + 14, 5*h = -u - 16 + 3. Let y be h/(-8) - (-4428)/480. Determine t so that -3/5*t**2 - y + 24/5*t = 0.
4
Suppose -a = -4, 2*a - 24 = 2*h + 5*a. Let u be (-2 + 18/15)/(h/15). Factor -2/3*q**2 + 0*q + u.
-2*(q - 1)*(q + 1)/3
Let v = -26 - -30. Let m be -6 + 124/12 - v. What is z in -1/3 + 2/3*z - m*z**2 = 0?
1
Let z(q) be the first derivative of -q**5/10 - q**4/2 - 2*q**3/3 - 8*q - 7. Let a(l) be the first derivative of z(l). Factor a(g).
-2*g*(g + 1)*(g + 2)
Let m be (((-4416)/(-80))/(-23))/((-6)/10). Factor m*p - 8 - 1/2*p**2.
-(p - 4)**2/2
Let t(r) = -15*r**2 - 714*r + 268. Let p(j) = 4. Let w(d) = -5*p(d) - t(d). Find v such that w(v) = 0.
-48, 2/5
Let d(i) be the second derivative of i**7/2100 + 7*i**6/600 + 3*i**5/50 - 7*i**4/6 + i. Let w(u) be the third derivative of d(u). Factor w(s).
6*(s + 1)*(s + 6)/5
Let g(q) = 2*q**4 + q**3 - 2*q**2 + q. Let t(u) = -3*u**4 - 9*u**3 - 2*u**2 + 11*u + 5. Let o(c) = -g(c) + t(c). What is w in o(w) = 0?
-1, 1
Let q(n) be the third derivative of n**5/120 + 5*n**4/24 - 16*n**2 + 8. Factor q(h).
h*(h + 10)/2
Factor -4/7*f**2 + 44/7 + 40/7*f.
-4*(f - 11)*(f + 1)/7
Let k be 2 + -1 + 42/4158*33. Factor 8 + k*d**2 + 20/3*d.
4*(d + 2)*(d + 3)/3
Let v(y) be the first derivative of 2/3*y**3 - 1/6*y**6 - 2/5*y**5 + 0*y**4 + 0*y + 1/2*y**2 - 33. Factor v(r).
-r*(r - 1)*(r + 1)**3
Suppose -3*s = -4*l - 9, -2*s + 3*l + 3 = -s. Factor -4 + 0*h**2 - h + s*h - h**2 + 2*h.
-(h - 2)**2
Let z(l) = 17*l + 7. Let o be z(-3). Let n = -41 - o. Suppose 1/4*y**4 + 0 - 1/4*y**2 + 0*y + 0*y**n = 0. What is y?
-1, 0, 1
Find x such that 0 - 12/5*x**2 - 16/5*x - 2/5*x**3 = 0.
-4, -2, 0
Suppose 4*h = -12, -5*m + h + 103 + 220 = 0. Let z = -62 + m. Solve 0*r + 0 + 2/7*r**z = 0 for r.
0
Suppose 4*n = -3*f + 19, 0*n = 5*f + 4*n - 29. Suppose 2*x = h - 3*x + 25, 2*h = f*x - 25. Factor 0*b + 0*b**4 + h + 2/5*b**3 + 0*b**2 - 2/5*b**5.
-2*b**3*(b - 1)*(b + 1)/5
Let r = -515 - -291. Let m = r - -228. Factor -m*c**2 - 16/3*c + 0 + 4/3*c**3.
4*c*(c - 4)*(c + 1)/3
Suppose 0 = -h - r - 21, h = r + 2*r - 1. Let q(a) = a**2 + 17*a + 18. Let l be q(h). Suppose -1/4*n**3 + 0 + 1/4*n + 0*n**l = 0. What is n?
-1, 0, 1
Let t be 62/8 + (-3)/(-12). Suppose 0 = -0*l - 4*l + t. Determine y so that l*y**3 - 2*y**3 - 2*y**4 + y**3 + 3*y**4 = 0.
-1, 0
Let x(s) be the second derivative of -1/30*s**6 - 1/3*s**3 + 1/10*s**5 + 12*s + 1/2*s**2 + 0 + 0*s**4. Factor x(t).
-(t - 1)**3*(t + 1)
Determine u so that -55*u**2 + 483*u - 230*u - 5*u**4 - 5*u**5 - 233*u + 45*u**3 = 0.
-4, 0, 1
Let h be 3*2/45*1. Let o(g) be the first derivative of -1/3*g**2 - 2/9*g**3 + 3 + 1/6*g**4 + h*g**5 + 0*g. Find c such that o(c) = 0.
-1, 0, 1
Let q be (-64)/40*25/(-2). Suppose -2*g = 3*g - q. Determine c, given that g - 1 + 2*c**4 + 4 - 5 - 4*c**2 = 0.
-1, 1
Let l(u) be the second derivative of -1/13*u**2 + 0 + 2/39*u**3 - 1/78*u**4 - 19*u. Factor l(h).
-2*(h - 1)**2/13
Let m(f) = -2*f**3 + 4*f**2 - 3*f + 3. Let d(n) = 10*n**3 - 20*n**2 + 16*n - 16. Let r(g) = 3*d(g) + 16*m(g). Factor r(x).
-2*x**2*(x - 2)
Suppose -24*f + 4 + 68 = 0. Let d(n) be the first derivative of -4 + 3/16*n**4 + 0*n**2 - 1/2*n**f + 0*n. Solve d(o) = 0.
0, 2
Let l(q) = 8*q**3 + 13*q**2 - q - 3. Let p(f) = -f**2 + f + 1. Suppose 5 + 1 = 2*o. Let z(u) = o*p(u) + l(u). Find b, given that z(b) = 0.
-1, -1/4, 0
Let n be -54*1/(-16)*32/48. Factor -n*d**3 - 1/4*d**5 + 0 + d**2 + 0*d + 3/2*d**4.
-d**2*(d - 4)*(d - 1)**2/4
Let j(a) be the third derivative of a**8/40