*q = 0 for q.
-1, 2/9, 1
Factor 2/11*l**2 + 30/11 - 32/11*l.
2*(l - 15)*(l - 1)/11
Suppose 4*x = -5*d + 37, 3*d = -x - 2*d + 28. Suppose -11 + 2*i**x + 11 = 0. What is i?
0
Let d(w) = -w**4 + 105*w**3 - 2*w**2 + 6*w. Let k(i) = -4*i**4 + 315*i**3 - 7*i**2 + 21*i. Let v(y) = -21*d(y) + 6*k(y). Factor v(u).
-3*u**3*(u + 105)
Let v(p) be the first derivative of p**7/420 - p**6/180 - p**5/15 + p**4/3 - 25*p**3/3 + 33. Let c(s) be the third derivative of v(s). Factor c(w).
2*(w - 2)*(w - 1)*(w + 2)
Let y(j) = 62*j - 7. Let t be y(1). Let x be t/(-66)*8/(-10). Factor 14/3*u**4 + 32/3*u + x*u**5 + 38/3*u**3 + 8/3 + 50/3*u**2.
2*(u + 1)**3*(u + 2)**2/3
Determine k, given that 0*k + 0 - 2/11*k**5 + 128/11*k**2 - 160/11*k**3 + 34/11*k**4 = 0.
0, 1, 8
Suppose -2 - 6 = -2*h. Factor 11*b - 2*b + 3*b**2 + 0*b**4 - 8*b**4 + 5*b**h - 9*b**3.
-3*b*(b - 1)*(b + 1)*(b + 3)
Suppose i + 28 = 8*i. Suppose -i*r - 10 = -9*r. Solve 1/3 - 1/6*c**r - 1/6*c = 0 for c.
-2, 1
Let f(v) be the third derivative of 1/30*v**5 + 1/90*v**7 + 0*v - 7/18*v**4 + 0 - 4/9*v**3 + 23/360*v**6 + 24*v**2. Find y, given that f(y) = 0.
-2, -2/7, 1
Let g(d) be the first derivative of -d**4/2 + 6*d**3 - 8*d**2 + 73. Factor g(t).
-2*t*(t - 8)*(t - 1)
Suppose 3*w = -3*w + 13524. Factor 4*z**3 + z**4 - 2251*z**2 + w*z**2 + 0*z**3.
z**2*(z + 1)*(z + 3)
Let h = -1120/9 - -12338/99. Factor -20/11*a**3 + h - 2/11*a**5 + 10/11*a**4 + 20/11*a**2 - 10/11*a.
-2*(a - 1)**5/11
Suppose 4*p = 2*k + 24, 16*k - 13*k - 4*p = -24. Let k - 1/5*j**5 + 0*j + 0*j**2 + 0*j**3 + 1/5*j**4 = 0. What is j?
0, 1
Suppose -2*g = -4*q - 8, -g + 0*g + 3*q + 5 = 0. Let s = 0 + g. Factor -2*d**s - 6*d - 5 - 12 + 17.
-2*d*(d + 3)
Let b(j) = j + 12. Suppose 2*a = -10 - 10. Let w be b(a). Determine x so that 13*x**3 - 16*x**2 - 36*x**w + 24 - 60*x - 34*x**3 - 26*x**2 = 0.
-2, 2/7
Let l(s) = 5*s**5 + 35*s**4 + 20*s**3 - 30*s**2 - 35*s - 5. Let z(p) = 5*p**5 + 35*p**4 + 19*p**3 - 29*p**2 - 36*p - 6. Let r(m) = 6*l(m) - 5*z(m). Factor r(c).
5*c*(c - 1)*(c + 1)**2*(c + 6)
Let z(b) be the first derivative of -b**6/36 + 67*b**5/30 - 65*b**4/8 + 193*b**3/18 - 16*b**2/3 + 375. Let z(h) = 0. Calculate h.
0, 1, 64
Factor 0*u**2 + 0*u - 86/25*u**5 + 0 - 176/25*u**4 - 8/25*u**3.
-2*u**3*(u + 2)*(43*u + 2)/25
Let u(c) be the first derivative of c**4/4 + 4*c**3/3 + 41. Suppose u(m) = 0. Calculate m.
-4, 0
Let a(f) be the third derivative of -f**5/15 + f**4 + f**3/3 - 34*f**2. Let z(g) = -21*g**2 + 120*g + 11. Let t(m) = 11*a(m) - 2*z(m). What is x in t(x) = 0?
0, 12
Suppose -24 = 5*h + 6. Let n(t) = t**2 - 5*t. Let k(x) = 2*x**2 - 9*x. Let l(q) = h*k(q) + 10*n(q). Determine v, given that l(v) = 0.
0, 2
Let i(o) be the first derivative of 0*o**2 + 1/12*o**4 - 8/3*o**3 + 4 + 1/540*o**6 - 1/45*o**5 + 0*o. Let m(q) be the third derivative of i(q). Solve m(u) = 0.
1, 3
Let r(y) = -y**4 + y**3 + y**2 + y + 2. Let m(o) = 8*o**4 + 2*o**3 + 6*o**2 + 2*o - 10. Let s(l) = 2*m(l) + 12*r(l). Factor s(q).
4*(q + 1)**4
Let y(x) be the second derivative of x**6/90 + x**5/10 + x**4/3 + 23*x**3/6 - 29*x. Let i(z) be the second derivative of y(z). Suppose i(a) = 0. Calculate a.
-2, -1
Let q(p) be the third derivative of 0 + 17*p**2 - 1/360*p**6 + 0*p + 1/72*p**4 + 0*p**3 + 1/630*p**7 - 1/180*p**5. Let q(d) = 0. What is d?
-1, 0, 1
Factor 0 - 5/9*b**3 + 5/9*b - 4/9*b**2 + 4/9*b**4.
b*(b - 1)*(b + 1)*(4*b - 5)/9
Let b(d) = d**2 + d - 2. Let g(a) = -4*a**2 - 6*a + 4. Let i(v) = -6*b(v) - g(v). Determine t so that i(t) = 0.
-2, 2
Factor 0*c - 32/7*c**3 + 0 + 12/7*c**4 - 12/7*c**2.
4*c**2*(c - 3)*(3*c + 1)/7
Suppose -114 + 74 = -4*h. Solve 8 + 47*t - 242*t**3 + 154*t**2 + h*t + 23*t = 0 for t.
-2/11, 1
Let d(j) be the third derivative of 0*j**4 + j**2 + 1/35*j**7 - 1/16*j**6 + 0 + 0*j + 0*j**3 + 1/20*j**5 - 1/224*j**8. Let d(t) = 0. Calculate t.
0, 1, 2
Let r be 1*-2*(210/45)/(4/(-4)). Factor 73/6*j**2 - r*j - 1/6*j**5 - 43/6*j**3 + 11/6*j**4 + 8/3.
-(j - 4)**2*(j - 1)**3/6
Solve q**4 + 1/4*q**2 + 0 + 3/8*q**5 + 0*q + 7/8*q**3 = 0 for q.
-1, -2/3, 0
Let d(n) = -n**2 - 19*n - 18. Suppose -4*l - 23 = 49. Let m be d(l). Factor m + 1/2*t**2 + 1/2*t**3 + 0*t.
t**2*(t + 1)/2
Let z(u) be the third derivative of -u**8/840 + u**7/105 + u**6/300 - u**5/30 + 3*u**2 + 8. Suppose z(o) = 0. What is o?
-1, 0, 1, 5
Let y(j) be the third derivative of j**7/84 - 7*j**6/48 + j**5/4 + 293*j**2. Find f such that y(f) = 0.
0, 1, 6
Suppose -5 = -a - 3*c, c + 1 = -a + 6. Factor -32*q**5 + 60*q**a - 32*q**5 - 4*q**4.
-4*q**4*(q + 1)
Let m(o) be the second derivative of -o**8/210 + o**7/42 - o**6/30 - o**5/30 + o**4/6 + 7*o**3/6 - 3*o. Let c(a) be the second derivative of m(a). Factor c(y).
-4*(y - 1)**3*(2*y + 1)
Suppose -280/3*l + 1225/3*l**2 + 16/3 = 0. What is l?
4/35
Let x(m) = -m**4 - m**3 + m**2 + m + 1. Let n(o) = 25*o**4 + 85*o**3 - 220*o**2 + 140*o - 35. Let r(s) = n(s) + 5*x(s). Factor r(h).
5*(h - 1)*(h + 6)*(2*h - 1)**2
Let v = 92 - 86. Suppose i - 4*x = 18, x = -i - x - v. Solve -3/4*j**3 + 0*j + 0*j**4 + 3/4*j**5 + 0 + 0*j**i = 0 for j.
-1, 0, 1
Let s = -9 - -11. Let g be (-8)/12*(-45)/s. Factor 0*d + 6 - 6*d**3 - g*d**2 - 7*d + 4*d.
-3*(d + 1)*(d + 2)*(2*d - 1)
Let n(h) = -6*h**2 - 55*h - 64. Let c(z) = z**2 - z + 1. Let m(v) = -5*c(v) - n(v). Let m(k) = 0. What is k?
-59, -1
Let a(g) = 239*g**2 + 85*g + 5. Let t(r) = -27 - 1435*r**2 + 75*r - 586*r + 6 - 10. Let h(o) = 34*a(o) + 6*t(o). Factor h(k).
-4*(11*k + 2)**2
Let s(a) be the second derivative of 0*a**2 + 3/100*a**5 + 3/20*a**4 - 10*a + 1/5*a**3 + 0. Factor s(h).
3*h*(h + 1)*(h + 2)/5
Suppose 0 = -2*y + 34 - 2. Find a, given that -y*a + 19 + 4*a - 8*a + 5*a**2 - 4 = 0.
1, 3
Let x = 1912 - 5716/3. Factor -x*f**2 - 10*f**4 - 8/3*f**5 + 2/3 - 40/3*f**3 + 0*f.
-2*(f + 1)**4*(4*f - 1)/3
Let o(m) = m**3 + m + 3. Let s be o(0). Find q, given that 0 - 1/3*q + 1/3*q**s + 0*q**2 = 0.
-1, 0, 1
Let j(r) be the first derivative of -r**5/45 - r**4/9 - 2*r**3/9 - 20*r**2 - 12. Let t(n) be the second derivative of j(n). Determine q so that t(q) = 0.
-1
Let u be (-47 - -32)*((-99)/30 + 3). Determine c, given that u*c**4 + 1/2 - 6*c**3 - c**2 + 2*c = 0.
-1/3, 1
Let d(f) = f**3 + 5*f**2 - 2*f + 2. Let o = 0 + 10. Let h(u) = 3*u**3 + 11*u**2 - 4*u + 5. Let j(l) = o*d(l) - 4*h(l). Factor j(r).
-2*r*(r - 2)*(r - 1)
Let u(d) be the first derivative of d**4/16 - 9*d**3/4 - 7*d**2/2 - 475. Solve u(o) = 0.
-1, 0, 28
Let c(d) = d + 2. Let r be c(0). Let i be (-57)/(-12) + 2 + (-3)/(-12). Determine x so that x**r - 2*x - 4*x**2 + i*x + 4*x = 0.
0, 3
Let n(g) be the first derivative of -g**6/36 - 3*g**5/5 - 97*g**4/24 - 8*g**3 - 16*g**2/3 + 669. Factor n(i).
-i*(i + 1)**2*(i + 8)**2/6
Let d be (66/(-18) + 4)/((-1)/(-6)). Suppose -d*t = 4*t. Factor 0 + t*i + 4/3*i**2 - 2*i**3 + 2/3*i**5 + 0*i**4.
2*i**2*(i - 1)**2*(i + 2)/3
Let h(r) = -r + 6. Let g be h(5). Suppose -3 = -2*z + g, -w + 6 = 3*z. Let -m**2 - m + 5 - 3 + 0*m + w = 0. What is m?
-2, 1
Let n be (-613)/(-2) - 2/(8/(-6)). Factor -13 + n*o**2 - 32*o + 8 - 11.
4*(7*o - 2)*(11*o + 2)
Let f(x) be the first derivative of x**5/10 - 2*x**4/5 + 13*x**3/30 - x**2/10 - 179. Factor f(w).
w*(w - 2)*(w - 1)*(5*w - 1)/10
Factor -51/7*x**3 + 624/7*x**2 + 1/7*x**4 + 676/7*x + 0.
x*(x - 26)**2*(x + 1)/7
Let u = 708 - 706. Factor 5/3*t**5 + 0*t**u + 5*t**3 + 0 - 20/3*t**4 + 0*t.
5*t**3*(t - 3)*(t - 1)/3
Let j(f) be the first derivative of f**4/96 - 3*f - 7. Let g(b) be the first derivative of j(b). Factor g(p).
p**2/8
Let f be (8/42)/((-330)/(-1155)). Let 0*w**4 + 1/3*w**5 + 0*w + 0 - w**3 + f*w**2 = 0. What is w?
-2, 0, 1
Let d(g) be the third derivative of g**7/420 + g**6/30 - g**5/4 - 25*g**4/3 - 875*g**3/12 - 7*g**2 - 5*g. Solve d(j) = 0.
-5, 7
Let l(n) be the third derivative of -n**8/56 - 43*n**7/210 - 59*n**6/120 - 11*n**5/30 - 155*n**2 - n. Suppose l(h) = 0. Calculate h.
-11/2, -1, -2/3, 0
Let r = 1854 + -1852. Determine u, given that -4/7*u**4 + 4/7 + 16/7*u**2 + 2/7*u**5 - 4/7*u**3 - r*u = 0.
-2, 1
Let l be (16929/4158 - (-7)/(-2)) + 80/154. Factor 0 + 0*r**2 + l*r**4 + 0*r - 18/11*r**3 - 2/11*r**5.
-2*r**3*(r - 3)**2/11
Let o(x) = x + 4. Let s be o(-2). Factor 110*p**s - 110*p**2 - 2*p**3.
-2*p**3
Let z be 28/35*10/4. Factor 2*y + 8*y + 4*y**2 - 6*y**z.
-2*y*(y - 5)
Let r(q) = -q**3 + 10*q**2 