4 + 14*w**2 + 2*w. Factor a(k).
5*k*(k - 3)*(k - 1)*(7*k - 2)
Let y(l) be the second derivative of -l**7/189 - 7*l**6/135 - l**5/6 - l**4/6 - 4*l - 6. Suppose y(n) = 0. Calculate n.
-3, -1, 0
Let a(w) be the first derivative of 9/5*w**5 + 0*w**2 - 15/4*w**4 + w**3 + 7 + 0*w + 9/2*w**6. Suppose a(f) = 0. What is f?
-1, 0, 1/3
Let g(c) be the third derivative of 0*c**3 + 9/8*c**6 - 1/21*c**7 + 0 - 245/24*c**4 + 0*c + 26*c**2 - 7*c**5. Find k, given that g(k) = 0.
-1/2, 0, 7
Let s(z) be the first derivative of -4*z**5 - 28*z**4 - 44*z**3 + 36*z**2 + 553. Factor s(a).
-4*a*(a + 3)**2*(5*a - 2)
Let q = 32 + -20. Solve 0*i**5 - q*i**2 + 50*i**3 + 0*i**5 - 3*i**5 - 6*i**4 - 29*i**3 = 0.
-4, 0, 1
Let u be (48/60)/(8/20). Suppose 0 - 1/10*p**u - 1/2*p = 0. Calculate p.
-5, 0
Suppose 7*b = 10 + 18. Let c be ((-1)/(-20))/(b/16). Suppose c*x**2 - 1/5 + 0*x = 0. Calculate x.
-1, 1
Let u(q) be the third derivative of 0*q**3 - 11*q**2 + 0 + 0*q - 1/360*q**5 + 1/1260*q**7 + 0*q**6 + 0*q**4. Find o such that u(o) = 0.
-1, 0, 1
Let o(x) = x**2. Let v(j) = 5*j**2 - 18*j - 5. Let g(i) = 6*o(i) - v(i). Let p(n) = -n**2 + 2*n. Let b(d) = g(d) - 4*p(d). Solve b(w) = 0.
-1
Let b(h) be the second derivative of h**5/30 - 55*h**4/36 + 61*h**3/9 + 25*h**2/2 - 544*h. Determine k so that b(k) = 0.
-1/2, 3, 25
Let m(x) be the second derivative of x**6/120 + 3*x**5/80 + x**4/24 + 13*x. Factor m(g).
g**2*(g + 1)*(g + 2)/4
Let s = -28 - -5. Let p = 71/3 + s. Factor -p*n**4 + 2/3*n**2 + 0 + 2/3*n**3 - 2/3*n.
-2*n*(n - 1)**2*(n + 1)/3
Find o, given that 0*o + 0 - 2/5*o**3 - 3/5*o**2 + 1/5*o**4 = 0.
-1, 0, 3
Let a(u) be the second derivative of u**6/60 - u**5/4 - 23*u**4/24 - u**3 - u + 307. Solve a(d) = 0.
-1, 0, 12
Let t(d) = -5*d**2 + 4*d - 3. Let c = 51 - 45. Let x(h) = 4*h**2 - 3*h + 3. Let k(l) = c*x(l) + 5*t(l). Factor k(j).
-(j - 3)*(j + 1)
Let j(n) be the second derivative of -7*n**6/75 - 4*n**5/5 - 17*n**4/10 + 6*n**3/5 - 22*n. Factor j(x).
-2*x*(x + 3)**2*(7*x - 2)/5
Let q be 24/35 + -1*18/45. Factor q*h**4 + 4*h**3 + 122/7*h**2 + 72/7 + 24*h.
2*(h + 1)**2*(h + 6)**2/7
Let r(y) = -15*y + 3. Let a be r(0). Let f be (-18)/(-81)*a/2. Determine o, given that 0 - f*o + o**2 = 0.
0, 1/3
Let s(y) = 5*y - 13. Let j be s(3). Suppose 7*c + j - 2*c**3 - 10*c + 5*c - 2*c**2 = 0. Calculate c.
-1, 1
Suppose x - 40 = -16. Suppose -n + 5 = 5*h - 6*n, 4*h = -n + x. Solve -8*c**2 + h - 5 + 7*c**2 = 0 for c.
0
Let c be (-39)/(-15) - (-5)/((-100)/(-8)). Let q(h) be the first derivative of -1 + 3/16*h**4 + 9/4*h**c + 81/8*h**2 + 81/4*h. Factor q(s).
3*(s + 3)**3/4
Let n = -212 + 383. Let c = n - 169. Factor 1/3*p - 2/3*p**c + 1/3*p**3 + 0.
p*(p - 1)**2/3
Let r(x) be the first derivative of -1/30*x**6 + 0*x - 1/6*x**4 + 1 + 0*x**3 + 3*x**2 - 2/15*x**5. Let a(n) be the second derivative of r(n). Factor a(b).
-4*b*(b + 1)**2
Let d(v) = v**2 + 6*v - 4. Let i be d(-7). Suppose -i*c + 6 = -0*c. Solve 9*w**2 - 4*w**3 - w**c + 4*w**2 - 8*w = 0 for w.
0, 1, 2
Let x(p) be the first derivative of -p**4/2 + 13*p**2 - 24*p + 787. Suppose x(u) = 0. Calculate u.
-4, 1, 3
Let m = 2022 - 2022. Factor 3*t + 3/2*t**4 + m + 0*t**3 - 9/2*t**2.
3*t*(t - 1)**2*(t + 2)/2
Suppose 1729*i**2 + 4*i**4 + 128000*i + 640000 + 320*i**3 + 1790*i**2 + 6081*i**2 = 0. What is i?
-20
Let q = 207 - 205. Find z such that -2/9*z**q - 2/3*z + 0 = 0.
-3, 0
Let t be (32/(-56) - 2/(-28))*-4. Let a(h) be the second derivative of 0*h**t + h**3 + 1/4*h**4 + 11*h + 0. Find g, given that a(g) = 0.
-2, 0
Find j such that 126*j**2 - 446*j**2 + 127*j + 40*j + 105*j**3 + 50 + 13*j + 30 = 0.
-2/7, 4/3, 2
Let d = -6/137 + 292/411. Let p(b) be the first derivative of 0*b**2 - 5 + d*b**3 - 1/2*b**4 + 0*b. Factor p(n).
-2*n**2*(n - 1)
Let j = -2484 + 27328/11. Factor 0 - 2/11*k**2 + j*k.
-2*k*(k - 2)/11
Let 3/8*t**2 + 3/4*t**3 + 0 + 3/8*t**4 + 0*t = 0. What is t?
-1, 0
Let p(s) = -2*s**3 - 3*s**2 - 3*s - 4. Let b be p(-2). Let h be (3 - 33/b)*-2. Determine m, given that -4*m**2 - 2*m + h*m**2 + 4*m + 0*m = 0.
-2, 0
Let m(f) be the second derivative of -3*f**4/4 - 133*f**3 - 264*f**2 + 26*f + 2. Factor m(b).
-3*(b + 88)*(3*b + 2)
Suppose 3 - 16 = -l. Suppose -m = l*m - m. Factor -1/2*q**2 - 25/8*q**4 + m + 0*q - 5/2*q**3.
-q**2*(5*q + 2)**2/8
Let z(y) be the first derivative of -4/3*y**3 - 4/3*y - 2*y**2 - 25 - 1/3*y**4. Factor z(v).
-4*(v + 1)**3/3
Let i(x) be the third derivative of -x**7/630 - x**6/60 - 2*x**5/45 - 132*x**2. Let i(c) = 0. What is c?
-4, -2, 0
Let f(y) be the third derivative of y**6/300 - y**5/15 - 53*y**2. Solve f(n) = 0 for n.
0, 10
Let q = -7362 - -7365. Factor 35/2*z**q - 45/2*z**2 + 5*z + 0.
5*z*(z - 1)*(7*z - 2)/2
Let m(h) = -h**3 + 4*h + 2. Let c be m(-2). Suppose z = -c*z + 15. Let 2*x**5 - 9*x**5 + x**5 + z*x**5 + x**3 = 0. What is x?
-1, 0, 1
Let t(b) be the first derivative of 20/3*b**3 - 10*b + 16 + 15/4*b**4 - 25/2*b**2. Solve t(a) = 0 for a.
-2, -1/3, 1
Find y, given that 1/6*y**2 + 243/2 - 9*y = 0.
27
Let t = -7/4107 + 1490890/28749. Factor 66/7*a - 3/7*a**2 - t.
-3*(a - 11)**2/7
Let a(o) be the third derivative of o**5/30 - o**4/12 - 2*o**3/3 - o**2 + 51. Factor a(v).
2*(v - 2)*(v + 1)
Let r(s) be the first derivative of 2*s - 1/3*s**3 + 1/2*s**2 + 7. Solve r(b) = 0 for b.
-1, 2
Let v(o) = 5*o**4 - 33*o**3 + 25*o**2 - 3*o - 3. Let c(i) = 35*i**4 - 230*i**3 + 175*i**2 - 20*i - 20. Let l(b) = 3*c(b) - 20*v(b). Solve l(p) = 0.
0, 1, 5
Suppose 2*z = -6*z + 16. Solve -3*r + r**3 + 16 + 30*r**2 + 3*r**3 - 10*r**z + 35*r = 0.
-2, -1
Let i(d) be the third derivative of 0*d + 0 + 2*d**3 - 1/60*d**6 + 4/15*d**5 - 50*d**2 - 13/12*d**4. Factor i(w).
-2*(w - 6)*(w - 1)**2
Let m(c) = c + 5 - 53*c**2 - 2*c + 55*c**2. Let g(u) = u**2 + 2. Let o(d) = -5*g(d) + 2*m(d). Solve o(h) = 0.
-2, 0
Suppose -2*c + 5*x = -26, -2*c - 5*x - 72 = -6*c. Suppose -y + 5*z - c = 0, -y + 4*z = 15 + 3. Factor -1/4*p**3 - 3/4*p**y - 3/4*p - 1/4.
-(p + 1)**3/4
Let i = 36485/798 + -631/14. Let g = i + -6/19. Suppose 2/3 - t**2 - g*t + 1/3*t**4 + 1/3*t**3 = 0. Calculate t.
-2, -1, 1
Let v(y) = -13*y**2 - 135*y + 223. Let l(h) = -6*h**2 - 66*h + 112. Let j(p) = -9*l(p) + 4*v(p). Factor j(u).
2*(u - 2)*(u + 29)
Let r(n) be the first derivative of -n**7/840 + n**6/270 + n**5/360 - n**4/36 - n**3 + 11. Let f(g) be the third derivative of r(g). Factor f(x).
-(x - 1)**2*(3*x + 2)/3
Let d(n) be the first derivative of n**6/420 + n**5/70 + n**4/42 + 6*n**2 - 7. Let l(x) be the second derivative of d(x). Suppose l(s) = 0. What is s?
-2, -1, 0
Let -10*t**3 + 2*t**2 - t**4 - t + 11*t - t**4 = 0. Calculate t.
-5, -1, 0, 1
What is j in 29*j + j**2 + 53*j**2 + 8*j**3 + j - 12 + 4*j = 0?
-6, -1, 1/4
Let f = 10 - 10. Suppose -w + f = -6. Factor -12 - w - 9 - 18*p - 3*p**2.
-3*(p + 3)**2
Let f(y) be the first derivative of -y**5/15 + y**4/3 - 4*y**3/9 - 7*y - 10. Let a(v) be the first derivative of f(v). Factor a(l).
-4*l*(l - 2)*(l - 1)/3
Let x(j) be the third derivative of j**6/108 + 4*j**5/135 - 56*j**2. Let x(w) = 0. Calculate w.
-8/5, 0
Let n be (-2)/(-72) - (144/972)/((-4)/6). Suppose -n*g**2 - 25 - 5*g = 0. What is g?
-10
Let n(j) be the first derivative of -j**6/90 + j**5/30 - j + 4. Let x(m) be the first derivative of n(m). Factor x(h).
-h**3*(h - 2)/3
Factor -1/4*u**2 + 55/4*u + 14.
-(u - 56)*(u + 1)/4
Let n(p) = 13*p**2 - 220*p - 15. Let z be n(17). Determine b so that 12/7 + 0*b - 3/7*b**z = 0.
-2, 2
Suppose 5*v - 15 = -0*v. Let i(q) be the first derivative of v*q - q**3 - 2*q**2 + 1 - 2*q**2 + 4*q**2. Let i(r) = 0. Calculate r.
-1, 1
Suppose 24 = 3*r - 7*r. Let q be (0 + -1)*(r - -4). Find h such that 3*h**3 - h**5 - 6*h**3 + 3*h**4 + 0*h**3 + 0*h**5 + h**q = 0.
0, 1
Let p(t) be the first derivative of -4 - 32*t**2 + 8*t**3 + 1/20*t**5 + 6*t - t**4. Let f(o) be the first derivative of p(o). Let f(n) = 0. What is n?
4
Let w(q) = 3*q - 1. Let f be w(1). Factor -o**3 - 3*o**3 - 12*o**f - 2*o - 6*o + 12*o**3.
4*o*(o - 2)*(2*o + 1)
Let b(p) be the first derivative of p**4/4 - 5*p**3/3 + p**2 - 8*p - 14. Let x be b(5). What is i in 0*i**x - 3/4*i + 0 + 3/4*i**3 = 0?
-1, 0, 1
Let y(q) = -q**3 - 2*q**2 + 8*q + 3. Let g be y(-4). Factor n**5 + n**g + 7*n + 10*n**2 - 8*n - 2*n**5 + n**3 - 5*n**4 - 5.
-(n - 1)**2*(n + 1)**2*(n + 5)
Suppose 3*s = 35*s. Let c(r) b