. Let s be x(20). Let d(q) be the first derivative of -1/24*q**4 + 0*q**s + 1/30*q**5 - 2 + 0*q + 0*q**3. Factor d(g).
g**3*(g - 1)/6
Let w = 11 + -6. Suppose -21 + w = -4*a. Factor -o**3 - 2*o - o**3 + a*o**3.
2*o*(o - 1)*(o + 1)
Let s(o) be the first derivative of -3*o**4/28 - 4*o**3 + 177*o**2/14 - 90*o/7 + 40. Suppose s(g) = 0. What is g?
-30, 1
Let j = 5 - 2. Suppose -6*b = -j*b - 30. Let v(m) = 6*m**3 + 3*m**2 + 6*m. Let a(p) = -p**3 - p**2 - p. Let r(d) = b*a(d) + 2*v(d). Find s such that r(s) = 0.
0, 1
Let s(u) = -u**4 - u**3 - u. Let c(j) = -j**5 - j**4 + 16*j**3 + 4*j**2 - 9*j. Let g(f) = c(f) + 3*s(f). Find d, given that g(d) = 0.
-6, -1, 0, 1, 2
Let j(a) = -120*a**4 + 1000*a**3 - 3530*a**2 + 900*a + 6005. Let v(t) = 11*t**4 - 91*t**3 + 321*t**2 - 81*t - 546. Let x(n) = 6*j(n) + 65*v(n). Solve x(y) = 0.
-1, 3, 12
Let l(h) = -150*h - 7. Let m be l(-1). Let x = -140 + m. Factor 0*i + 0 + 4/3*i**2 - 2/3*i**x.
-2*i**2*(i - 2)/3
Let h(k) = -k + 8*k**2 + 4*k**3 - 7*k**2 - 3*k**3. Let z(y) = 3*y**3 + 20*y**2 - 18*y + 2. Let t(a) = 21*h(a) - 3*z(a). Determine b so that t(b) = 0.
1/4, 1, 2
Let v(u) be the second derivative of -10*u + 7/30*u**3 + 1/20*u**4 + 0 + 1/5*u**2. Factor v(f).
(f + 2)*(3*f + 1)/5
Factor -6*p - 2/3*p**2 + 0.
-2*p*(p + 9)/3
Let w(q) be the third derivative of -q**7/105 + q**6/6 + 37*q**5/30 + 13*q**4/6 - 199*q**2. Factor w(r).
-2*r*(r - 13)*(r + 1)*(r + 2)
What is k in 15*k**2 + 21*k**3 + 0*k**2 + 9*k**4 - 48*k**3 + 3*k**5 = 0?
-5, 0, 1
Let n = 19 - 35. Let t = 19 + n. Factor 3*k**5 - t*k**4 + 7*k**2 - k**2 + 209 + 3*k - 6*k**3 - 212.
3*(k - 1)**3*(k + 1)**2
Let j be (-2)/(1/(-16)*2). Factor -j*a**4 + 54*a**2 + 12*a**3 - 46*a**2 - 16*a**5 - 3 - 4*a + 3.
-4*a*(a + 1)**2*(2*a - 1)**2
Let i(z) = 5*z**4 - 7*z**2 - 3*z - 1. Let y(b) = 10*b**2 + 3*b - 14*b - 37*b**2 - 3 + 19*b**4. Let c(r) = 22*i(r) - 6*y(r). Factor c(f).
-4*(f - 1)**2*(f + 1)**2
Let f(p) be the first derivative of 3*p**3/2 - 39*p**2/4 + 127. Factor f(o).
3*o*(3*o - 13)/2
Let c(u) be the first derivative of u**5/20 + u**4/4 - u**3/12 - 2*u**2 - 3*u - 325. Suppose c(o) = 0. What is o?
-3, -2, -1, 2
Let f(p) be the second derivative of p**5/30 + 7*p**4/18 + 5*p**3/3 + 3*p**2 - 75*p. Factor f(r).
2*(r + 1)*(r + 3)**2/3
Let r(c) = c**2 - 13*c + 20. Let f(d) = 6*d**2 - 90*d + 138. Let u = 20 - -7. Let i(k) = u*r(k) - 4*f(k). Factor i(b).
3*(b - 1)*(b + 4)
Let j(p) be the first derivative of -3*p - 1/2*p**3 - 9/4*p**2 - 28. Factor j(c).
-3*(c + 1)*(c + 2)/2
Suppose 0 = r + 5*v + 15, 0 = 4*v + 9 + 3. Suppose -13*p + 15*p = r. What is y in 28*y**3 - 32*y**3 + 8*y + 4*y**2 + 0*y + p*y = 0?
-1, 0, 2
Let y = 6075/4 + -1518. Factor -15/4*r + 3 + y*r**2.
3*(r - 4)*(r - 1)/4
Let q(k) be the first derivative of k**4/12 - 10*k**3/9 - k**2/6 + 10*k/3 - 133. Factor q(l).
(l - 10)*(l - 1)*(l + 1)/3
Let k(w) be the second derivative of 0*w**4 + 0*w**2 - 10*w + 3/100*w**5 + 0*w**3 + 1/150*w**6 + 0. Suppose k(i) = 0. Calculate i.
-3, 0
Let h(l) be the second derivative of -l**5/40 - l**4/48 + l**3/24 - l + 71. Factor h(p).
-p*(p + 1)*(2*p - 1)/4
Let o(v) be the third derivative of -1/280*v**7 + 1/40*v**5 - 9*v**2 + 1/80*v**6 + 0 + 0*v - 1/8*v**3 - 1/32*v**4 - 1/448*v**8. Find k, given that o(k) = 0.
-1, 1
Factor -4/9*a**2 - 8/3*a - 32/9.
-4*(a + 2)*(a + 4)/9
Let w(x) be the first derivative of -1/3*x**4 + x + 2/3*x**3 + 0*x**2 - 8. Let g(j) be the first derivative of w(j). Factor g(s).
-4*s*(s - 1)
Let d(x) be the first derivative of 24*x + 3/2*x**2 - 3/4*x**4 - 8*x**3 + 53. Factor d(l).
-3*(l - 1)*(l + 1)*(l + 8)
Factor 5/3 + 11/2*k + 8/3*k**3 + 0*k**4 + 19/3*k**2 - 1/6*k**5.
-(k - 5)*(k + 1)**3*(k + 2)/6
Let k be 1/((48/(-36))/(-4)). Solve -4/13*c - 2/13*c**5 - 18/13*c**k + 0 - 14/13*c**2 - 10/13*c**4 = 0 for c.
-2, -1, 0
Let y be -8*(-4 - (-21)/6). Solve 2894*b**2 + 1276*b**3 - 446*b**2 - 224*b + 976*b - 484*b**y + 64 = 0.
-1, -2/11, 4
Let z(n) be the second derivative of -22*n + 0 - 1/15*n**3 + 1/90*n**4 + 2/15*n**2. Suppose z(k) = 0. Calculate k.
1, 2
Solve -24/5 + 0*j**4 + 1/5*j**5 - 68/5*j - 66/5*j**2 - 23/5*j**3 = 0 for j.
-2, -1, 6
Let f be 1 + (-1 - (-2)/9). Let s = 4649/4 - 41809/36. Factor -f*o**2 + s*o - 2/3.
-2*(o - 3)*(o - 1)/9
Let p(d) = -d**2 + 1. Let a(v) = 2*v**2 - 8*v - 10. Let f be (18/54)/(1/(-9)). Let k(t) = f*p(t) - a(t). Factor k(b).
(b + 1)*(b + 7)
Let y(v) = 3*v**2 + 5*v + 2. Let g be 3*-1 - 9/((-36)/(-8)). Let d(h) = -15*h**2 - 24*h - 9. Let c(o) = g*d(o) - 24*y(o). Find m, given that c(m) = 0.
-1, 1
Let l = -11 - -17. Factor -11*g - 6 + 14*g - 4*g**2 - l + 13*g.
-4*(g - 3)*(g - 1)
Let x(b) be the first derivative of 6/5*b**5 + 0*b**3 - 1/2*b**6 + 0*b - 6 + 0*b**2 + 0*b**4. Factor x(a).
-3*a**4*(a - 2)
Find q, given that -16/3*q**3 + 384/5 + 2/3*q**4 + 2/15*q**5 + 64*q - 56/3*q**2 = 0.
-6, -1, 4
Let t(h) be the first derivative of h**6/2 + 12*h**5/5 + 3*h**4 - 2*h**3 - 15*h**2/2 - 6*h - 105. Factor t(x).
3*(x - 1)*(x + 1)**3*(x + 2)
Let p be ((-144)/(-864))/((-2)/(-2)). Factor 5/6*l + 1/3*l**4 + p + 3/2*l**2 + 7/6*l**3.
(l + 1)**3*(2*l + 1)/6
Let x be 0/(-1 + -3 - 1). Solve -2*z + 38 + x*z**2 + z**2 - 38 = 0.
0, 2
Let r(n) = n**3 - 10*n**2 - 25*n + 37. Let l(j) = -2*j**3 - j**2 + j - 1. Let i(z) = -5*l(z) - 5*r(z). What is x in i(x) = 0?
-6, 1
Let r(b) be the second derivative of 5*b**4/12 + 15*b**3 + 85*b**2/2 - 72*b. Determine q so that r(q) = 0.
-17, -1
Let x(q) be the third derivative of -q**6/80 - 3*q**5/5 - 21*q**4/4 - 20*q**3 - 108*q**2. Factor x(u).
-3*(u + 2)**2*(u + 20)/2
Let a(o) be the first derivative of 6/5*o**5 + 2*o**4 + 4 - 4/3*o**3 - 4*o**2 - 2*o. Suppose a(b) = 0. Calculate b.
-1, -1/3, 1
Let k be (-10)/45 - 102/27. Let d = k - -14. Solve -d*l**4 + 11*l**4 + 0*l**3 - l**3 - l**5 - l**2 + 2*l**5 = 0.
-1, 0, 1
Let j(h) = -h**3 + 11*h**2 + 41*h + 5. Let u(x) = -6*x**2 - 21*x - 3. Let g(v) = -3*j(v) - 5*u(v). Factor g(c).
3*c*(c - 3)*(c + 2)
Let z(f) be the second derivative of 0*f**2 - 7/24*f**4 + 1/120*f**6 + 0*f**3 + 0 - 13/80*f**5 + 59*f. Factor z(g).
g**2*(g - 14)*(g + 1)/4
Let h = 18/281 + 436/1967. Find z, given that 0 + 18/7*z - 12/7*z**2 + h*z**3 = 0.
0, 3
Let h(t) be the third derivative of -t**6/120 + 97*t**5/20 - 9409*t**4/8 + 912673*t**3/6 + 7*t**2 - 27. Find j such that h(j) = 0.
97
Let m(x) be the second derivative of -x**4/6 + x**3 - x**2 - 8*x. Let g(z) = -z. Let k(b) = -2*g(b) - m(b). Suppose k(d) = 0. What is d?
1
Let t(a) = -2*a**4 - a**3 + a**2 - 1. Let b(l) = 20*l**4 - 54*l**3 - 617*l**2 + 317*l - 38. Let f(u) = -b(u) - 2*t(u). Factor f(z).
-(z - 8)*(z + 5)*(4*z - 1)**2
Let v be (-27307)/73320 - 3/(-8). Let s(q) be the third derivative of 3*q**2 - v*q**5 + 1/26*q**4 + 0*q - 3/13*q**3 + 0. Suppose s(k) = 0. What is k?
3
Let n(v) be the second derivative of v**7/1620 - 19*v**6/3240 - v**5/90 - 2*v**4/3 - 31*v. Let y(p) be the third derivative of n(p). Factor y(w).
2*(w - 3)*(7*w + 2)/9
Let t be (-1)/12 - ((-7)/(-168))/((-5)/70). Factor t - 1/4*y**3 + 5/4*y - 1/4*y**4 + 3/4*y**2.
-(y - 2)*(y + 1)**3/4
Let m(g) = 2*g**2 - 96*g - 213. Let c(w) = -w**2 + 93*w + 214. Let r(a) = -7*c(a) - 6*m(a). Factor r(i).
-5*(i + 4)*(i + 11)
Let n = -598 - -601. Let v(p) be the second derivative of 3*p - 1/30*p**n + 0*p**2 + 0 - 9/100*p**5 - 1/10*p**4 - 2/75*p**6. Find w, given that v(w) = 0.
-1, -1/4, 0
Let f(h) = 2*h**2 - 58*h + 156. Let n be f(26). Solve -15/8*t**4 - 3*t**3 + 3/4*t + n - 3/8*t**2 = 0 for t.
-1, 0, 2/5
Let s = 11344/17019 + 2/17019. Factor -u - 1/3*u**5 + 2/3*u**2 - s + 0*u**4 + 4/3*u**3.
-(u - 2)*(u - 1)*(u + 1)**3/3
Let s = -9557 - -9564. Factor -1 + 51/4*b**2 - s*b.
(3*b - 2)*(17*b + 2)/4
Let t(p) be the second derivative of -p**4/15 + 16*p**3/15 - 32*p**2/5 - 6*p + 1. Find j, given that t(j) = 0.
4
Let y(f) = f**5 + 10*f**4 + 12*f**3 - 2*f**2 - 5*f. Let u(j) = 6*j**5 + 51*j**4 + 60*j**3 - 9*j**2 - 24*j. Let r(w) = -4*u(w) + 21*y(w). Solve r(c) = 0.
-1, 0, 1, 3
Let s(g) be the third derivative of 0*g**5 + 0*g**4 + 0*g**3 + 0 + 0*g + 1/1890*g**7 + 1/1080*g**6 - 7*g**2. Factor s(z).
z**3*(z + 1)/9
Let 104/3 - 2/3*j**3 + 46/3*j**2 + 152/3*j = 0. Calculate j.
-2, -1, 26
Let s(u) = -25*u**2 - 440*u + 8375. Let f(y) = y**2 + y + 1. Let w(m) = 30*f(m) + s(m). Factor w(a).
5*(a - 41)**2
Let i(o) be the first derivative