
Let t(i) = i**2 - 2*i + 1. Let d be t(3). Factor 9*m**3 + 7*m**3 + d*m**3 - 8*m**2.
4*m**2*(5*m - 2)
Let v(s) = -s**2 - 3*s + 1. Let i(c) = c**3 + c**2 + 8*c - 1. Let g(x) = -5*i(x) - 15*v(x). Factor g(h).
-5*(h - 2)*(h - 1)*(h + 1)
Suppose 5*v - 45 = -5*n - 0*v, -4*n = -5*v. Let -15 + 6 - 20*c - 11 - n*c**2 = 0. What is c?
-2
Let k be (4 - (-51)/(-15))/((-108)/(-120)). Solve k*n**2 + 32/3 + 16/3*n = 0.
-4
Suppose 2/7*f + 2/21*f**5 + 4/21 - 4/21*f**2 + 0*f**4 - 8/21*f**3 = 0. Calculate f.
-1, 1, 2
Factor -2*y**2 + 147 - 204 + 99 - 15*y - y**2.
-3*(y - 2)*(y + 7)
Let r = 52 + -50. Let g be (-2)/(((-8)/(-6))/(-2)). Factor 0*k**g - 3*k**r + 3*k + 2*k**3 - 1 - 2*k**3 + k**3.
(k - 1)**3
Let z(y) = -5*y**4 - 156*y**3 - 312*y**2 - 161*y + 3. Let j(s) = -7*s**4 - 156*s**3 - 311*s**2 - 162*s + 4. Let f(r) = 3*j(r) - 4*z(r). Factor f(c).
-c*(c - 158)*(c + 1)**2
Let i(o) be the first derivative of 2*o**7/21 + o**6/30 - 16*o**5/75 + 2*o**4/15 - 8*o**2 - 8. Let g(f) be the second derivative of i(f). Factor g(t).
4*t*(t + 1)*(5*t - 2)**2/5
Let i = -27484/5 - -5504. Determine o, given that -i*o - 3/5*o**3 - 24/5 - 18/5*o**2 = 0.
-2
Let g(l) be the third derivative of 1/270*l**5 + 2/27*l**4 - 3*l**2 + 4*l - 1/3*l**3 + 0. Solve g(u) = 0 for u.
-9, 1
Factor 2/5*r**4 - 18/5*r**2 - 8/5 + 2/5*r**3 + 22/5*r.
2*(r - 1)**3*(r + 4)/5
Let p(w) = -w**3 + 4*w**2 - 2*w + 1. Let z be p(3). Let l(y) be the second derivative of -3/4*y**5 + 2*y - 1/2*y**3 + y**z + 1/5*y**6 + 0 + 0*y**2. Factor l(b).
3*b*(b - 1)**2*(2*b - 1)
Let y(j) be the first derivative of 2*j**3/9 + 20*j**2/3 + 38*j/3 + 69. Solve y(o) = 0 for o.
-19, -1
Let t(s) be the second derivative of 3/28*s**4 + 1/2*s**3 + 3/7*s**2 - 7*s + 0. Factor t(y).
3*(y + 2)*(3*y + 1)/7
Let k be 1/(-3)*(4 - -16)/(-20). Let t(w) be the second derivative of 0 + 14*w - k*w**4 - w**5 + 10/3*w**3 - 4*w**2 + 2/5*w**6. Factor t(l).
4*(l - 1)**2*(l + 1)*(3*l - 2)
Let i(r) be the first derivative of 5*r - 1 - 11/10*r**5 - 4/3*r**3 + 0*r**2 + 2*r**4 + 1/5*r**6. Let v(a) be the first derivative of i(a). Factor v(d).
2*d*(d - 2)*(d - 1)*(3*d - 2)
Let y(v) be the third derivative of 2*v**7/175 - 4*v**6/75 - 2*v**5/25 + 4*v**4/15 + 2*v**3/5 - 226*v**2. Determine i, given that y(i) = 0.
-1, -1/3, 1, 3
Let n(t) be the first derivative of -3*t**5/5 - 21*t**4/4 + t**3 + 21*t**2/2 - 418. Solve n(g) = 0.
-7, -1, 0, 1
Let h(d) be the second derivative of 2*d**7/63 + 4*d**6/45 - d**5/15 - 2*d**4/9 + 87*d. Let h(f) = 0. Calculate f.
-2, -1, 0, 1
Let w be (-28)/14 + 8 + -1*4. Let q(h) be the second derivative of -2*h - 3/20*h**5 + 0 - 3/4*h**4 + 1/2*h**3 + 9/2*h**w. Find v such that q(v) = 0.
-3, -1, 1
Let k = -834 + 836. Let j(h) be the first derivative of 1/2*h**3 + 0*h**k + 0*h + 5. Let j(c) = 0. Calculate c.
0
Let f be 65 + 15*1/3. Let n be (-15)/f*2*1/(-3). Factor 1/7*z - 1/7*z**2 + 1/7 - n*z**3.
-(z - 1)*(z + 1)**2/7
Let i(j) = -5*j**3 - 17*j**2 - 63*j + 81. Let h(w) = -4*w**3 - 17*w**2 - 63*w + 81. Let a(v) = -4*h(v) + 3*i(v). Factor a(u).
(u - 1)*(u + 9)**2
Solve -7609*s**4 + 179*s**3 + 24*s**2 - 14*s**5 - 3*s**3 + 7663*s**4 = 0.
-2, -1/7, 0, 6
Factor 12*n**2 + 0 + 16*n**3 + 4/3*n**4 - 88/3*n.
4*n*(n - 1)*(n + 2)*(n + 11)/3
Let o(z) = z**3 + 5*z**2 + 4. Let s be o(-5). Suppose 2*v + 6 = 2*g - 3*g, s*v + 32 = 3*g. Factor x**g + 6*x**2 - 1 - 4*x**3 - 4*x + 0 + 2.
(x - 1)**4
Suppose -5*d + 3*r + 10 - 85 = 0, -r = 5*d + 55. Let n be (-4)/d - (-15)/63. Factor 0 + 2/7*s**3 + n*s + 6/7*s**2.
2*s*(s + 1)*(s + 2)/7
Factor w**4 - 17/4*w - 9/4 + 65/4*w**2 - 43/4*w**3.
(w - 9)*(w - 1)**2*(4*w + 1)/4
Let r(b) be the first derivative of -b**2 - 14/45*b**3 - 1/30*b**4 - 6/5*b - 10. Factor r(k).
-2*(k + 1)*(k + 3)**2/15
Let k(f) = f**3 + 4*f**2 - 7*f - 11. Let y be k(-5). Let t(p) = p - 1. Let w(i) = -14*i**2 + 4*i - 8. Let g(n) = y*w(n) + 8*t(n). Factor g(d).
2*d*(7*d + 2)
Find q such that 0 + 0*q**2 - 7/4*q**4 - 5/2*q**3 - 1/4*q**5 + 0*q = 0.
-5, -2, 0
Let t = 17975 + -17973. Let f be 116/48 + (-1)/(-4). Let -8/3*h - 2/3*h**t - f = 0. Calculate h.
-2
Let f(h) be the first derivative of -h**4/17 - 2*h**3/17 + 3*h**2/17 + 4*h/17 - 436. Let f(j) = 0. What is j?
-2, -1/2, 1
Let d be -21 - -29 - 2/1. Let z(m) be the second derivative of -8/3*m**3 + 0*m**2 + 16/3*m**4 - 10/3*m**6 + 0 - m**5 - d*m. Factor z(w).
-4*w*(w + 1)*(5*w - 2)**2
Let s(r) = -4 + 0*r**2 - 9*r**2 - 1 + 4*r + 5*r. Let z(v) = -v**2 + v - 1. Let o(t) = s(t) - 5*z(t). Let o(u) = 0. Calculate u.
0, 1
Let m(k) be the first derivative of 1/3*k**3 + k**2 - 1/4*k**4 + 0*k - 44. Solve m(o) = 0 for o.
-1, 0, 2
Let s(d) be the second derivative of -d**9/35280 - d**8/15680 + 7*d**4/4 - 33*d. Let g(w) be the third derivative of s(w). Let g(c) = 0. What is c?
-1, 0
Let f(n) be the second derivative of -16*n + 0*n**2 - 20/3*n**4 + 0 + 14/5*n**5 + 16/3*n**3 - 2/5*n**6. Factor f(w).
-4*w*(w - 2)**2*(3*w - 2)
Find r such that 100/9*r**3 - 200/9 - 292/9*r - 4/9*r**4 + 4/3*r**2 = 0.
-1, 2, 25
Let p(i) = i**2 + 4*i + 3. Let a(q) = -q - 1. Let d(s) = -4*a(s) - p(s). Let b(w) = 5*w**3 - 6*w**2 + 6. Let r(z) = b(z) - 6*d(z). Factor r(x).
5*x**3
Let k(z) be the second derivative of -z**8/1680 + z**7/210 - z**6/90 + z**4/3 + 7*z. Let r(s) be the third derivative of k(s). Factor r(n).
-4*n*(n - 2)*(n - 1)
Let q(u) = u**5 - u**4 + u**3 + u**2 - 2*u - 1. Let z(j) = -5*j**5 + 2*j**4 - 10*j**2 + 13*j + 6. Let l(h) = -6*q(h) - z(h). Solve l(g) = 0.
0, 1
Let d = -4 + 14. Factor 6*o**3 - 6 + 5*o**3 - 13*o**3 - 8*o**2 + 2 - d*o.
-2*(o + 1)**2*(o + 2)
Let h(z) be the first derivative of -2*z**5/5 + 2*z**3 + 2*z**2 + 221. Let h(g) = 0. What is g?
-1, 0, 2
Factor -k**4 + 46*k**2 + 6*k**4 + k**5 + 5 - 56*k**2 + k - 2*k**3 + 0*k**4.
(k - 1)**2*(k + 1)**2*(k + 5)
Let l(g) be the first derivative of 5/18*g**3 - 1/3*g**2 - 1/9*g**4 - 2 - 4*g + 1/60*g**5. Let n(m) be the first derivative of l(m). Factor n(j).
(j - 2)*(j - 1)**2/3
Let x(j) = -170*j - 4587. Let r be x(-27). Factor 4/15 + 2/15*q - 4/15*q**2 - 2/15*q**r.
-2*(q - 1)*(q + 1)*(q + 2)/15
Let k = -1 + 0. Let z(q) = -33*q + 19. Let p(r) = -r**2 - 1. Let m(n) = k*z(n) - 5*p(n). Solve m(h) = 0.
-7, 2/5
Let 0 + 0*g - 8/5*g**2 - 2/5*g**5 + 6/5*g**4 + 0*g**3 = 0. Calculate g.
-1, 0, 2
Factor 5/2*o**5 + 25/2*o**2 - 5*o - 5/2*o**4 + 0 - 15/2*o**3.
5*o*(o - 1)**3*(o + 2)/2
Suppose 54 = 7*o - 4*o. Suppose 0 = -8*i - i + o. Factor 0 + 1/6*b**i + 1/6*b.
b*(b + 1)/6
Let a(x) be the third derivative of x**6/900 + 2*x**5/75 + 7*x**4/60 - 7*x**3 - 3*x**2. Let h(v) be the first derivative of a(v). Factor h(f).
2*(f + 1)*(f + 7)/5
Let z(l) be the second derivative of -l**5/60 - l**4/6 + 16*l**2/3 + 3*l + 11. Factor z(k).
-(k - 2)*(k + 4)**2/3
Factor -1445*a + 54*a**2 + 802*a + 3*a**5 - 48*a**3 - 6*a**5 + 886*a + 162 - 24*a**4.
-3*(a - 2)*(a + 1)*(a + 3)**3
Determine w so that -5821 + 666*w - 2237 + 6233 - 21288 - 13850 - 3*w**2 = 0.
111
Let k(t) = 4*t**2 - 296*t + 5464. Let z(b) = 4*b**2 - 296*b + 5467. Let f(r) = 3*k(r) - 4*z(r). Suppose f(s) = 0. What is s?
37
Let u be (-20)/1 - (-1572)/78. Factor 0 - 2/13*w**5 + u*w + 0*w**3 - 4/13*w**2 + 4/13*w**4.
-2*w*(w - 1)**3*(w + 1)/13
Let v(m) = -m**2 - 31*m - 35. Let i(p) = -4*p**2 - 92*p - 104. Let l(q) = 5*i(q) - 16*v(q). Factor l(y).
-4*(y - 10)*(y + 1)
Let s(z) be the second derivative of -z**4/54 + 7*z**3/27 + z + 49. Solve s(m) = 0.
0, 7
Let b = 212/357 + 26/357. Let x = -12/7 + 113/21. Solve x*u**2 + 0 + b*u = 0 for u.
-2/11, 0
Let i(k) = -5*k**3 + 55*k**2 - 315. Let y(f) = -2*f**3 + 27*f**2 - 157. Let l(g) = 3*i(g) - 5*y(g). Factor l(r).
-5*(r - 4)**2*(r + 2)
Factor 2/5*y**2 + 152/5*y - 312/5.
2*(y - 2)*(y + 78)/5
Let b = 84 + -179. Let z = 100 + b. Factor 5/3*i**z - 5/3*i**4 + 5/3*i - 5/3 - 10/3*i**3 + 10/3*i**2.
5*(i - 1)**3*(i + 1)**2/3
Let q(i) be the first derivative of -5/2*i**2 + 16 - 9/2*i - 1/6*i**3. Let q(c) = 0. What is c?
-9, -1
Let c be 10/(-15) + 1 - (-34)/6. Suppose 4*q - 4*m - 8 = 0, q - 4*q = -2*m - c. Suppose -42/5*z**3 + 10*z**4 - 18/5*z**5 + 0 + 6/5*z**q + 4/5*z = 0. What is z?
-2/9, 0, 1
Let v(t) be the first derivative of 3/22*t**4 - 3/11*t**2 + 2/33*t**3 + 6 - 2/11*t. Find p, given that v(p) = 0.
-1, -1/3, 1
Factor -177*c**3 + 3*c - 4*c**2 - 6*c + 176*c**3.
-c*(c + 1)*(c + 3)
Let l(i) = -5*i**3 + 11*i**2 + 34*i -