/50 + m**4/5 - 4*m**3/15 - m**2. Factor p(z).
-2*(3*z - 2)**2/5
Let o(z) = 0*z**2 + z - 1 + 0*z - 4*z - z**2. Let s(n) = -2*n. Let f(a) = 2*o(a) - 5*s(a). Find r such that f(r) = 0.
1
Let m = 29 + -27. Let n(t) be the first derivative of 0*t - 2/9*t**3 + 1/3*t**m + 1. Factor n(c).
-2*c*(c - 1)/3
Let y be (24/(-270))/((-8)/20). Factor y + 2/9*g**2 + 4/9*g.
2*(g + 1)**2/9
Let h(j) = -j**3 - 3*j**2 + 4*j + 3. Suppose w = -0*w - 4. Let g be h(w). Factor g*i**3 - 18*i**2 - 9 - 15 + 16*i + 27*i - 7*i.
3*(i - 2)**3
Suppose 3*y = 4*o + 100, 0*y - 4*y = -4*o - 132. Solve 4*d**4 + 0 - 4 - 16*d**4 - 28*d**3 - 18*d - 2*d**5 - y*d**2 = 0 for d.
-2, -1
Let a = 5 + -1. Let j(g) be the first derivative of 1/2*g**6 + g**3 + 0*g - 3 - 3/4*g**a + 0*g**2 - 3/5*g**5. Factor j(d).
3*d**2*(d - 1)**2*(d + 1)
Let b(n) be the third derivative of n**6/60 + n**5/30 - n**4/12 - n**3/3 + 8*n**2. Let b(u) = 0. What is u?
-1, 1
Let c = -9/10 + 7/5. Suppose -27 + 21 = -3*r. Factor 1/4*f - c + 1/4*f**r.
(f - 1)*(f + 2)/4
Let h = -20 - -22. Let r(q) be the first derivative of -1/6*q**2 + 1/12*q**4 - 1/3*q - h + 1/9*q**3. Factor r(x).
(x - 1)*(x + 1)**2/3
Let m(f) = -f**3 - 13*f**2 - 4*f + 6. Let b(l) = 3*l**3 + 27*l**2 + 9*l - 13. Let v(z) = 6*b(z) + 13*m(z). Factor v(w).
w*(w - 1)*(5*w - 2)
Let l(v) be the second derivative of 0 + 0*v**4 + 1/15*v**6 + 1/5*v**5 - 2/3*v**3 - 2*v - v**2. What is p in l(p) = 0?
-1, 1
Let i(o) be the second derivative of 0*o**4 + 1/20*o**5 - 1/6*o**3 + 0*o**2 + 0 + o. Factor i(j).
j*(j - 1)*(j + 1)
Let r(w) be the third derivative of -w**7/210 + w**6/120 + w**5/20 - w**4/24 - w**3/3 + 4*w**2. Determine g, given that r(g) = 0.
-1, 1, 2
Let u = -2075/11 + 189. Let a(m) be the first derivative of -u*m + 1 + 3/11*m**2 - 2/33*m**3. Solve a(c) = 0.
1, 2
Suppose 0 = -y + 2*y - 2. Suppose -2*t - y = -8. Factor -3*a**3 - a**t + 4*a**3 - a**3 + 2*a**2.
-a**2*(a - 2)
Let m(i) = 15*i**4 + 27*i**3 + 6*i**2 - 24*i - 24. Let u(r) = -r**4 - r**3 + r**2 + r. Let s(t) = m(t) + 12*u(t). Determine f, given that s(f) = 0.
-2, 1
Factor 8/7*r**4 + 0*r - 2/7*r**5 + 0 + 0*r**2 - 6/7*r**3.
-2*r**3*(r - 3)*(r - 1)/7
Let z(w) = 2*w**3 - 33*w**2 + 47*w - 28. Let x be z(15). Factor -2/9*j**3 + 0 + 2/9*j**4 + 2/9*j - 2/9*j**x.
2*j*(j - 1)**2*(j + 1)/9
Let y = 32 + -32. Factor y - 10/3*x**2 + 4/3*x.
-2*x*(5*x - 2)/3
Factor 1/4 - 1/4*c**2 + 0*c.
-(c - 1)*(c + 1)/4
Suppose -4*i = 3*y - 11, 2*i + 2*y - 4 = -0*i. Solve 5*o**5 - 3*o**i + 5*o**5 - 4*o**5 = 0 for o.
0
Let x(a) be the second derivative of -a**6/1260 - a**5/420 - a**3/6 + 4*a. Let b(m) be the second derivative of x(m). Factor b(p).
-2*p*(p + 1)/7
Let v(s) be the second derivative of s**9/7560 - s**8/1120 + s**7/420 - s**6/360 - s**4/6 + s. Let c(d) be the third derivative of v(d). Factor c(h).
2*h*(h - 1)**3
Let y(g) be the third derivative of 5*g**8/112 + g**7/35 - g**6/4 - g**5/5 + 5*g**4/8 + g**3 + 2*g**2 + 18*g. Determine d, given that y(d) = 0.
-1, -2/5, 1
Let s(b) be the second derivative of b**6/45 - 4*b. Factor s(x).
2*x**4/3
Let i(c) be the first derivative of -c**5/2 + c**4/3 + 3*c - 3. Let j(n) be the first derivative of i(n). Factor j(b).
-2*b**2*(5*b - 2)
Let r(g) = 51*g**3 + 138*g**2 + 120*g + 15. Let t(w) = -26*w**3 - 69*w**2 - 60*w - 7. Let q(y) = -5*r(y) - 9*t(y). Determine k so that q(k) = 0.
-2, -1, -2/7
Let x(i) = i**2 - 1. Let b(c) be the second derivative of c**5/10 + 5*c**4/6 + c**3/3 - 3*c**2 - 3*c. Let z(o) = -b(o) + 6*x(o). Factor z(a).
-2*a*(a + 1)**2
Let s = 11/54 + 8/27. Factor 0*v**3 + 0*v + 0*v**2 + 0 + s*v**4.
v**4/2
Factor 11/5*h**2 - 2/5 + h + 4/5*h**3.
(h + 1)*(h + 2)*(4*h - 1)/5
Let a(q) = q**2 - 4*q + 0*q**2 + 3 + 8*q. Let n be a(-4). Suppose 2 + 0*k**3 + k**4 + 4*k + 4*k**n - 1 + 6*k**2 = 0. What is k?
-1
Let m = -347/15 + 116/5. Let u(f) be the third derivative of m*f**5 + 1/6*f**3 + 0*f + 0 + 5/24*f**4 - 2*f**2. Factor u(y).
(y + 1)*(4*y + 1)
Let u(y) be the first derivative of -y**4/7 + 60*y**3/7 - 1350*y**2/7 + 13500*y/7 - 27. Factor u(o).
-4*(o - 15)**3/7
Let o(x) be the second derivative of x**7/280 - 3*x**6/160 + 3*x**5/80 - x**4/32 - x**2/2 + x. Let t(i) be the first derivative of o(i). Factor t(c).
3*c*(c - 1)**3/4
Let g(p) be the third derivative of -p**7/945 + p**5/45 + 2*p**4/27 + p**3/9 - 6*p**2 - 3. Factor g(a).
-2*(a - 3)*(a + 1)**3/9
Find q, given that 0*q + 1/4 - 1/4*q**2 = 0.
-1, 1
Let x be (0 - -1)/((-6)/42). Let a(m) = m**2 + 7*m + 2. Let r be a(x). Factor -2*z**r - 9*z + 2*z + 5*z.
-2*z*(z + 1)
Let q be 8/(-44) + 387/11. Let a be ((-20)/q)/((-4)/14). Factor 0*o - o + o**3 + 2*o - a*o**2.
o*(o - 1)**2
Factor 0*g - 1/6*g**2 + 2/3.
-(g - 2)*(g + 2)/6
Let n(x) be the first derivative of x**6/1080 - 2*x**3/3 - 2. Let t(u) be the third derivative of n(u). Factor t(w).
w**2/3
Let i(c) be the first derivative of -1/5*c**2 + 0*c**4 - 1/5*c**3 + 2 + 1/25*c**5 + 0*c. Suppose i(k) = 0. Calculate k.
-1, 0, 2
Let g(a) be the third derivative of 1/150*a**5 + 0*a + 0*a**3 + 0 + 0*a**4 + 1/300*a**6 + 2*a**2. Solve g(i) = 0.
-1, 0
Factor 3*m**3 + 45*m + 27*m**2 - 12 - 11 + 44.
3*(m + 1)**2*(m + 7)
Let r = 4 - 2. Determine y so that -r + y**3 + 5 - 3 = 0.
0
Let y(r) be the first derivative of -r**4/24 - 5*r**3/18 - 2*r**2/3 - 2*r/3 - 18. Find x such that y(x) = 0.
-2, -1
Let i(u) be the second derivative of -u**4/42 - u**3/21 + 8*u. Suppose i(v) = 0. Calculate v.
-1, 0
Determine h, given that -271*h**2 - 2*h**3 - 25 + 47*h**3 + 155*h + 16*h**2 = 0.
1/3, 5
Let b(y) = y**3 + 5*y**2 + 2. Let w be b(-5). Suppose -3*v - 4*s + 38 = 0, -s = 2*v - 4*s + 3. Solve f + f**3 + 11*f + 0 + 8 + v*f**w = 0 for f.
-2
Let x(l) be the first derivative of 9/2*l**2 - 3/5*l**5 - 5*l**3 - 2*l + 11/4*l**4 - 2. Factor x(z).
-(z - 1)**3*(3*z - 2)
Let a(p) = -2*p**2 + 4*p + 2. Let s be a(4). Let v = -14 - s. Factor 0*t - 1/4*t**4 + 0 - 1/2*t**3 + v*t**2.
-t**3*(t + 2)/4
Suppose 2*q**2 + 18*q - 12*q + 2*q**4 - 54*q + 32 + 12*q**3 = 0. What is q?
-4, 1
Suppose 4*u - 2*g - 16 = 0, 3*g + 1 = -u - 9. Let l(k) be the first derivative of -2/3*k**3 + 0*k**2 - u + 2*k. Solve l(b) = 0 for b.
-1, 1
Let a(s) be the first derivative of -s**7/588 + s**6/180 - s**5/210 + s**3/3 + 1. Let f(r) be the third derivative of a(r). Let f(z) = 0. Calculate z.
0, 2/5, 1
Let b(a) be the third derivative of 1/6*a**4 + 0*a + 0 + 10*a**2 + 1/60*a**5 + 2/3*a**3. Determine o, given that b(o) = 0.
-2
Let o = 20 + -17. Let t(n) be the second derivative of 0*n**2 + n + 1/20*n**5 - 1/18*n**o + 0*n**4 + 1/45*n**6 + 0. Suppose t(r) = 0. Calculate r.
-1, 0, 1/2
Let l(u) be the second derivative of u**4/12 - 5*u**3/6 + 3*u**2 - 47*u. Factor l(h).
(h - 3)*(h - 2)
Let z(m) be the first derivative of -m**5/390 + m**4/78 + 3*m**2 - 2. Let u(x) be the second derivative of z(x). Find o, given that u(o) = 0.
0, 2
Suppose 3*j - 2*v + 12 = 36, 3*v = 4*j - 31. Let -1 + x**5 + 5*x - 9*x**2 - 5*x**4 + 0*x**5 - x**2 + j*x**3 = 0. Calculate x.
1
Let d(m) = 27*m**3 + 15*m**2 + 9. Let o(h) = 13*h**3 + 7*h**2 + 4. Let p(n) = -4*d(n) + 9*o(n). Let p(k) = 0. What is k?
-1/3, 0
Let q(m) = -8*m**5 - m**4 + m**3 - 6*m**2 - 7*m. Let w(o) = o**5 + o**2 + o. Let b(u) = -5*q(u) - 35*w(u). Factor b(f).
5*f**2*(f - 1)*(f + 1)**2
Suppose -4*g = -16, -2*l = -11*g + 7*g + 12. Factor -1/5 - 1/5*x**l + 2/5*x.
-(x - 1)**2/5
Suppose 3 = 2*b - 1. Let q(c) be the second derivative of 1/6*c**3 - 2*c + 0*c**b - 1/24*c**4 + 0 - 1/40*c**5. Find g such that q(g) = 0.
-2, 0, 1
Let z(x) be the first derivative of -3*x**4/16 + 8. Factor z(m).
-3*m**3/4
Let j be (-28)/6*15/(-10). Let g = j - 4. Determine i so that 1/4 + 5/4*i**4 - 5/4*i - 5/2*i**g - 1/4*i**5 + 5/2*i**2 = 0.
1
Suppose 3*r + 12 = 3*l - 0*r, 4*l - 2*r = 20. Let i be (-4)/l*(-2 - 1). Factor -2/7*o**3 - 2/7*o + 4/7*o**i + 0.
-2*o*(o - 1)**2/7
Let p(d) be the third derivative of d**6/1080 + d**5/270 - 7*d**4/216 + 2*d**3/27 - 2*d**2 + 4. What is l in p(l) = 0?
-4, 1
Let u be (-14)/20*(-11)/((-462)/(-24)). Suppose 2/5*x**3 + 0 + u*x + 4/5*x**2 = 0. What is x?
-1, 0
Let m(u) be the first derivative of u**6/300 - u**5/75 + u**2/2 + 3. Let g(r) be the second derivative of m(r). Factor g(i).
2*i**2*(i - 2)/5
Let n(c) = -5*c**2 - 2*c. Let p(y) = 2*y + 4*y - 4*y + 4*y**2. Let u(t) = -t - 4. Let b be u(-6). Let f(s) = b*n(s) + 3*p(s).