1*n(z). Factor i(g).
5*(g - 3)**2*(g - 2)
Let b be 0/4 + -2 + 9. Factor -9*j**3 + j - j**4 + j + b*j**4 + j.
3*j*(j - 1)**2*(2*j + 1)
Suppose -3*r - 7*z + 3*z + 27 = 0, -7 = -2*r + z. Let u(j) be the third derivative of 1/60*j**6 + 1/30*j**r + 0*j**3 + 0 - 2*j**2 + 0*j + 0*j**4. Factor u(f).
2*f**2*(f + 1)
Determine i so that i**4 + 0 + 1/2*i**3 - 1/2*i - i**2 = 0.
-1, -1/2, 0, 1
Let j = 42/1445 + 228487/143055. Let z = -13/11 + j. Factor -2/9*c**2 - 2/9 - z*c.
-2*(c + 1)**2/9
Let t = 25 + -27. Let f be (-1)/t + 6/4. Factor -2/9*p**3 - 2/9 + 2/9*p**f + 2/9*p.
-2*(p - 1)**2*(p + 1)/9
Let r(i) be the third derivative of i**5/6 + 7*i**4/12 + 2*i**3/3 + 16*i**2. Suppose r(m) = 0. What is m?
-1, -2/5
Solve -11*v**4 + 8*v**4 + 8*v**2 + 4*v**3 + 0*v**3 - v**4 = 0 for v.
-1, 0, 2
Let a(h) be the second derivative of -h**5/4 - 5*h**4/3 - 25*h**3/6 - 5*h**2 - 12*h. What is q in a(q) = 0?
-2, -1
Find h such that 0 - 1/5*h**2 + 1/5*h**3 + 0*h = 0.
0, 1
Let q(g) = 6*g**2 - 6*g + 6. Let l(a) = a**2 + 1. Let k(n) = -3*l(n) + q(n). Factor k(z).
3*(z - 1)**2
Let g(c) be the third derivative of -c**6/90 + c**4/6 + 4*c**3/9 + 6*c**2. What is m in g(m) = 0?
-1, 2
Let t(g) be the third derivative of -g**6/480 + g**5/120 - g**4/96 + 25*g**2. Factor t(m).
-m*(m - 1)**2/4
Solve -337*j**2 + j**5 + 2*j + 0*j**5 + j**4 + 336*j**2 - 3*j**3 = 0.
-2, -1, 0, 1
Let g be (-6)/14 - (-2)/2. Let x = 187/581 - 3/83. Factor -6/7*p**3 + 0 + x*p - g*p**5 + 10/7*p**4 - 2/7*p**2.
-2*p*(p - 1)**3*(2*p + 1)/7
Suppose 10 - 2 = 4*c + 4*m, -5*c = -5*m - 10. Solve -22/9*d + 2*d**c + 4/9 = 0 for d.
2/9, 1
Factor 1/11*t**4 + 0 + 0*t + 0*t**2 + 2/11*t**3.
t**3*(t + 2)/11
Let o(c) = -c**3 - c**2 + c - 1. Let n(g) = -9*g**3 + 71*g**2 - 311*g + 241. Let h(t) = n(t) - 4*o(t). Find f such that h(f) = 0.
1, 7
Suppose -s = -0*s + 2, -29 = 5*y + 2*s. Let z = y + 7. Determine k, given that -3*k**4 + 2*k**4 - 7*k**3 + 4*k**z - k**5 - 9*k**4 - 2*k**5 + 4*k = 0.
-2, -1, 0, 2/3
Suppose 2*y = b, 0 = 9*b - 11*b - 5*y + 9. Factor -14/9*h**b - 4/9 + 2*h.
-2*(h - 1)*(7*h - 2)/9
Let m(w) be the second derivative of w**8/840 - w**7/420 - w**6/180 + w**5/60 - w**3/3 - 2*w. Let f(t) be the second derivative of m(t). Factor f(c).
2*c*(c - 1)**2*(c + 1)
Let b = 37/84 - 3/28. Let z = -351 - -353. Factor b*l**z + 0 + 0*l + 0*l**3 - 1/3*l**4.
-l**2*(l - 1)*(l + 1)/3
Find n, given that 0*n + 3/5 - 3/5*n**2 = 0.
-1, 1
Factor 6/17*t + 2/17*t**4 - 10/17*t**2 + 2/17*t**3 + 0.
2*t*(t - 1)**2*(t + 3)/17
Suppose 4*n**3 - 3*n**4 - 4*n**5 - 3*n**4 + 6*n**4 = 0. Calculate n.
-1, 0, 1
Factor -4*a**3 + 0 + 0 - a**4 + 3*a**3.
-a**3*(a + 1)
Let b(k) = 4*k**2 + 5*k - 33. Let s(p) = -2*p**2 - 2*p + 16. Let g(f) = 4*b(f) + 9*s(f). Factor g(u).
-2*(u - 3)*(u + 2)
Let z(d) be the second derivative of -d**5/20 + d**4/18 + d**3/18 + 9*d. Let z(a) = 0. Calculate a.
-1/3, 0, 1
Determine d, given that -32 + 7*d**2 - 2*d**2 + 12 + 2*d - 17*d = 0.
-1, 4
Suppose 4 = 4*h - 4. Let n(y) be the first derivative of -y**5 - 7/4*y**4 + h*y + y**3 + 7/2*y**2 - 3. Factor n(d).
-(d - 1)*(d + 1)**2*(5*d + 2)
Suppose -2*a + 1 = -5. Solve -4*x**2 + 2*x**2 + 5*x**4 - 3*x + 4*x - 3*x**4 - x**a = 0.
-1, 0, 1/2, 1
Factor 29*q**2 + 2*q**3 - 23*q**2 + 9*q - q**3 - 4*q**3.
-3*q*(q - 3)*(q + 1)
Let t(a) be the first derivative of a**4 + 4*a**3/3 - 10*a**2 + 12*a + 4. Find f such that t(f) = 0.
-3, 1
Factor 2*t**3 + t**4 - 6*t**5 - t**3 - t**2 + 5*t**5.
-t**2*(t - 1)**2*(t + 1)
Factor -6 - 2*b - 6*b - 2*b**2 + 0*b**2.
-2*(b + 1)*(b + 3)
Suppose -11*h - 8*h + 6*h = 0. Let v(n) be the third derivative of -3/8*n**4 + 0*n**5 - n**3 + 1/40*n**6 + 0*n + h + 2*n**2. Factor v(o).
3*(o - 2)*(o + 1)**2
Let p(o) be the third derivative of o**6/120 - o**5/10 + 3*o**4/8 - 3*o**2. Factor p(w).
w*(w - 3)**2
Let g(l) be the third derivative of -l**8/448 + l**7/280 + l**6/80 - l**5/40 - l**4/32 + l**3/8 + 6*l**2. Factor g(n).
-3*(n - 1)**3*(n + 1)**2/4
Let r(h) = -3*h - 5. Let g be r(-4). Let i = g - 4. Suppose -2 + 3*b**i + 4*b**2 - 5*b**3 - 2*b**2 + 2*b = 0. Calculate b.
-1, 1
Let d = -8 - -12. Factor 3 + 2*c**2 - d*c + 2 - 3.
2*(c - 1)**2
Let x be ((-16)/(-64))/(0 + (-30)/(-8)). Let k(h) be the second derivative of 0*h**2 + x*h**6 - 2*h - 1/6*h**4 + 0 + 1/3*h**3 - 1/10*h**5. Factor k(l).
2*l*(l - 1)**2*(l + 1)
Let s(d) be the first derivative of 2/7*d**2 - 2/7*d**4 - 2/7*d + 2/7*d**3 - 8/35*d**5 - 2. Solve s(v) = 0 for v.
-1, 1/2
What is o in 5*o**3 + 5 - 3 - 32 - 40*o**2 + 65*o = 0?
1, 6
Suppose 0 = -13*p + 18*p - 20. Let v(c) be the first derivative of 3/2*c**6 + 20/3*c**3 - p + 37/4*c**4 + 0*c + 2*c**2 + 6*c**5. Find n, given that v(n) = 0.
-1, -2/3, 0
Let g(r) be the second derivative of -r**6/240 + r**5/60 + r**4/16 - 3*r**2/2 - 4*r. Let o(v) be the first derivative of g(v). Suppose o(a) = 0. What is a?
-1, 0, 3
Factor -6/11*q**4 - 14/11*q**2 + 0 - 16/11*q**3 - 4/11*q.
-2*q*(q + 1)**2*(3*q + 2)/11
Let q(o) = -o**3 + 5*o**2 + 12*o + 3. Let d(a) = 4*a**3 - 16*a**2 - 36*a - 8. Let g(m) = -3*d(m) - 8*q(m). Determine v so that g(v) = 0.
-1, 0, 3
Let a(h) = h**2 - 9*h - 49. Let t be a(13). Factor -1/3*u**t + 0 + 1/3*u**2 + 1/3*u**5 - 1/3*u**4 + 0*u.
u**2*(u - 1)**2*(u + 1)/3
Factor 4/3 + 13/3*h - 13/3*h**2 - 4/3*h**3.
-(h - 1)*(h + 4)*(4*h + 1)/3
Let o(k) be the first derivative of -k**6/6 + 4*k**5/5 - k**4 - 4. Solve o(r) = 0.
0, 2
Let d = 1/75 + 293/525. Factor -2/7*h**2 + d - 2/7*h.
-2*(h - 1)*(h + 2)/7
Let r = 17 + -16. Let u(s) be the first derivative of 2/9*s**3 - r + 2/3*s + 2/3*s**2. Factor u(f).
2*(f + 1)**2/3
Suppose 2*x - 5*x = -6. Let q(d) = d**3 + 3*d**2 - d + 1. Let u(g) = g**3 - g**2 - g - 1. Let s(l) = x*u(l) + q(l). Factor s(i).
(i - 1)*(i + 1)*(3*i + 1)
Let q(b) = 3*b + 49. Let x be q(-15). Solve -9/4*i**2 + 9/4*i**3 + 3/4*i - 3/4*i**x + 0 = 0 for i.
0, 1
Let -36/7*h**5 + 0 - 60/7*h**4 - 4*h**3 + 0*h - 4/7*h**2 = 0. Calculate h.
-1, -1/3, 0
Let c(j) = j**2 + 59*j + 196. Let d(z) = -3*z**2 - 117*z - 392. Let m(f) = -5*c(f) - 3*d(f). Solve m(w) = 0.
-7
Let x(v) be the third derivative of v**8/224 - v**7/84 + v**6/120 - 11*v**2. Factor x(h).
h**3*(h - 1)*(3*h - 2)/2
Let m(f) = 49*f**3 - 24*f**2 - 16*f - 9. Let s(r) = -12*r**3 + 6*r**2 + 4*r + 2. Let v(w) = -4*m(w) - 18*s(w). Factor v(p).
4*p*(p - 1)*(5*p + 2)
Let t(b) be the first derivative of b**7/189 - 2*b**6/135 + b**5/90 + 5*b + 3. Let m(c) be the first derivative of t(c). Factor m(r).
2*r**3*(r - 1)**2/9
Let r(k) = -5*k + 7*k + 2*k**2 - 7 + 5*k + 3. Suppose q - 2*v = -1, 4*q + 11 = -4*v - 17. Let g(f) = -f. Let p(j) = q*g(j) - r(j). Determine h so that p(h) = 0.
-2, 1
Let c be (0 + (-12)/(-15))*(-230)/(-92). Find v, given that -1/2*v + 1/2*v**c - 1 = 0.
-1, 2
Let y(q) be the third derivative of 1/30*q**5 + 0*q - 1/105*q**7 + 1/60*q**6 + 2*q**2 - 1/12*q**4 + 0 + 0*q**3. Suppose y(k) = 0. Calculate k.
-1, 0, 1
Factor -189*s**2 + 231*s**2 + 63*s + 3*s**3 + 84*s.
3*s*(s + 7)**2
Factor 81*g + 19*g**3 - 30*g**3 + 14*g**3 + 27*g**2 + 81.
3*(g + 3)**3
Let j(d) be the second derivative of -d**5/6 - d**4/28 + 2*d**3/21 - d**2 - 6*d. Let w(x) be the first derivative of j(x). Factor w(v).
-2*(5*v - 1)*(7*v + 2)/7
Suppose 2*u - 13 = 7. Let c be ((-15)/u)/(-1*3). Factor 1/2*b**5 + 0 - 1/2*b**3 + 0*b + c*b**4 - 1/2*b**2.
b**2*(b - 1)*(b + 1)**2/2
Let w(g) = 2*g**3 - 4*g**2 - 2*g + 3. Let o be w(3). Let n be (3/o)/((-8)/(-20)). Factor -3/4*k + 1/4*k**2 + n.
(k - 2)*(k - 1)/4
Let t(d) = d**3 + 12*d**2 + 3. Let k be t(-12). Factor -2/3 - i**2 + 4/3*i**k - 3*i.
(i - 2)*(i + 1)*(4*i + 1)/3
Let r be -1*(-1 - 7/(-14)). Factor 0 + 1/4*i**4 + 0*i - r*i**2 - 1/4*i**3.
i**2*(i - 2)*(i + 1)/4
Let g(y) = -3*y**2 + 10*y + 15. Let l(o) = 15*o**2 - 49*o - 75. Let h(b) = -11*g(b) - 2*l(b). Factor h(m).
3*(m - 5)*(m + 1)
Let k(y) = -3*y - 6. Let n be k(5). Let f be (-1)/(0 - n/(-6)). What is h in -f - 18/7*h**2 + 12/7*h = 0?
1/3
Let c be (495/10)/11 + -4. Let f(b) be the first derivative of -1/12*b**4 - c*b**2 + 4 - 1/3*b**3 - 1/3*b. Suppose f(u) = 0. Calculate u.
-1
Suppose 0*o + 9 = 5*y - 4*o, 0 = 4*y - 5*o. Let i = y + -3. Factor -j**3 + 4*j**3 - i*j**2 - j**3.
2*j**2*(j - 1)
Let j(y) = y**2 - 1. Let r = -1 + 0. Let d be j(r). Factor 1/3*z**5 - 1/3*z**3 + 0 + d*z - 1/3*z**2 + 1/3*z**4.
z**2*(z - 1)*(z + 1)**2/3
Determine k so that 0 + 2/