8 + 0 - 2*m**2. Factor a(f).
f*(f - 1)**2*(f + 1)**2
Suppose -7 = f + 5*v, 3*f + 7*v - 7 = 6*v. What is m in -3/5*m**2 - 6/5*m + 6/5*m**f + 0 + 3/5*m**4 = 0?
-2, -1, 0, 1
Factor 77*s + 135 + 6*s**3 - 9*s**3 - 7*s**3 + 13*s + 5*s**4 - 60*s**2.
5*(s - 3)**2*(s + 1)*(s + 3)
Let h = 3 - -1. Let t(d) = d**3 - d**2 - d + 1. Let o(p) = -2*p**4 - 12*p**3 - 2*p**2 + 12*p + 4. Let j(z) = h*t(z) + o(z). Factor j(n).
-2*(n - 1)*(n + 1)*(n + 2)**2
Suppose -2*f = -3*z - 36, -3*f + 15 = 2*f. Let h = -2 - z. Factor d**2 + 12*d - h*d**3 - 2 - 4*d + 2*d**4 - 6 + 5*d**2.
2*(d - 2)**2*(d - 1)*(d + 1)
Let u(g) be the third derivative of g**8/5040 + g**7/315 + g**6/60 + g**5/20 - 6*g**2. Let o(d) be the third derivative of u(d). Factor o(t).
4*(t + 1)*(t + 3)
Let u(k) be the third derivative of -k**7/700 + k**6/225 - k**5/300 - k**3/2 - 6*k**2. Let l(w) be the first derivative of u(w). Factor l(b).
-2*b*(b - 1)*(3*b - 1)/5
Let g(d) = -4*d**3 - 5*d**2 - 3*d. Let o(b) = -5*b**3 - 6*b**2 - 4*b. Let y(n) = -4*g(n) + 3*o(n). Factor y(f).
f**2*(f + 2)
Suppose -5*a = -s - 0*s + 22, a = -s - 2. Factor -1/5*g**s - 1/5*g + 0.
-g*(g + 1)/5
Let b(g) be the first derivative of 6*g**5/115 - 7*g**4/23 + 16*g**3/69 + 65. Factor b(p).
2*p**2*(p - 4)*(3*p - 2)/23
Suppose -4*j + 125 + 315 = 0. Let l be (8/j)/(1/5). Find f such that 6/11*f - l - 2/11*f**2 = 0.
1, 2
Suppose 5*m - 16 = 9. Factor 2*b**2 - b**m + 3*b**5 - 4*b**2 - 6*b**4 + 6*b**3.
2*b**2*(b - 1)**3
Let b = -7 + 11. Suppose -b*o = o. Factor -1/3*a + 2/3*a**2 + o.
a*(2*a - 1)/3
Let h(f) be the first derivative of -f**7/14 + 3*f**5/10 - f**3/2 + f - 2. Let v(q) be the first derivative of h(q). Let v(d) = 0. Calculate d.
-1, 0, 1
Suppose 18 = -4*s - 14. Let z = -4 - s. Factor -x**4 - 2*x**3 - x**z + 4*x**3.
-2*x**3*(x - 1)
Find y such that 2*y**2 - 4*y**2 - 5*y - 4*y - 14 + 25*y = 0.
1, 7
Let i = 7 + -5. Let q(r) = r**2 + 4*r + 3. Let f(g) = -5*g**2 + g + 1. Let c be f(-1). Let d(o) = 2*o**2 + 9*o + 7. Let k(y) = c*q(y) + i*d(y). Factor k(s).
-(s + 1)**2
Suppose 19*j - 48 = 7*j. Suppose 0 + 7/3*m**3 - j*m**2 - 4/3*m = 0. What is m?
-2/7, 0, 2
Let g(c) be the third derivative of -c**5/300 - c**4/60 - c**3/30 + 24*c**2. Factor g(y).
-(y + 1)**2/5
Let t(b) = 4*b**3 + 2*b**2 - 14*b + 10. Let g(z) = -4*z**3 - 3*z**2 + 15*z - 11. Let a(i) = -2*g(i) - 3*t(i). Suppose a(q) = 0. What is q?
-2, 1
Let z(g) be the second derivative of g**6/6 - 5*g**4/12 - 12*g. Factor z(s).
5*s**2*(s - 1)*(s + 1)
Let a(b) be the first derivative of b**4/14 + 10*b**3/21 + 18. Find y, given that a(y) = 0.
-5, 0
Let u be ((-4)/40)/((-12)/(-45)). Let d = -7/40 - u. Find f such that -f + 2/5 + 1/5*f**3 - d*f**4 + 3/5*f**2 = 0.
-2, 1
Let p(s) = -s**3 + 8*s**2 + s + 1. Let c be p(8). Let y(g) = -g**2 + 8*g + 9. Let f be y(c). Factor -1/5*o + 0*o**2 + 1/5*o**3 + f.
o*(o - 1)*(o + 1)/5
Suppose 2*b + 3*b - 15 = 0. Suppose b*s = s + 10. Determine f so that 2*f**4 - f**5 - 5*f**4 - 2*f**s = 0.
-1, 0
Let i = 52/115 + 8/23. Let o be (-4)/36 - 354/(-270). Find j such that 0 + i*j**3 + 2/5*j + o*j**2 = 0.
-1, -1/2, 0
Let k(l) be the second derivative of l**6/285 - l**5/190 - l**4/57 + 19*l. Find v, given that k(v) = 0.
-1, 0, 2
Factor 2*f - 2*f + f**3 - 36*f**2 + 39*f**2.
f**2*(f + 3)
Let c(a) be the third derivative of -a**6/270 + a**5/270 + 5*a**4/108 + 2*a**3/27 + 3*a**2. Solve c(f) = 0 for f.
-1, -1/2, 2
Let k(t) be the first derivative of -t**6/540 + t**5/180 + 4*t**3/3 + 2. Let i(c) be the third derivative of k(c). Determine f, given that i(f) = 0.
0, 1
Find u such that 0 + 2/9*u**3 + 8*u - 8/3*u**2 = 0.
0, 6
Suppose -5*p = 2*s - 20, 5*s - 3*s - 6 = 2*p. Suppose 2*a - 13 + s = 0. Determine m, given that 2/9*m**a - 2/9*m**2 + 4/9*m**3 + 0 - 4/9*m = 0.
-2, -1, 0, 1
Let p(t) be the third derivative of -t**6/120 + t**5/30 - t**4/24 + 6*t**2. Find x, given that p(x) = 0.
0, 1
Let o(h) be the second derivative of 3/2*h**2 + 1/20*h**5 + 0 - 1/12*h**4 + 2*h + 0*h**3 - 1/120*h**6. Let u(k) be the first derivative of o(k). Factor u(m).
-m*(m - 2)*(m - 1)
Suppose j - 4 - 2 = 0. Let p(u) be the first derivative of -u**5 - 1/4*u**4 - u**2 + 5/3*u**3 - 2 + 1/2*u**j + 0*u. Factor p(r).
r*(r - 1)**2*(r + 1)*(3*r - 2)
Let n(l) be the first derivative of -l**5 + 15*l**4/4 - 10*l**3/3 + 12. Factor n(v).
-5*v**2*(v - 2)*(v - 1)
Let w = 23 - 21. Suppose -4*v + 5*v = 5*c, -c = w*v. Determine z so that 1/5*z**2 + 1/5*z + v = 0.
-1, 0
Let x(c) = 8*c**4 + 26*c**3 + 20*c**2 + 2*c - 2. Let n(d) = 39*d**4 + 131*d**3 + 101*d**2 + 9*d - 11. Let h(l) = -2*n(l) + 11*x(l). Factor h(i).
2*i*(i + 1)**2*(5*i + 2)
Let r(s) be the first derivative of -8/3*s + 1/12*s**4 - 3 + 2*s**2 - 2/3*s**3. Suppose r(u) = 0. Calculate u.
2
Let g = 33/2 + -15. Suppose 3/4*f**3 - g*f**4 + 0*f**2 + 0*f + 3/4*f**5 + 0 = 0. Calculate f.
0, 1
Let z(c) be the first derivative of -c**6/30 + 11*c**5/25 - 9*c**4/5 + 32*c**3/15 + 16*c**2/5 - 48*c/5 + 28. Suppose z(t) = 0. Calculate t.
-1, 2, 6
Let y(v) = 14*v**4 + 28*v**3 + 8*v**2 + 4. Let d(h) = -h**3 + 1. Let f(a) = -4*d(a) + y(a). Let f(c) = 0. Calculate c.
-2, -2/7, 0
Let m(a) be the first derivative of -5*a**4/18 - 2*a**3/9 + 4*a**2/3 - 8*a/9 + 4. Find w, given that m(w) = 0.
-2, 2/5, 1
Let c(h) = h**2 - 2*h - 4. Let d(x) = -3*x**2 + 3*x + 7. Suppose 1 = -3*g - 2, g + 21 = -5*i. Let m(j) = i*d(j) - 7*c(j). Factor m(v).
v*(5*v + 2)
Let o(h) be the third derivative of h**8/12 - 6*h**7/35 - h**6/6 + 3*h**5/5 - h**4/3 + 5*h**2. Let o(b) = 0. Calculate b.
-1, 0, 2/7, 1
Suppose 14 = -4*l - 2*x, 14 = -3*l - 3*x - 4. Let q(u) = 6*u**2 - 6*u - 4. Let o(f) = f**2 - f - 1. Let s(b) = l*q(b) + 4*o(b). Determine g so that s(g) = 0.
0, 1
Suppose -18 = 19*x - 18. Factor x*d + 0*d**2 + 0*d**3 + 2/5*d**5 + 0 - 2/5*d**4.
2*d**4*(d - 1)/5
Let v(g) = -g + 1. Let y be v(1). Let w(f) be the second derivative of 1/24*f**6 + y*f**2 - 3/80*f**5 - 1/24*f**4 + 0*f**3 + 3*f + 0. Factor w(z).
z**2*(z - 1)*(5*z + 2)/4
Let r be (1 - (-65)/(-39)) + (-1 - -2). Factor 0 + 7/6*c**2 + r*c + 5/6*c**3.
c*(c + 1)*(5*c + 2)/6
Let y(o) be the second derivative of -o**5/60 + o**4/36 + 5*o**3/18 + o**2/2 - 5*o. Factor y(w).
-(w - 3)*(w + 1)**2/3
Factor -11*f + 0*f**4 - f**4 + f**5 + 24*f - 3*f**3 + f**2 - 11*f.
f*(f - 2)*(f - 1)*(f + 1)**2
Let r(b) be the first derivative of b**3/3 - b**2 + 7. Factor r(t).
t*(t - 2)
Let c be 2/(1 + 4/(-6)). Determine a so that a**2 - 13*a**3 + 9*a**3 - c*a**4 + a**2 = 0.
-1, 0, 1/3
Let x = 2684/193 + -860629/49215. Let u = 1/51 - x. Factor 12/5*c - u*c**2 + 8/5*c**3 - 2/5.
2*(c - 1)**2*(4*c - 1)/5
Let i = 37 - 47. Let l = 11 + i. Factor 1/4*b**2 - l + 0*b.
(b - 2)*(b + 2)/4
Factor -16/5*u + 4/5*u**2 + 12/5.
4*(u - 3)*(u - 1)/5
Let 376*b**2 - 51*b**4 + 3*b**4 + 8*b**5 - 454*b**2 - 118*b**3 - 16*b = 0. What is b?
-1, -1/2, 0, 8
Factor -2*h**3 + 7*h**3 - 3*h**3.
2*h**3
Let o(p) = -p**2 + 4*p - 3. Let a be o(4). Let z = 0 - a. Factor i - z*i**5 - 2*i**2 + 2*i**4 + i**5 + i**5 + 0*i**4.
-i*(i - 1)**3*(i + 1)
Suppose 8*c - 12*c + 12 = 0. Let x(y) be the first derivative of y**2 - 2/3*y**c + 2 + 2*y - 1/2*y**4. Find n, given that x(n) = 0.
-1, 1
Let w(q) = 18*q**2 + 24*q. Let u(a) = 36*a**2 + 47*a + 1. Let g(y) = 3*u(y) - 5*w(y). Factor g(s).
3*(s + 1)*(6*s + 1)
Let u = 70201/150 + -468. Let d(m) be the third derivative of -u*m**5 + 1/15*m**4 - 4/15*m**3 + 0 - 2*m**2 + 0*m. Suppose d(x) = 0. What is x?
2
Let t = -50 + 151/3. Factor 4/3*b**2 + t*b**3 + 4/3*b + 0.
b*(b + 2)**2/3
Let a(y) be the first derivative of 2*y**3/51 - 26*y**2/17 + 338*y/17 - 6. Determine m so that a(m) = 0.
13
Determine s so that 1/2*s**2 + 1/2*s - 1 = 0.
-2, 1
Let k = 40499/189 + -2318/27. Let m = 129 - k. Suppose 0*q**3 + 2/7*q - 2/7*q**5 + 4/7*q**4 - m*q**2 + 0 = 0. Calculate q.
-1, 0, 1
Let d(y) be the first derivative of y**7/105 - y**5/30 + y**2/2 - 1. Let w(h) be the second derivative of d(h). Factor w(p).
2*p**2*(p - 1)*(p + 1)
Suppose -7*r + 30 = -2*r. Factor r*i**2 + 28*i + 12*i**3 - 4*i**2 + 13 - 5 + 30*i**2.
4*(i + 1)**2*(3*i + 2)
Let d be 3/(7 + -1)*(6 - 6). Let y = 5 - 3. Suppose d*u**y - 2/3*u**3 - 4/3 + 2*u = 0. Calculate u.
-2, 1
Let u(p) be the first derivative of -2*p**6/9 - p**5/5 + p**4/12 + 7. Determine v, given that u(v) = 0.
-1, 0, 1/4
Let f(l) be the first derivative of -l**7/560 - l*