 1/5*j**3 - 1/5*j**2 + 0*j + w.
j**2*(j - 1)/5
Suppose 9*m = -7 + 34. Let d = -1/6 + 3/2. Determine f so that d*f + 5/6*f**2 + 2/3 + 1/6*f**m = 0.
-2, -1
Let n(v) be the third derivative of 0 - 1/60*v**5 + 0*v**3 + 0*v - 1/120*v**6 + 1/24*v**4 - 7*v**2 + 1/210*v**7. Factor n(m).
m*(m - 1)**2*(m + 1)
Suppose -5*i = 6*i. Factor i - 1/4*o + 1/4*o**2.
o*(o - 1)/4
Let h(i) be the first derivative of i**4/12 - i**3/9 - i**2/6 + i/3 + 3. Solve h(z) = 0.
-1, 1
Factor 3*a**2 + 6*a**2 + 4 - 11*a**2 - 2*a.
-2*(a - 1)*(a + 2)
Let b(m) = 68*m**4 + 220*m**3 + 112*m**2 - 40*m. Let v(g) = -27*g**4 - 88*g**3 - 45*g**2 + 16*g. Let q(y) = -5*b(y) - 12*v(y). Factor q(z).
-4*z*(z + 1)*(z + 2)*(4*z - 1)
Suppose -23 = -4*m + 3*y, -2 - 8 = 2*y. Factor 3 - 4 + 4 + 1 - m*c**2 + 2*c.
-2*(c - 2)*(c + 1)
Let w(j) = -3*j**2 + j. Let s be w(1). Let t be 2 + (-1 - -3) + s. Factor 0*d**t - 1/4 + 1/2*d**3 - 1/2*d + 1/4*d**4.
(d - 1)*(d + 1)**3/4
Let j(w) be the first derivative of -w**3/5 - 3*w**2/5 - 3*w/5 + 19. Factor j(q).
-3*(q + 1)**2/5
Let o(m) be the third derivative of -1/1344*m**8 + 0*m + 0*m**6 + 1/96*m**4 + 1/420*m**7 + 0 + 0*m**3 - 2*m**2 - 1/120*m**5. What is z in o(z) = 0?
-1, 0, 1
Suppose -4*r - 3*n = 2*n - 10, r - 5*n - 15 = 0. Find g such that 4/5*g**2 - 2/5*g + 0 + 0*g**3 + 2/5*g**r - 4/5*g**4 = 0.
-1, 0, 1
Suppose 4*m = -2*f, f - 6*f + 11 = -m. Suppose -f + 4 = k. Suppose -4*h**k - 16*h**3 + 18*h**2 - 24*h**4 - 2*h - 8*h**4 = 0. What is h?
-1, 0, 1/4
Factor 8/7*b - 10/7 + 2/7*b**2.
2*(b - 1)*(b + 5)/7
Suppose 11 = 4*x - 5. Factor 2*l**3 + l**2 + 0*l**4 + l**x + 0*l**4.
l**2*(l + 1)**2
Let n(m) be the second derivative of 2*m + 1/4*m**2 - 1/8*m**3 - 5/48*m**4 + 0. Suppose n(x) = 0. What is x?
-1, 2/5
Factor 2/23*s**3 - 8/23*s**2 - 6/23*s + 4/23*s**4 + 0.
2*s*(s + 1)**2*(2*s - 3)/23
Suppose 4*m + 3 - 15 = 0. Factor -5*h**3 - 3*h**2 + 6*h**m + h**4 + 3*h**2.
h**3*(h + 1)
Let u(s) be the second derivative of 2*s**7/21 + 4*s**6/15 - 2*s**4/3 - 2*s**3/3 + 5*s. Factor u(k).
4*k*(k - 1)*(k + 1)**3
Let o = 0 - -5. Suppose -o = -3*m + 7. Factor 3*f - m*f**2 + 0*f**3 + f**3 - 2*f + 2*f**2.
f*(f - 1)**2
Let y = -10 + 14. Let o be 48/70 - y/10. Solve o*q**2 - 4/7*q**3 + 4/7*q + 0 - 2/7*q**4 = 0.
-2, -1, 0, 1
Suppose -14 = 5*r - 14. Solve r*i - 7/4*i**5 + 0 - 11/4*i**3 - 1/2*i**2 - 4*i**4 = 0 for i.
-1, -2/7, 0
Let v be (0/4)/(16 + -11). Solve v + 2/9*y**4 + 0*y + 2/9*y**3 - 2/9*y**5 - 2/9*y**2 = 0 for y.
-1, 0, 1
Let y(p) be the first derivative of 0*p + 4/15*p**5 + 1/6*p**4 - 2 + 0*p**2 - 2/9*p**3. Suppose y(l) = 0. Calculate l.
-1, 0, 1/2
Let z(u) = 2*u**2 + 68*u + 564. Let t(s) = 2. Let l(y) = -14*t(y) - 2*z(y). Factor l(k).
-4*(k + 17)**2
Let x(r) = r**2 - 3*r - 3. Let a be x(4). Let u be -1*(-1*3)/a. Factor -b + 5*b - 2*b**3 - b**u + 3*b**4 - 4*b**4.
-b*(b - 1)*(b + 2)**2
Find n, given that -291*n**3 + 303*n**3 + n**5 - 6*n**4 - 9*n**2 + n**2 = 0.
0, 2
Let p(a) = a**5 + 3*a**4 + 4*a**3 + a**2 + a + 1. Let j(k) = k**3 + k + 1. Let b(t) = -4*j(t) + 4*p(t). Factor b(f).
4*f**2*(f + 1)**3
Let i be ((-12)/15)/((-2)/5). Factor 4*y**2 - i*y**4 - 2*y**4 + 2*y**4 - 2.
-2*(y - 1)**2*(y + 1)**2
Factor 4*c**2 - 4*c - 1 + 1.
4*c*(c - 1)
Factor 12*g - 17*g**2 - 12*g**3 + 3*g**4 - 2 + 26*g**2 - 10.
3*(g - 2)**2*(g - 1)*(g + 1)
Let t be (-1)/(-3*3/27). Let c(f) be the first derivative of 0*f**4 - f**2 + 4/3*f**t - 1 + 1/3*f**6 - 4/5*f**5 + 0*f. Determine r, given that c(r) = 0.
-1, 0, 1
Suppose 0 = -0*x - 2*x - 6. Let y be x/12 + 42/8. Determine s, given that -10*s**2 + 0*s**5 + 2*s + 12*s**3 + 4*s**y - 14*s**4 + 6*s**3 = 0.
0, 1/2, 1
Let r = 8 - 5. Factor -5*o**r - 2*o - 4 + 4*o**2 + 2*o**3 + 5*o**3.
2*(o - 1)*(o + 1)*(o + 2)
Suppose 0 = -4*i + 2 + 2. Let q(w) = 2*w**2 + 4*w - 1. Let c(o) = o**2 + o - 1. Let z(j) = i*q(j) - 3*c(j). Determine h so that z(h) = 0.
-1, 2
Let q(v) be the third derivative of -v**5/40 + v**4/16 + 5*v**2. Factor q(b).
-3*b*(b - 1)/2
Suppose -5*t + z + 0*z = 5, 5*t + z = 5. Suppose 2*b + 5*o + 2 = t, -5*o + 0 = 5*b - 10. What is f in 2*f**3 + 0*f - 2*f - 1 + 0*f + f**b = 0?
-1, 1
Suppose t = -2*x - 1, -5*x + t = -0*x - 1. Solve 2*o**2 - 2*o + x*o**2 - 32*o**3 + 34*o**3 - 2*o**4 = 0.
-1, 0, 1
Let b = -132 - -400/3. Let h(f) be the first derivative of b*f + 2/9*f**3 - 3 - f**2. Factor h(w).
2*(w - 2)*(w - 1)/3
Let k(z) be the first derivative of 0*z + 2/7*z**2 + 6 - 4/21*z**3. Factor k(t).
-4*t*(t - 1)/7
Let q be 24/42*(-28)/(-72). Factor 2/3*t**4 - q + 4/3*t**2 - 16/9*t**3 + 0*t.
2*(t - 1)**3*(3*t + 1)/9
Suppose -3*j = -4 - 2. Factor -m**3 + m + 0*m + 3*m**2 - 3*m**j.
-m*(m - 1)*(m + 1)
Solve -30*i**5 - 20*i**2 + 2*i**5 + 24*i - 32*i + 36*i**3 + 20*i**4 = 0 for i.
-1, -2/7, 0, 1
Let b = -1 - 16. Let k = b + 19. Let k*w + 2*w**2 + 0 + 1/2*w**3 = 0. What is w?
-2, 0
Let t(x) be the third derivative of -x**6/540 + x**5/180 + x**4/18 - 2*x**3/3 - 9*x**2. Let d(n) be the first derivative of t(n). Factor d(l).
-2*(l - 2)*(l + 1)/3
Determine d so that -8/9*d - 2/9*d**2 + 0 = 0.
-4, 0
Let t = 2 + 1. Factor 2*s**2 - s**2 + 2 + t*s - s**2 + s**2.
(s + 1)*(s + 2)
Factor 0*x - 1/7 + 1/7*x**2.
(x - 1)*(x + 1)/7
Suppose 0 = -0*l - 3*l + 36. Suppose 4*j + 0*j - l = 0. Factor 0 + 1/2*o**2 + 1/4*o**j + 1/4*o.
o*(o + 1)**2/4
Let n(i) be the third derivative of -i**6/60 - i**5/12 - i**4/12 - 28*i**2. Determine o so that n(o) = 0.
-2, -1/2, 0
Let x(t) be the second derivative of t**7/21 - 4*t**6/15 + 3*t**5/5 - 2*t**4/3 + t**3/3 + t. Factor x(h).
2*h*(h - 1)**4
Let u(r) be the third derivative of 2*r**5/15 + r**4/2 + 2*r**2. Let i(f) = 9*f**2 + 13*f. Let v(s) = -6*i(s) + 7*u(s). Factor v(j).
2*j*(j + 3)
Let u(p) = 9 + 6 + 4 - 4 - 21*p**2 + 12*p. Let v(r) = -r**2 + r + 1. Let j(b) = u(b) - 18*v(b). Factor j(q).
-3*(q + 1)**2
Let q(s) = s**2 + s - 4. Let b be q(3). Suppose -4*h + 23 = -5*l, -h + b = -3*l - 3. Factor 4*z**2 - z**3 - z**5 - 3*z**4 - 2*z**3 - 5*z**h.
-z**2*(z + 1)**3
Let y(h) = h**2 - h. Let z(d) = 2*d**2 - 15*d + 49. Let a(t) = 3*y(t) - 3*z(t). Factor a(m).
-3*(m - 7)**2
Let s(l) be the second derivative of -1/8*l**2 - 1/48*l**4 - 8*l + 1/12*l**3 + 0. Solve s(g) = 0.
1
Let g(f) be the third derivative of -13*f**5/20 + f**4/4 + 48*f**2. Suppose g(c) = 0. Calculate c.
0, 2/13
Let d(b) be the second derivative of b**6/10 + 3*b**5/20 - 4*b. Factor d(c).
3*c**3*(c + 1)
Let o(m) be the third derivative of -11*m**5/15 + 13*m**4/6 - 4*m**3/3 + 6*m**2. Factor o(t).
-4*(t - 1)*(11*t - 2)
Let p be (-4)/22 + 815/(-55). Let v be (1 + (p - 0))/(-3). What is x in -10/3*x**2 - 4/3 + v*x = 0?
2/5, 1
Let d be 4/(-18) + (-35)/(-819). Let w = 2/13 - d. Let 1/3*o**2 + w - 2/3*o = 0. What is o?
1
Let b(c) = c. Let u be b(2). Let n(f) = f**2 + 2*f - 4. Let m be n(-4). Factor -p**4 + u*p**2 + 0*p**2 - p**m.
-2*p**2*(p - 1)*(p + 1)
Let l(n) be the first derivative of 1/12*n**4 + 4 + 2/3*n - 2/9*n**3 - 1/6*n**2. Suppose l(g) = 0. Calculate g.
-1, 1, 2
Let f(w) be the first derivative of 3*w**4 + 8/3*w**3 + 8/5*w**5 + w**2 + 1/3*w**6 + 2 + 0*w. Factor f(g).
2*g*(g + 1)**4
Suppose -43*v - 30 + 62*v - 28*v + 3*v**2 = 0. Calculate v.
-2, 5
Let r(b) be the second derivative of b**6/120 - b**4/48 + b. Factor r(k).
k**2*(k - 1)*(k + 1)/4
Factor -49/8 + 7/4*n - 1/8*n**2.
-(n - 7)**2/8
Let q be (-728)/(-98) + 4/7. What is v in -q*v**3 + 4*v**5 + 66*v**4 - 66*v**4 + 4*v = 0?
-1, 0, 1
Factor 0*i**2 + i**3 - 14 + 4*i + 2*i**2 + 6 - 8*i.
(i - 2)*(i + 2)**2
Let l be (-1)/4 + 1/4. Let w(u) = -u + 2. Let k be w(l). Factor 3*c + c**2 + 2 - c**k - c**3.
-(c - 2)*(c + 1)**2
Let v(q) be the second derivative of -3*q - 1/54*q**4 - 4/27*q**3 + 0 - 4/9*q**2. Find f, given that v(f) = 0.
-2
Let i(c) be the second derivative of -1/63*c**7 + 0*c**2 + 1/30*c**5 + 0 - 1/18*c**4 + 0*c**3 + 1/45*c**6 + 8*c. Factor i(b).
-2*b**2*(b - 1)**2*(b + 1)/3
Let -6 - 3*n - 3/4*n**4 + 9/2*n**2 + 3/4*n**3 = 0. What is n?
-2, -1, 2
Let g = 8 + -4. Let s(l) = l**3 + 3*l**2 - l - 1. Let v be s(-3). Factor y**3 - y**4 - y - y**4 - y**v + 3*y**g.
y*(y - 1)*(y + 1)**2
Let t = 11/6 + -3/2. Let j(p) be the second derivative of 1/36*p**4 + 3*p - 1/6*p**3 + 0 + t*p**2. Factor j(y).
(y - 2)*(y - 1)/3
Let l(u) be the third derivative of u**6/360 - u**5/45 + u**4/18 + 12*u**2. Factor l(p).
p*(p - 2)**2/3
Let u(s) = -2*s**4 - 50*s**3 - 165