**2 - 4. Let d(i) = 5*i**2 - i - 3. Let q(w) = -3*a(w) + 4*d(w). Factor q(x).
2*x*(x - 2)
Suppose -12*r + 16 = -8. Factor 4/7*x - 2/7*x**r - 2/7.
-2*(x - 1)**2/7
Let h(v) be the first derivative of 2*v**5/25 - 2*v**4/5 + 2*v**3/5 - 9. Factor h(p).
2*p**2*(p - 3)*(p - 1)/5
Let j(h) be the first derivative of -h**4/3 + 7*h**3/18 - h**2/6 - 6*h + 1. Let c(s) be the first derivative of j(s). Solve c(w) = 0 for w.
1/4, 1/3
Find o such that -41*o**3 - 16*o - o**4 + 17*o**2 + 7*o**2 + 29*o**3 + 3*o**4 = 0.
0, 2
Let t(r) = 22*r - 108. Let x be t(5). Factor -1/3*h**3 - 2/3*h + 0 + h**x.
-h*(h - 2)*(h - 1)/3
Let r = 1139/1516 - 1/758. Find t such that -3/8*t**2 - r - 9/8*t = 0.
-2, -1
Let a(t) = 6*t**5 - 15*t**4 + 15*t**3 + 12*t. Let c(h) = h**5 - h**4 + h**3 + h. Let s be (1 - (-9)/(-6))*2. Let q(i) = s*a(i) + 12*c(i). Factor q(z).
3*z**3*(z + 1)*(2*z - 1)
Suppose 0 = -5*i - 3*n + 18 + 45, n - 1 = 0. Let k be 1/(4/i) + -3. Factor k*y**4 - 4/9*y**3 + 2/9*y + 0 + 0*y**2 + 2/9*y**5.
2*y*(y - 1)**2*(y + 1)**2/9
Suppose -l = a + 4*l + 12, a = -2*l - 3. Factor 5 + 3*v**5 + a*v**4 - 5.
3*v**4*(v + 1)
Let l(o) be the third derivative of 1/75*o**5 + 0*o**4 - 3*o**2 + 0 + 0*o**3 + 0*o. Factor l(n).
4*n**2/5
Let q(m) = 3*m**3 - 27*m**2 - 39*m + 81. Let l(h) = -5*h**3 + 54*h**2 + 79*h - 161. Let c(w) = -6*l(w) - 11*q(w). What is d in c(d) = 0?
-5, 1
Let z = -13 - -45. Let q be ((-4)/16)/((-10)/z). Factor 0*b**2 - q*b**3 + 2/5*b**5 + 2/5*b + 0*b**4 + 0.
2*b*(b - 1)**2*(b + 1)**2/5
Let w(l) be the second derivative of 7/120*l**4 - 1/60*l**5 + 0 - 1/15*l**3 - 1/2*l**2 - l. Let k(s) be the first derivative of w(s). Let k(n) = 0. What is n?
2/5, 1
Let f = -3/34 - -77/102. Suppose 1 = -t + a, 3*a - 20 = -4*t - a. Factor 2/3*p + f*p**t + 0.
2*p*(p + 1)/3
Let k = 559/378 + 4/189. Factor -7/2*i**2 - k*i**3 + 5/2*i**4 + 1 + 3/2*i.
(i - 1)**2*(i + 1)*(5*i + 2)/2
Let w be -7 + 12 + (1 - 3). Let -6/5*b**2 + 2/5*b + 6/5*b**w + 0 - 2/5*b**4 = 0. What is b?
0, 1
Let v(l) = l**3 - 8*l**2 + 8*l. Let a be v(7). Suppose 0 = -f + 5*y - 9, a = 4*f + y + 1. Factor 2*o + 2*o**3 + o**4 - 4*o + 0*o**3 - f.
(o - 1)*(o + 1)**3
Let w(z) be the second derivative of 0*z**2 + 0 + 1/50*z**5 + 0*z**4 - 2*z + 0*z**3 - 1/75*z**6. Let w(i) = 0. Calculate i.
0, 1
Suppose -10*t + 53 = -7. Let p(w) be the third derivative of 1/24*w**4 + 0 + 0*w**5 - 1/120*w**t + 0*w**3 - w**2 + 0*w. Find f, given that p(f) = 0.
-1, 0, 1
Let r(o) = -o**3 - 4*o**2 - 2*o. Let s be r(-4). Factor -23*j**2 + s*j**2 - 4 + 36*j - 8.
-3*(j - 2)*(5*j - 2)
Let h be (4 - -213)*(-1)/(-18). Let o = h - 86/9. Factor -3*f**3 + o*f**4 - 2*f**2 + 4*f - 1/2*f**5 + 0.
-f*(f - 2)**3*(f + 1)/2
Suppose -2*c - 14 + 3 = 3*l, 3*c = -2*l - 9. Let n = 3 + c. Factor -2*d**3 - 2*d**2 + 0*d**n + 4*d**3.
2*d**2*(d - 1)
Factor 8/19*q**2 + 8/19*q + 0 + 2/19*q**3.
2*q*(q + 2)**2/19
Let a(q) be the second derivative of q**5/120 + q**4/72 - 7*q. Find z, given that a(z) = 0.
-1, 0
Let n(x) be the second derivative of -4*x + 5/39*x**3 + 0 + 1/195*x**6 - 1/26*x**4 - 2/13*x**2 - 1/130*x**5. Factor n(j).
2*(j - 1)**3*(j + 2)/13
Let w be 3/9 - (-37)/(-3). Let r = -9 - w. Factor -4/5*a**2 + 0*a + 0 + 2/5*a**r.
2*a**2*(a - 2)/5
Determine q so that -2/9*q + 2/9*q**3 - 2/9 + 2/9*q**2 = 0.
-1, 1
Let l(t) be the third derivative of -t**8/1008 + t**7/315 + t**6/360 - t**5/90 - 40*t**2. What is q in l(q) = 0?
-1, 0, 1, 2
Let w(g) be the first derivative of g**6/180 - g**5/60 - g**4/6 + g**3/3 + 2. Let x(c) be the third derivative of w(c). Find k, given that x(k) = 0.
-1, 2
Let y(p) be the third derivative of 3/64*p**4 + 0*p**3 + 0 + 0*p + 10*p**2 + 1/960*p**6 - 1/80*p**5. Factor y(n).
n*(n - 3)**2/8
Let q(k) be the second derivative of k**6/135 - k**4/27 + k**2/9 - 27*k. Factor q(v).
2*(v - 1)**2*(v + 1)**2/9
Let u(o) be the second derivative of -o**4/12 - o**3/3 - o**2/2 + 6*o. What is y in u(y) = 0?
-1
Factor -3 + 72*g**2 + 3 + 3*g**3 - 66*g**2.
3*g**2*(g + 2)
Let p(y) be the third derivative of -y**9/3780 + y**7/630 + 5*y**4/12 + 3*y**2. Let b(d) be the second derivative of p(d). Factor b(w).
-4*w**2*(w - 1)*(w + 1)
Let p(b) be the third derivative of 0 - 4/735*b**7 + 1/60*b**6 - 1/105*b**5 + 0*b + 0*b**3 - 1/84*b**4 - b**2. Factor p(n).
-2*n*(n - 1)**2*(4*n + 1)/7
Let u(w) be the second derivative of w**7/840 - w**6/240 + w**4/48 - w**3/24 + 5*w**2/2 + 3*w. Let m(c) be the first derivative of u(c). What is s in m(s) = 0?
-1, 1
Let i(f) be the second derivative of f**4/42 - 4*f**3/21 + 3*f**2/7 + 12*f. What is n in i(n) = 0?
1, 3
Let y = -2701/70 - -483/10. What is p in 18/7*p**5 + 2/7*p + 92/7*p**3 + 48/7*p**2 - 4/7 + y*p**4 = 0?
-1, 2/9
Let 3*u**3 + 4*u**5 - 5*u**3 - 2*u**3 - 2*u**5 + 2*u = 0. Calculate u.
-1, 0, 1
Let n(k) be the first derivative of -k**4/24 - k**3/3 - k**2 - 4*k/3 + 2. Factor n(p).
-(p + 2)**3/6
Let x(c) = -c + 12. Let a be x(9). Let q(l) be the first derivative of 0*l + 1/6*l**a + 3/8*l**4 + 0*l**2 - 2. Factor q(t).
t**2*(3*t + 1)/2
Let i(y) be the second derivative of y**5 + 2*y**4/3 - 10*y**3/3 - 4*y**2 + 6*y. Suppose i(f) = 0. What is f?
-1, -2/5, 1
Let x(m) be the second derivative of -m**6/5 - 3*m**5/20 + m**4/4 + 10*m. Factor x(o).
-3*o**2*(o + 1)*(2*o - 1)
Find s, given that 116 - 32*s + 10*s**2 - 132 - 30*s**2 - 4*s**3 = 0.
-2, -1
Suppose -1 = 2*v + 1. Let r = v - -4. Factor 3*t**2 + t + 2*t**3 - t**4 + t**r - 6*t**2.
-t*(t - 1)**3
Factor -26*k**2 + 200 + 185*k - 3*k**3 + 7*k**3 + 74*k**2 - 5*k.
4*(k + 2)*(k + 5)**2
Factor -4/11 + 1/11*j**2 + 3/11*j.
(j - 1)*(j + 4)/11
Let r be 9/411*(-852)/(-45). Let x = r - 2/137. Factor x*o**3 - 4/5*o**2 + 2/5*o + 0.
2*o*(o - 1)**2/5
Let a(k) = -k + 7. Let t be a(5). Factor 9*o**2 - 12*o**4 - o**2 + 4*o**3 + 3*o**2 - 3*o**t.
-4*o**2*(o - 1)*(3*o + 2)
Let a(t) = -4*t + 5*t + 3 - 2 + 0*t. Let n(u) = u**2 - 6*u + 2. Let b(l) = -2*a(l) - n(l). Solve b(v) = 0 for v.
2
Let d = -72534006/5339 + 774536/57. Let i = d - -2/281. Factor i*g**3 + 4*g**2 + 8/3*g + 2/3 + 2/3*g**4.
2*(g + 1)**4/3
Suppose -l = 2 - 8. Let f = -3 + l. Factor 2*o + 0*o**2 - o**3 + 3*o**f + 4*o**2.
2*o*(o + 1)**2
Suppose 4 + 8 = 4*t. Suppose 3*z - 4*z**4 + t*z**2 + 6*z**3 + 4*z**4 - 3*z**4 - 9*z = 0. Calculate z.
-1, 0, 1, 2
Let z(d) be the second derivative of 0*d**4 + 0 + 2*d + 1/4*d**2 - 1/80*d**5 + 1/8*d**3. Suppose z(w) = 0. What is w?
-1, 2
Suppose -8*n - 13 = -9*n. Suppose 5*u - 8*m + 3*m = -15, -n = -4*u - m. Factor 1/6*h**u + 0 + 1/6*h**3 - 1/3*h.
h*(h - 1)*(h + 2)/6
Let v(d) be the third derivative of 2*d**7/21 + 13*d**6/30 + 3*d**5/5 - d**4/6 - 4*d**3/3 + d**2 - 8*d. Factor v(i).
4*(i + 1)**3*(5*i - 2)
Let j = -2/34361 - 17421023/68722. Let o = 265 + j. Factor 13/2*q**2 + 0 + 27/2*q**3 + 7/2*q**5 + q + o*q**4.
q*(q + 1)**3*(7*q + 2)/2
Let b be 1/(-2)*(-8)/10. Let a be 2/(-10) - (0 - 1). Let -4/5*y**2 - b*y**5 + 0 + 2/5*y + a*y**4 + 0*y**3 = 0. Calculate y.
-1, 0, 1
Let q(f) = 4*f**3 + 9*f**2 + 24*f + 30. Let d(t) = 3*t**3 + 9*t**2 + 25*t + 29. Let y(x) = -3*d(x) + 2*q(x). Factor y(o).
-(o + 3)**3
Let q(s) = 4*s**2 - 32*s + 12. Let f(m) = -m**2 + 11*m - 4. Let y(t) = -8*f(t) - 3*q(t). Factor y(h).
-4*(h - 1)**2
Let w(f) = 15*f + 2. Let x be w(-6). Let j be (-4)/10 - x/20. Determine k, given that -1/2*k**3 + 3*k**2 + j - 6*k = 0.
2
Let s(a) be the third derivative of a**8/80640 - a**7/20160 - a**6/1440 - a**5/12 + 5*a**2. Let w(f) be the third derivative of s(f). Let w(o) = 0. What is o?
-1, 2
Let y(w) be the second derivative of -w**5/20 + 5*w**4/36 - w**3/18 - w**2/6 + 5*w. Factor y(d).
-(d - 1)**2*(3*d + 1)/3
Let o(s) = -3*s**2 - 11*s + 3. Let q = 0 + -4. Let d(b) = -b**2 - 4*b + 1. Let h(j) = q*o(j) + 11*d(j). Let h(u) = 0. What is u?
-1, 1
Suppose -4*f = -3*f - 6. Let b be 2/3*45/f. Factor 1/3 + 2/3*n**3 - 2/3*n**2 - 1/3*n - 1/3*n**b + 1/3*n**4.
-(n - 1)**3*(n + 1)**2/3
Let x = 6 + -4. Let u(j) be the second derivative of -1/10*j**5 + 0*j**x + 2/9*j**3 + 0 + 1/18*j**4 + j. Factor u(l).
-2*l*(l - 1)*(3*l + 2)/3
Factor 1/4*h + 1/2*h**2 + 1/4*h**3 + 0.
h*(h + 1)**2/4
Let x(p) = 2*p + 26. Let t be x(-12). Suppose -2*r = t*r. Let 1/2*v**2 + 0*v + r = 0. What is v?
0
Suppose 4*k = 13 + 11. Let v(a) = -4*a - 1. Let b be v(-2). Factor -5*y**2 - k*y + y + b*y**3 + 3*y.
y*(y - 1)*(7*y + 2)
Let d(k) be the second derivative of k**