 = -n + 20. Let a = -4 + 6. Factor 1 - 4*f + 2*f**2 - 3 - n*f**a.
-2*(f + 1)**2
Let j(b) be the second derivative of 5*b**4/12 + 5*b**3/3 - 18*b. Factor j(w).
5*w*(w + 2)
Let y(u) = 3*u**3 - 9*u**2 - 15*u - 9. Let h(p) be the first derivative of -7*p**4/4 + 6*p**3 + 31*p**2/2 + 19*p + 5. Let b(w) = -6*h(w) - 13*y(w). Factor b(j).
3*(j + 1)**3
Let u(i) = -2*i**2 - 12*i - 10. Let b(d) = d + 3 - 2 + 0*d. Let f(x) = -12*b(x) - u(x). Find z, given that f(z) = 0.
-1, 1
Let c(k) be the third derivative of -k**7/280 - k**6/80 - k**5/80 + 54*k**2. Factor c(d).
-3*d**2*(d + 1)**2/4
Let n = 21 - 21. Let h(a) be the second derivative of 0 - 1/4*a**2 + 1/24*a**4 + n*a**3 - 3*a. Factor h(r).
(r - 1)*(r + 1)/2
Let n be (144/(-200))/((-6)/15). Determine j, given that -21/5*j**4 + n*j**3 + 0 + 21/5*j**2 - 3*j**5 + 6/5*j = 0.
-1, -2/5, 0, 1
Let x be (-198)/(-2673)*9/1. Determine o, given that 3*o - x - o**2 - 4/3*o**3 = 0.
-2, 1/4, 1
Let h(a) be the first derivative of 3*a**4/4 + a**3 - 3*a**2/2 - 3*a - 6. Solve h(p) = 0.
-1, 1
Let m(o) be the third derivative of o**5/150 + o**4/20 - 4*o**3/15 - 12*o**2. Factor m(q).
2*(q - 1)*(q + 4)/5
Let o(p) be the second derivative of -p**7/4200 + p**6/600 + p**4/3 + 4*p. Let s(m) be the third derivative of o(m). Let s(x) = 0. Calculate x.
0, 2
Let t(a) be the first derivative of 0*a - 2 - 1/6*a**4 + 2/9*a**3 + 1/3*a**2 - 2/15*a**5. Suppose t(d) = 0. What is d?
-1, 0, 1
Let g(o) be the first derivative of 2*o**3/9 + o**2 + 4*o/3 + 6. Suppose g(y) = 0. Calculate y.
-2, -1
Let t(w) be the third derivative of w**7/70 + w**6/80 - w**5/20 - w**4/16 - 4*w**2. Let t(l) = 0. What is l?
-1, -1/2, 0, 1
Suppose 2*h - 46 = 4*d, -h - 3*h = 12. Let o be (-2)/8 + d/(-4). Factor -3*s**o - 1 + 2*s + 4*s**3 - 3*s**3 + s**4.
(s - 1)**3*(s + 1)
Let m be (-8 + 8)/(4/(-2)). Let u = m + 2. Factor 0*o + 6/7*o**5 - 2/7*o**u + 0 + 10/7*o**3 - 2*o**4.
2*o**2*(o - 1)**2*(3*o - 1)/7
Let b(z) be the second derivative of z**5/80 + 5*z**4/48 + z**3/3 + z**2/2 - 12*z. Factor b(d).
(d + 1)*(d + 2)**2/4
Factor -1 - 7*v**2 + v**2 - 8*v + 3*v**2 - 4*v**2.
-(v + 1)*(7*v + 1)
Let a(p) be the second derivative of p**7/280 - p**6/40 + p**5/20 - p**3/3 - 2*p. Let h(t) be the second derivative of a(t). Solve h(o) = 0 for o.
0, 1, 2
Factor 0*b**3 - b**3 - 2*b**3.
-3*b**3
Factor 0*n - 1/3*n**5 + n**3 + 0 - 2/3*n**2 + 0*n**4.
-n**2*(n - 1)**2*(n + 2)/3
Let c(s) be the third derivative of -s**5/60 + s**3/6 + 7*s**2. Suppose c(l) = 0. What is l?
-1, 1
Let a be 177/(-540) + 3/9*1. Let p(o) be the third derivative of 0*o + a*o**5 - 1/360*o**6 + 0 + 1/72*o**4 - 1/18*o**3 - 2*o**2. Find n, given that p(n) = 0.
-1, 1
Let u(n) be the second derivative of 1/4*n**4 + 1/10*n**5 + 0*n**3 + n + 0 - 1/2*n**2. Solve u(j) = 0 for j.
-1, 1/2
Let t(l) = -l**2 + l + 1. Let a(f) = 6*f**3 - 14*f + 8 - 8*f**2 + 14*f. Let m(p) = a(p) - 6*t(p). Factor m(u).
2*(u - 1)*(u + 1)*(3*u - 1)
Let y(m) be the first derivative of m**3 + 3*m**2/2 + 7. Let y(n) = 0. Calculate n.
-1, 0
Let b(v) = -v**3 - 6*v**2 - 5*v. Let a be b(-5). Solve 0*n**3 - 1/2 + n**2 - 1/2*n**4 + a*n = 0 for n.
-1, 1
Suppose 5*j - 3*k + 56 = 0, k - 40 = 3*j - 4*k. Let d = -8 - j. Factor 8/5 + 2/5*h**d + 8/5*h.
2*(h + 2)**2/5
Let d(o) be the first derivative of 0*o + o**2 - 5 + 2*o**4 + 21/5*o**5 - 11/3*o**3. Factor d(u).
u*(u + 1)*(3*u - 1)*(7*u - 2)
Let f(l) be the third derivative of l**2 + 0*l**3 + 0 + 0*l - 1/30*l**5 - 1/12*l**4. Find z, given that f(z) = 0.
-1, 0
Let l = -18 - -18. Let u(m) be the first derivative of -1 + 1/16*m**4 + l*m**3 + 0*m**2 - 1/10*m**5 + 1/24*m**6 + 0*m. What is t in u(t) = 0?
0, 1
Factor 0*j**3 + 0 - 1/7*j**5 + 0*j + 0*j**2 - 2/7*j**4.
-j**4*(j + 2)/7
Let i(j) = 0 - j**2 - 21*j + 6*j + 11*j - 3. Let x be i(-3). Determine y, given that -2/3*y**5 - 2/3*y**3 + 0*y**2 + 4/3*y**4 + 0*y + x = 0.
0, 1
Suppose 0 + 30*g**2 - 5/2*g**4 + 0*g - 5/2*g**5 + 20*g**3 = 0. Calculate g.
-2, 0, 3
Factor 2*c + 5*c + 5*c**2 - 5*c + 13*c.
5*c*(c + 3)
Let m be 3/((-42)/20) - (7 + -9). Factor -4/7*p**2 + 2/7*p**5 + 2/7 + 2/7*p + 2/7*p**4 - m*p**3.
2*(p - 1)**2*(p + 1)**3/7
Let r(a) = a**2 + 5*a - 6. Let y be r(-6). Solve y*o**2 + 4*o - 2 - o**2 + 1 - 2*o = 0.
1
Let b be 3*4/(-8) - (-12)/8. Let f be -2*-2*(-1)/(-16). Let b*x + 0 - f*x**3 - 1/4*x**4 + 0*x**2 = 0. What is x?
-1, 0
Let d = 83/170 + -3/34. Suppose -3*k = -5*k + 4. Factor 0 + 0*b + d*b**3 - 2/5*b**k.
2*b**2*(b - 1)/5
Let v(g) be the third derivative of -g**7/315 - 2*g**6/45 - 23*g**5/90 - 7*g**4/9 - 4*g**3/3 - 23*g**2. Solve v(f) = 0 for f.
-3, -2, -1
Factor 1/7*y**2 + 1/7 + 2/7*y.
(y + 1)**2/7
Let b(y) be the second derivative of -y**6/50 - 3*y**5/50 + y**3/5 + 3*y**2/10 - 4*y. Let b(l) = 0. Calculate l.
-1, 1
Solve -17*m**4 + 9*m**2 + 52*m**3 - 7*m**4 + 22*m - 57*m**2 - 6*m + 4*m**5 = 0 for m.
0, 1, 2
Let j = 83 - 331/4. Let x(b) be the first derivative of 0*b + 3/4*b**2 - j*b**3 - 3. Solve x(l) = 0.
0, 2
Let p = 43 - 40. Factor 4/15*c**p + 0 - 2/15*c + 0*c**2 - 2/15*c**5 + 0*c**4.
-2*c*(c - 1)**2*(c + 1)**2/15
Factor -6*b**2 - 2*b**3 - b**4 + 7*b**2 + 2*b**4.
b**2*(b - 1)**2
Factor 2/21*f**2 - 2/21*f - 4/21.
2*(f - 2)*(f + 1)/21
Let p be 130/(-200) + (-4)/(-6). Let o(t) be the third derivative of 1/300*t**6 + t**2 + 0*t - p*t**4 + 1/15*t**3 - 1/150*t**5 + 0. Find z such that o(z) = 0.
-1, 1
Factor 18/7*t**2 + 2 - 30/7*t - 2/7*t**3.
-2*(t - 7)*(t - 1)**2/7
Let n(j) be the first derivative of 1/6*j**4 + j**2 - 1/3*j**3 + 0*j - 1 - 1/30*j**5. Let l(o) be the second derivative of n(o). Factor l(g).
-2*(g - 1)**2
Let p(v) be the first derivative of -5*v**3/3 + 25*v**2 - 125*v - 3. Factor p(d).
-5*(d - 5)**2
Let d(z) be the second derivative of z**4/108 - z**3/18 - 2*z**2/9 - 2*z. Find x, given that d(x) = 0.
-1, 4
Let y be -4 - -5 - 4000/(-9). Let x = y + -445. Solve 4/9 - 4/9*p**3 + x*p**4 - 8/9*p**2 + 2/9*p + 2/9*p**5 = 0.
-2, -1, 1
Let b(o) = -o**3 + o**2 + o + 1. Let v(w) = 5*w + w**4 + 0*w**4 + 9*w**2 + 2 - 5*w**3 - 6*w**2 + 0. Let c(d) = 6*b(d) - 2*v(d). Factor c(x).
-2*(x - 1)**3*(x + 1)
Let a(r) = -2*r**2 + 3*r. Let i(q) = q**2 - q. Suppose 2*o - 10 = 0, 0*o - 11 = -3*y - o. Let b(v) = y*a(v) + 5*i(v). Factor b(k).
k*(k + 1)
Factor 0*k + 2/13*k**3 + 0*k**2 + 2/13*k**5 + 4/13*k**4 + 0.
2*k**3*(k + 1)**2/13
Let d(x) be the third derivative of 0*x**6 + 1/30*x**5 + 0 + 0*x**3 - 1/105*x**7 - 2*x**2 + 0*x**4 + 0*x. Suppose d(q) = 0. Calculate q.
-1, 0, 1
Let n(i) be the first derivative of i**7/105 - i**5/15 + i**3/3 + 3*i**2 + 1. Let a(f) be the second derivative of n(f). Factor a(h).
2*(h - 1)**2*(h + 1)**2
Let m = -1/56 - -29/56. Factor -m*o**4 + 1/2*o**2 + 0*o + 0*o**3 + 0.
-o**2*(o - 1)*(o + 1)/2
Let x(j) be the second derivative of j**7/4 - 4*j**6/5 + 33*j**5/40 - j**4/4 + 10*j. Factor x(d).
3*d**2*(d - 1)**2*(7*d - 2)/2
Let -3*p**4 - 3/2*p**5 + 3*p**2 + 0 + 3/2*p**3 + 0*p = 0. What is p?
-2, -1, 0, 1
Determine z so that -1/4*z**3 + 3/4*z**2 + 0 + 0*z = 0.
0, 3
Let m(p) be the second derivative of 2*p**5/5 - p**4/3 - 6*p. Factor m(k).
4*k**2*(2*k - 1)
Suppose -11 = -8*a + 13. Suppose 1/3*t**4 + 2/3*t - 2/3*t**a + 0*t**2 - 1/3 = 0. Calculate t.
-1, 1
Let y be (0 - 1 - 3)/(-2). Let m be -4 + (-3)/(-1) + 1. Factor m + 4/3*d - 2/3*d**y.
-2*d*(d - 2)/3
Let x = -1475/3 - -501. Let n = -9 + x. Suppose 1/3*b**2 + 0*b - n = 0. What is b?
-1, 1
Let v(r) be the third derivative of -r**6/300 + r**5/50 + r**4/60 - r**3/5 - 8*r**2. Factor v(s).
-2*(s - 3)*(s - 1)*(s + 1)/5
Let x(w) be the first derivative of -w**5 - 15*w**4/2 - 5*w**3/3 + 60*w**2 - 80*w + 74. Find p such that x(p) = 0.
-4, 1
Let h(m) be the third derivative of 2*m**7/105 + m**6/3 + 11*m**5/5 + 20*m**4/3 + 32*m**3/3 + 46*m**2. Factor h(u).
4*(u + 1)**2*(u + 4)**2
Let f be ((-24)/(-32))/(1/4). Factor 4 - 1 + 2*d**4 + f*d**3 - 7*d**3 - 5 + 4*d.
2*(d - 1)**3*(d + 1)
Suppose 4*d + 13 = 2*v + 3*v, d - 2*v + 7 = 0. Let a(k) be the first derivative of -1 - 1/3*k**2 - 4/3*k + 2/9*k**d. Factor a(l).
2*(l - 2)*(l + 1)/3
Let f(u) be the first derivative of 1/1620*u**6 + 0*u**2 - 2 + 0*u + 1/12*u**4 + 1/3*u**3 + 1/90*u**5. Let b(d) be the third derivative of f(d). Factor b(g).
2*(g + 3)**2/9
Let u(g) = g**2 - 14*g + 15. Let x be u(13). Let i(o) be the third derivative of o**x + 0 + 0*o + 1/70*o**5 - 1/42*o**4