et z be s(6). Factor 2/9*v**z - 2/9*v**2 - 2/3*v**4 + 0*v + 0 + 2/3*v**3.
2*v**2*(v - 1)**3/9
Let k be -1 + 4 + (0 - 1). Solve -4*i + 11*i**4 - 9*i**4 - k - 3*i**3 + 7*i**3 = 0 for i.
-1, 1
Let g(o) = -o**3 - 14*o**2 + 13*o - 27. Let f be g(-15). What is w in -1/4*w**5 - 3/4*w**4 + 0 + 0*w - 1/4*w**2 - 3/4*w**f = 0?
-1, 0
Let n(q) = -4*q**2 + 2. Let z(u) be the third derivative of -u**4/24 + 2*u**2. Let h = -2 - -1. Let d(k) = h*n(k) + 2*z(k). Factor d(b).
2*(b - 1)*(2*b + 1)
Let k(s) be the third derivative of -s**5/420 + s**4/21 - 8*s**3/21 + 5*s**2. Determine b so that k(b) = 0.
4
Let y = 2 + 1. Let j(i) be the first derivative of 1/2*i**2 - y - 1/3*i**3 + 0*i. Suppose j(z) = 0. Calculate z.
0, 1
Let r(a) be the first derivative of -2*a**5/5 + a**4 + 10*a**3/3 - 6*a**2 - 51. Factor r(q).
-2*q*(q - 3)*(q - 1)*(q + 2)
Let q(p) be the third derivative of p**7/840 - 18*p**2. Factor q(l).
l**4/4
Let m(x) = 63*x**3 + 399*x**2 + 447*x + 177. Let l(r) = -4*r**3 - 25*r**2 - 28*r - 11. Let v(h) = 33*l(h) + 2*m(h). Factor v(g).
-3*(g + 1)*(g + 3)*(2*g + 1)
Let u = -83 + 83. Let i(b) be the first derivative of u*b**4 + 2*b**3 + 0*b - 4 - 2*b**2 - 2/5*b**5. Let i(y) = 0. Calculate y.
-2, 0, 1
Let h = 3884/15 + -1143/5. Let r = h + -30. Factor 0*j + 0*j**2 + 0 - r*j**5 + 2/3*j**4 - 1/3*j**3.
-j**3*(j - 1)**2/3
Suppose -60 = -4*v - 20. Let x = v - 8. Determine z, given that 0*z**2 - 3*z - 6*z**x + 3*z**2 + 0*z**2 = 0.
-1, 0
Suppose -6*h - 9 = 3*p - 9*h, -15 = -3*h. Factor -2/3*a**p + 0 + 0*a - 1/3*a**3.
-a**2*(a + 2)/3
Let a(w) be the first derivative of 3*w**4/32 + 3*w**3/4 + 27*w**2/16 + 3*w/2 + 11. Factor a(v).
3*(v + 1)**2*(v + 4)/8
Suppose -4*n = -2*a + 30, 0*n - 35 = 3*n - 4*a. Let h(f) = -2*f**2 - 7*f - 5. Let y(j) = 4*j**2 + 13*j + 9. Let g(r) = n*h(r) - 3*y(r). Factor g(c).
-2*(c + 1)**2
Let z(g) be the first derivative of -g**5/25 + 2*g**3/5 + 4*g**2/5 + 3*g/5 - 12. Factor z(q).
-(q - 3)*(q + 1)**3/5
What is w in -3/2*w**3 + 6*w**2 - 9/2*w + 0 = 0?
0, 1, 3
Factor -10/13*f + 2/13 - 2*f**2 - 14/13*f**3.
-2*(f + 1)**2*(7*f - 1)/13
Let n(i) be the third derivative of i**6/30 + 4*i**5/15 + i**4/6 - 4*i**3 - 16*i**2. Factor n(p).
4*(p - 1)*(p + 2)*(p + 3)
Let z(g) = -g**4 + g**2 + g - 1. Suppose 8 + 0 = 4*x. Let j(f) = f + 2*f**3 + f - 3*f**4 - x - f**4 + 2*f**2. Let n(a) = j(a) - 2*z(a). Factor n(r).
-2*r**3*(r - 1)
Let n(j) be the third derivative of j**7/2100 + j**6/150 + j**5/25 + 2*j**4/15 + j**3/2 + j**2. Let p(v) be the first derivative of n(v). Factor p(z).
2*(z + 2)**3/5
Let j(h) be the second derivative of 0*h**3 + 1/50*h**5 + 0 + 0*h**2 - 1/75*h**6 + 0*h**4 + 4*h. Suppose j(q) = 0. Calculate q.
0, 1
Suppose -3*m + 12 = 3*z, 3*z - m + 6 = 5*z. Determine t, given that -t**2 + 5*t**2 - 5*t**2 + 3*t**z + 2*t = 0.
-1, 0
Let s(j) = -j**2 + 5*j - 2. Let q be s(5). Let g be q + 4 + (-5)/3. Factor g*n**4 + 2/3*n**3 + 0*n**2 - 1/3 - 2/3*n.
(n - 1)*(n + 1)**3/3
Let y = 6 + 2. Let d be 9*y/420*5. Solve -2*u - d*u**2 - 4/7 = 0 for u.
-2, -1/3
Let c(n) be the first derivative of 2*n**5/35 + n**4/7 + 2*n**3/21 - 5. Suppose c(j) = 0. What is j?
-1, 0
Let y(r) be the second derivative of -2*r - 1/50*r**5 + 1/3*r**3 - 1/10*r**4 + 1/75*r**6 + 0 - 2/5*r**2. What is o in y(o) = 0?
-2, 1
Let p(c) be the first derivative of -c**4/20 + c**2/10 - 6. Factor p(b).
-b*(b - 1)*(b + 1)/5
Solve 14/9*g + 0 + 2/9*g**2 = 0.
-7, 0
Let -3/4*p**2 - 11/4*p - 3/2 = 0. What is p?
-3, -2/3
Let p be 35/4 + 6/(-8). Suppose 3*g - 4*g - 4*j = -p, -2*g = -3*j + 6. Find n such that 1/2*n**2 - n + g = 0.
0, 2
Let t(f) be the third derivative of -3/40*f**6 - f**2 - f**3 + 1/20*f**5 + 0*f + 3/8*f**4 + 1/70*f**7 + 0. Factor t(x).
3*(x - 2)*(x - 1)**2*(x + 1)
Suppose -5*x + 30 = 3*v - 0*v, 4*v = 4*x + 8. Let m(b) = -b + 1. Let s be m(-4). Factor -z + 2*z**v - 2*z**2 + 2*z**4 + 0*z**s - 4*z**5 + 3*z**5.
z*(z - 1)*(z + 1)**3
Factor 44*d + 2 + d**2 - 40*d + d**2.
2*(d + 1)**2
Let o(j) = 8*j**5 + 4*j**4 - 8*j**3 - 8*j**2. Let f(u) = 7*u**5 + 4*u**4 - 7*u**3 - 7*u**2. Let h(a) = 4*f(a) - 3*o(a). Factor h(c).
4*c**2*(c - 1)*(c + 1)**2
Let d(m) be the first derivative of -m**6/4 - 7*m**5/5 - 13*m**4/4 - 4*m**3 - 11*m**2/4 - m + 1. Factor d(k).
-(k + 1)**4*(3*k + 2)/2
Let o be (-4)/(-10) + (-23)/(-5). Let v = o - 3. Factor -l + l + v*l**3 + 5*l**4.
l**3*(5*l + 2)
Let t(c) = 4*c - 5 + c + 0*c**2 - c**2. Let r(h) = h - 1. Suppose 0 = 3*v - 2 - 7. Let i(f) = v*t(f) - 15*r(f). Factor i(q).
-3*q**2
Let k = -8 - -12. Let a = k - 2. Determine s, given that -2/5*s**4 + 0*s**a + 0 + 2/5*s**3 + 0*s = 0.
0, 1
Let l(x) be the third derivative of 2*x**7/35 - x**6/5 - 11*x**5/20 - 3*x**4/8 - 26*x**2. Let l(c) = 0. Calculate c.
-1/2, 0, 3
Find d such that 4/11*d + 2/11*d**2 + 0 = 0.
-2, 0
Let o(i) be the second derivative of i**6/180 + i**3/3 - i. Let l(k) be the second derivative of o(k). Factor l(d).
2*d**2
Let h(m) be the third derivative of m**8/1344 + m**7/280 + m**6/160 + m**5/240 - 7*m**2. Solve h(r) = 0.
-1, 0
Suppose s - 4*s = -6. Let -2*y**s - 2 - 8*y + 1 - 8 + 1 = 0. Calculate y.
-2
Determine m so that -1/2*m**4 + 7/2*m**3 + 27 - 9/2*m**2 - 27/2*m = 0.
-2, 3
Let f = -16 + 20. Factor 0*l + 1/4*l**f - 1/2*l**3 + 1/4*l**2 + 0.
l**2*(l - 1)**2/4
Let c(q) be the second derivative of 1/80*q**5 + 0 + 4*q + 0*q**2 + 1/24*q**4 + 1/24*q**3. Factor c(x).
x*(x + 1)**2/4
Factor -31*v**2 - 2*v**5 + 4*v**5 + 6*v**3 + 31*v**2 - 8*v**4.
2*v**3*(v - 3)*(v - 1)
Let h(x) = 8*x**2 + x + 3. Let p(i) = 7*i**2 + 3. Let w(s) = 6*h(s) - 7*p(s). Let q be w(5). Factor q*l**3 + 3*l + 0*l**2 - l + 4*l**2.
2*l*(l + 1)**2
Solve 3/2*k + 3/4*k**2 + 0 = 0.
-2, 0
Determine k so that -8*k**2 - 4*k - 1 - 1 + 6*k**2 = 0.
-1
Let n(f) be the third derivative of -f**9/60480 + f**8/20160 - f**5/10 + 4*f**2. Let h(a) be the third derivative of n(a). Determine l, given that h(l) = 0.
0, 1
Let n(g) = g**2 + 15*g + 50. Let i be n(-5). Factor 1/5*x**2 + 0 + i*x.
x**2/5
Let y(v) be the first derivative of v**3/3 - 3*v**2/2 + 4. Let t be y(3). Determine l, given that 1/4*l + 1/4*l**4 + 3/4*l**2 + 3/4*l**3 + t = 0.
-1, 0
Let x(l) = 28*l**4 + 4*l**3 + 12*l**2 - 28*l + 8. Let g(o) = -o**4 - o**2 + o. Let y(t) = -24*g(t) - x(t). Factor y(d).
-4*(d - 1)**2*(d + 1)*(d + 2)
Let q be -4 - (4 + (-168)/20). Factor 2/5*o + 0*o**3 - q*o**5 + 0 - 4/5*o**4 + 4/5*o**2.
-2*o*(o - 1)*(o + 1)**3/5
Let w(s) = s**2 - s + 1. Let d be w(2). Let r be (d/(-6))/((-6)/4). Factor 0*n - r*n**2 + 0.
-n**2/3
Let c(i) be the first derivative of -i**6/180 - i**5/60 + i**3 + 3. Let w(l) be the third derivative of c(l). Factor w(u).
-2*u*(u + 1)
Suppose 16*t - 111 + 47 = 0. Determine y so that -3/8*y**t + 0 + 3/8*y**5 + 3/8*y**2 + 0*y - 3/8*y**3 = 0.
-1, 0, 1
Let z(f) be the first derivative of -2 - 9/8*f**4 + 1/4*f**3 + 3/4*f**2 + 0*f. Factor z(h).
-3*h*(2*h + 1)*(3*h - 2)/4
Let x = 2/3 + -1/3. Let m = 73/3 + -24. Suppose 2/3 - m*f - x*f**2 = 0. Calculate f.
-2, 1
Let o = 277/12 + -23. Let s(j) be the first derivative of o*j**4 + 1/3*j**3 + 1/3*j + 1 + 1/2*j**2. What is a in s(a) = 0?
-1
Let h be -5*(-8)/20 + 2. Suppose 6*y**2 + 4*y**h + 0 - 26/3*y**3 - 4/3*y = 0. What is y?
0, 1/2, 2/3, 1
Let s(l) be the first derivative of -l**5/20 + 5*l**4/36 + l**3/9 + 4*l - 5. Let u(z) be the first derivative of s(z). Factor u(c).
-c*(c - 2)*(3*c + 1)/3
Let b(z) be the second derivative of z**6/50 - 9*z**5/50 + 9*z**4/20 - 2*z**3/5 - 6*z. Let b(g) = 0. Calculate g.
0, 1, 4
Factor -21 + 6*u + 6*u - 2*u**2 + 3.
-2*(u - 3)**2
Solve 5 - 2 + 6*x + 2*x**2 + x**2 = 0.
-1
Let w(i) be the first derivative of i**3/15 + 3*i**2/10 + 9. Factor w(z).
z*(z + 3)/5
Factor 25*u + 16*u**4 - 25*u + 4*u**5 + 8*u**3 - 16*u**2 - 12*u.
4*u*(u - 1)*(u + 1)**2*(u + 3)
Suppose -3*z - 33 = -3*t, t - 5*t + 40 = -5*z. Suppose -4*j + t = -j. Factor 18*x**j - 16/3*x**2 + 24*x**3 + 0*x + 0 - 36*x**4.
2*x**2*(3*x - 2)**3/3
Solve 0 + 6/7*i**5 + 2*i**4 + 0*i + 10/7*i**3 + 2/7*i**2 = 0 for i.
-1, -1/3, 0
Let d(p) be the first derivative of -p**5/5 - 41. Factor d(w).
-w**4
Let d be 0 - (3 - -3) - 0. Let i be ((-8)/d + -2)*-3. Factor 1 + 5/2*j**3 + 6*j**i + 9/2*j.
(j + 1)**2*(5*j + 2)/2
Let x(c) be the second derivative of 0 + 1/4*c**5 + 1/6*c**3 + 1/3*c**2 - 5*c - 2/45*c**6 - 4/9*c**4. Determine t so that x(t) = 0.
-1/4, 1, 2
Le