*n = 8*n. Let b = -28/39 - -18/13. Factor 2/3*a**f + b - 4/3*a.
2*(a - 1)**2/3
Let t = 2 - -6. Let i(r) = r - 6. Let n be i(t). Factor -5*q + q - q**n + 2 + 3*q**2.
2*(q - 1)**2
Suppose 2*w + 6*w = 192. Let g = 29 - w. Factor 1/3*b**3 + 0*b**2 - 2/3*b**g + 0 + 0*b - 1/3*b**4.
-b**3*(b + 1)*(2*b - 1)/3
Let m be ((-1)/1)/((-1)/35). Suppose 0 = -31*z + m*z. Factor 3/2*n**3 - 1/2*n**2 - 3/2*n**4 + 0 + z*n + 1/2*n**5.
n**2*(n - 1)**3/2
Let s = 37/24 - 7/8. Let x(d) be the first derivative of -s*d**3 - 2*d - 1 + 2*d**2. Solve x(o) = 0.
1
Let o(z) be the first derivative of -4/9*z - 4 - z**2 - 14/27*z**3. Factor o(l).
-2*(l + 1)*(7*l + 2)/9
Let u(b) = 9*b**2 - 7*b + 8. Let y be 2 - (-3 - -2)*1. Let x(o) = 5*o**2 - 3*o + 4. Let f(c) = y*u(c) - 5*x(c). Factor f(g).
2*(g - 2)*(g - 1)
Let l(o) be the third derivative of 1/15*o**5 + 0 + 0*o**3 - 4*o**2 + 0*o + 0*o**4. What is f in l(f) = 0?
0
Factor -5*f + 20*f**2 - 10/3 - 35/3*f**3.
-5*(f - 1)**2*(7*f + 2)/3
Let v be (-4 - -5)/(2/(-16)). Let w(g) = 3*g**2 - 5*g. Let x(b) = 5*b**2 - 8*b. Let s(y) = v*w(y) + 5*x(y). Factor s(u).
u**2
Let q(s) be the second derivative of s**4/12 - 7*s**3/6 + 5*s**2 - 16*s. Find v such that q(v) = 0.
2, 5
Let n(h) = h**2 - h + 1. Let q(t) = -6*t**2 + 23*t - 86. Let l(u) = -5*n(u) - q(u). Factor l(k).
(k - 9)**2
Let f = 362/3 - 120. Factor 2*k + f*k**2 + 4/3.
2*(k + 1)*(k + 2)/3
Suppose 0 = -3*n - 0*n + 12. Let m(z) be the first derivative of -1/10*z**n + 1 + 0*z + 2/15*z**3 + 2/5*z**2. Factor m(u).
-2*u*(u - 2)*(u + 1)/5
Let i(x) be the third derivative of x**8/6720 + x**7/1680 - x**5/30 - 5*x**2. Let m(n) be the third derivative of i(n). Factor m(g).
3*g*(g + 1)
Let q be (5*(-12)/(-8))/6*4. Let v(y) be the second derivative of 1/6*y**4 - 1/10*y**q + 0 - 3*y - 1/30*y**6 - 1/2*y**2 + 1/6*y**3 + 1/42*y**7. Solve v(s) = 0.
-1, 1
Let v = -2950274033/1017 - -2900958. Let w = v + -3/113. Determine y so that 0*y**2 + 4/9*y**3 - w*y**5 + 0 + 0*y**4 - 2/9*y = 0.
-1, 0, 1
Factor -12/5*u - 32/5*u**2 + 4*u**5 + 88/5*u**3 - 72/5*u**4 + 8/5.
4*(u - 1)**4*(5*u + 2)/5
Let m(t) be the first derivative of 3*t**5/5 + 3*t**4 + 3*t**3 - 6*t**2 - 12*t + 3. Factor m(c).
3*(c - 1)*(c + 1)*(c + 2)**2
Let h(t) = 10*t**2 + 24*t - 11. Let a(i) = -i**2 - i + 1. Let y(b) = 22*a(b) + 2*h(b). Suppose y(c) = 0. Calculate c.
0, 13
Let g = 5 - 5. Let c(h) be the third derivative of 2*h**2 - 1/6*h**3 + 0 - 1/60*h**5 + g*h + 1/12*h**4. Factor c(p).
-(p - 1)**2
Let f(c) be the second derivative of -c**6/540 - c**5/90 - c**3/3 + c. Let d(n) be the second derivative of f(n). Factor d(q).
-2*q*(q + 2)/3
Let z = 61/390 - -2/195. Let f(r) be the second derivative of -r**2 - z*r**4 - 2*r + 0 + 2/3*r**3. Suppose f(t) = 0. What is t?
1
Let x(z) be the first derivative of -1/540*z**6 + 1/90*z**5 + 0*z + 0*z**2 + z**3 - 1/36*z**4 + 1. Let j(r) be the third derivative of x(r). Factor j(i).
-2*(i - 1)**2/3
Let z(m) be the first derivative of 0*m**2 + 2 + 6/5*m**5 + 2/9*m**3 - m**4 + 0*m - 4/9*m**6. Suppose z(c) = 0. Calculate c.
0, 1/4, 1
Factor -48*w - 29 - 45 - w**3 + 28 - 18 - 12*w**2.
-(w + 4)**3
Let x(m) be the first derivative of -3*m**4/16 - 3*m**3/4 - 9*m**2/8 - 3*m/4 + 11. Suppose x(s) = 0. What is s?
-1
Let h(i) be the first derivative of -i**6/105 - i**5/35 - i**4/42 + 2*i - 2. Let v(q) be the first derivative of h(q). Suppose v(o) = 0. Calculate o.
-1, 0
Let n be ((-6)/10)/((-7)/35). Let z(g) be the second derivative of -1/14*g**4 + 1/70*g**5 - 1/7*g**2 + 2*g + 1/7*g**n + 0. Factor z(q).
2*(q - 1)**3/7
Suppose 0 = -4*z + 8*z - 24. Suppose 20 = z*s + 2. Factor 2/3*x**4 + 2/3 + 0*x - 4/3*x**2 + 0*x**s.
2*(x - 1)**2*(x + 1)**2/3
Let p be 2*(2 - (-622)/4). Let r be (18/p)/(2/10). Determine g, given that 2/7*g**2 - r*g**3 + 2/7*g - 2/7 = 0.
-1, 1
Let q(j) = 4*j**5 + 7*j**4 + 3*j**3 - 2*j - 2. Let u(o) = 4*o**5 + 8*o**4 + 4*o**3 - 3*o - 3. Let w(k) = 3*q(k) - 2*u(k). Factor w(c).
c**3*(c + 1)*(4*c + 1)
Let p(h) = -6*h**3 + 24*h**2 - 22*h + 2. Let w(o) = 19*o**3 - 72*o**2 + 67*o - 7. Let l(u) = -7*p(u) - 2*w(u). Solve l(j) = 0 for j.
0, 1, 5
Let i(j) be the third derivative of -j**8/672 + j**7/140 - j**6/240 - j**5/40 + j**4/24 - 2*j**2. Determine a, given that i(a) = 0.
-1, 0, 1, 2
Let g(a) be the third derivative of -a**8/448 - a**7/70 - a**6/40 + 17*a**2. Find k, given that g(k) = 0.
-2, 0
Let x(g) = -7 + 0 - 3 + 1 - g. Let w be x(-9). Determine n, given that 1/2*n**3 + 0*n + 1/4*n**2 - 3/4*n**4 + w = 0.
-1/3, 0, 1
Factor x**2 + 4 + 3*x**2 - 2 - 10 - 4*x.
4*(x - 2)*(x + 1)
Let m(w) = 11*w**2 - 18*w - 29. Let a(n) = 2*n**2 - 3*n - 5. Let b(f) = -34*a(f) + 6*m(f). Factor b(u).
-2*(u + 1)*(u + 2)
Let j be (1 - (2 - 4)) + 3. Let r(n) be the second derivative of -1/60*n**j + 1/20*n**5 + n + 0 + 0*n**4 - 1/6*n**3 + 1/4*n**2. Factor r(w).
-(w - 1)**3*(w + 1)/2
Let z(m) = 27*m**3 + 75*m**2 + 96*m + 45. Let b(q) = q**4 + 26*q**3 + 74*q**2 + 96*q + 46. Let x(i) = 3*b(i) - 2*z(i). Determine d so that x(d) = 0.
-2
Suppose -60*o = -o - 118. Factor 32/5 + 2/5*g**o - 16/5*g.
2*(g - 4)**2/5
Let f = -225/22 + 129/11. Let -f*k**4 + 0*k**3 + 0 - 3/4*k + 3/4*k**5 + 3/2*k**2 = 0. What is k?
-1, 0, 1
Let p(q) be the third derivative of -q**6/600 + q**5/100 - q**4/40 + q**3/30 + 10*q**2. Factor p(y).
-(y - 1)**3/5
Suppose 11 - 31 = -5*d. Let k(n) = n**2 - n - 2. Let l be k(3). Factor 2*p + l - 2*p**3 + p + d*p - p.
-2*(p - 2)*(p + 1)**2
Let u be (0/4)/((-2)/2) + 0. Let s(b) be the third derivative of 0*b + u - 1/9*b**3 + 3*b**2 + 1/90*b**5 + 0*b**4. Let s(c) = 0. Calculate c.
-1, 1
Solve -10*s + s**2 + 8 + 20*s + s**2 = 0 for s.
-4, -1
What is r in -4/7*r - 6/7 + 2/7*r**2 = 0?
-1, 3
Let o(r) = 18*r**3 - 34*r**2 + 14*r. Let u(i) = 18*i**3 - 35*i**2 + 13*i. Let a(c) = 5*o(c) - 6*u(c). What is d in a(d) = 0?
0, 2/9, 2
Let b(i) be the second derivative of 1/12*i**3 + 0 - 3*i + 3/80*i**5 - 5/48*i**4 + 0*i**2. Factor b(p).
p*(p - 1)*(3*p - 2)/4
Let o(w) be the first derivative of -w**6/3 - 14*w**5/5 - 9*w**4 - 44*w**3/3 - 13*w**2 - 6*w + 3. Find s such that o(s) = 0.
-3, -1
Let p(q) be the second derivative of q**7/1050 - q**6/225 - q**3/3 - 4*q. Let a(x) be the second derivative of p(x). Factor a(s).
4*s**2*(s - 2)/5
Let n(m) be the third derivative of m**5/180 - m**4/24 + 4*m**2. Factor n(i).
i*(i - 3)/3
Suppose -11*g + 36 = -2*g. Find o such that -14/11*o**2 + 16/11*o**5 + 2/11 + 36/11*o**g - 6/11*o + 14/11*o**3 = 0.
-1, 1/4, 1/2
Factor -1/2*s + 1/4*s**4 + 1/2*s**3 - 1/4 + 0*s**2.
(s - 1)*(s + 1)**3/4
Let 6*h**3 - h**4 + 3*h**4 + 5*h**2 + h**4 - 2*h**2 = 0. What is h?
-1, 0
Suppose 0 = -0*y + 3*y - r - 1, 2*r - 14 = -2*y. What is q in -6*q**4 + 4*q**2 - 2*q**3 + 4*q**2 - 2*q**3 - 6*q**y = 0?
-1, 0, 1/3
Let y(z) = -51*z**3 - 12*z**2 + 21*z + 12. Let f(k) = -13*k**3 - 3*k**2 + 5*k + 3. Let u(o) = -15*f(o) + 4*y(o). Factor u(x).
-3*(x - 1)*(x + 1)*(3*x + 1)
Let f(c) = c**3 + 4*c**2 + 4. Let s(a) = -2*a + 4. Let d be s(4). Let x be f(d). Factor 0*i**x + 2/3*i**5 + 4/3*i**2 + 0*i - 2*i**3 + 0.
2*i**2*(i - 1)**2*(i + 2)/3
Suppose -6*a + 5 = -a. Let s = a - -2. Suppose 1 - s*o + 1 - 4 - o**2 = 0. Calculate o.
-2, -1
Let r(j) = j + 0 - 3 - 3. Let i be r(8). Let 3 - 4 - f**i + 0 + 2*f = 0. What is f?
1
Let b be (-8)/6 - (-38)/6. Determine w, given that -8/3*w**2 - 4*w**3 - 2/3*w + 0 - 8/3*w**4 - 2/3*w**b = 0.
-1, 0
Find c such that -19*c + 0*c**5 - 4*c**4 + 4*c**2 + 2*c**5 + 17*c = 0.
-1, 0, 1
Let p(r) = -5*r**3 + 8*r**2 + 8*r. Let z(k) = -3*k**3 + 5*k**2 + 5*k. Let w(a) = 5*p(a) - 8*z(a). What is h in w(h) = 0?
0
Suppose t - 17 = -17. Let n(k) be the first derivative of 1/6*k**3 - 3 + t*k - 1/8*k**4 + 0*k**2. Factor n(h).
-h**2*(h - 1)/2
Let l(s) = 2*s**2 + 4*s + 3. Let x be l(-2). Let d(t) be the third derivative of -1/27*t**x + 0*t - 1/90*t**5 - 1/27*t**4 - t**2 + 0. Factor d(u).
-2*(u + 1)*(3*u + 1)/9
Let z = -24 - -20. Let g be (z/(-18))/(10/90). Find i, given that 8/11*i**5 + 0 + 12/11*i**3 + 18/11*i**4 + 2/11*i**g + 0*i = 0.
-1, -1/4, 0
Solve -1/4 + 1/4*j**3 - 1/4*j + 1/4*j**2 = 0.
-1, 1
Let k = 4861/858 - -1/858. Suppose k*t - 2/3 + t**3 - 41/3*t**2 + 21*t**4 = 0. Calculate t.
-1, 2/7, 1/3
Factor 0 - 4/5*f**3 + 0*f + 0*f**2.
-4*f**3/5
Let n(k) = -k**2 + 2*k + 3. Let a be n(3). Suppose -2*i + 0*o + 6 = -2*o, 0 = -o - 3. Factor a*u - 2/5*u