3, 1
Let y be (-6)/(162/(-33)) + 1/(-1). Factor 8/9*x - 4/3*x**2 - 2/9 + 8/9*x**3 - y*x**4.
-2*(x - 1)**4/9
Let h(b) be the second derivative of 7*b**4/36 - 5*b**3/18 - b**2/3 + 7*b - 2. Determine j so that h(j) = 0.
-2/7, 1
Let u(s) be the second derivative of -s**6/90 - s**5/5 - 23*s**4/18 - 10*s**3/3 - 25*s**2/6 + 23*s. Factor u(f).
-(f + 1)**2*(f + 5)**2/3
Determine y, given that -5*y**2 + 5*y**4 + 10*y**3 - 10*y - 2246 + 2246 = 0.
-2, -1, 0, 1
Let r be (-46)/(-8) - 6/(-24). Determine m, given that -m**4 + 2*m - r*m + 3*m**3 + m + 4*m**4 - 3*m**2 = 0.
-1, 0, 1
Let n(s) = 28*s**4 - 39*s**3 + 5*s**2 + 3*s + 3. Let t(u) = -28*u**4 + 40*u**3 - 4*u**2 - 4*u - 4. Let z(q) = 4*n(q) + 3*t(q). Factor z(v).
4*v**2*(v - 1)*(7*v - 2)
Let l be 282/42 - (-4)/14. Suppose 0 = 2*z - l - 3. Factor -2*c**z + c**5 - c**5 + 2*c**4.
-2*c**4*(c - 1)
Let f(h) be the third derivative of -h**8/1176 - 2*h**7/735 - h**2. What is d in f(d) = 0?
-2, 0
Let k = -7 - -5. Let a = 4 + k. Factor -4*m**a + 2*m**4 + 6*m**4 + 6*m**3 + 2*m**2.
2*m**2*(m + 1)*(4*m - 1)
Factor -1/6*y**5 + 2/3*y**2 + 0 - 4/3*y**3 + 5/6*y**4 + 0*y.
-y**2*(y - 2)**2*(y - 1)/6
Suppose 5*v - 25 = 20. Suppose -2*o - v = -5*o + 3*k, -5 = -2*o + 3*k. Factor -j**2 - j + 3*j**5 - j**3 - 3*j**o - j**5 + 4*j**2.
j*(j - 1)**2*(j + 1)*(2*j - 1)
Factor -8/9*q + 8/9 + 2/9*q**2.
2*(q - 2)**2/9
Factor 0 - 16/5*t**2 - 14/5*t**3 - 4/5*t**4 - 6/5*t.
-2*t*(t + 1)**2*(2*t + 3)/5
Let y(d) be the second derivative of -d**2 + 3*d + 1/24*d**4 - 1/4*d**3 + 0. Determine u so that y(u) = 0.
-1, 4
Suppose 14*n + 15 = 17*n. Let u(g) be the third derivative of 1/72*g**4 + 0*g**3 + 0 + 1/360*g**6 - 2*g**2 + 0*g - 1/90*g**n. Factor u(p).
p*(p - 1)**2/3
Solve -5/4 - 1/4*n**2 - 3/2*n = 0 for n.
-5, -1
Let h(p) = -p**2 + 3*p + 2. Let m be h(3). Factor -118*w**3 - 134*w**3 + 3 - 42*w + 246*w**m - 63*w**2 + 108*w**4.
3*(w - 1)**2*(6*w - 1)**2
Let i(w) be the first derivative of w**4 - 4*w**3/3 - 4*w**2 - 1. Solve i(p) = 0.
-1, 0, 2
Let w(p) be the first derivative of -p**5 + 5*p**4/4 - 20. Let w(r) = 0. What is r?
0, 1
Let g be (-1240)/12 - (-2)/3. Let q = 104 + g. Suppose q - 2/3*j**2 - 2/3*j = 0. What is j?
-2, 1
Let v(n) = -n**3 + 10*n**2 - n + 10. Let m be v(10). Suppose 3*w - 4*j - 32 = m, 5*w - 41 = w + 5*j. Factor -2 + 4 - 4*z**2 - w + 5*z + z**2.
-(z - 1)*(3*z - 2)
Let r(g) be the third derivative of -g**11/997920 + g**10/453600 - g**5/30 - g**2. Let b(u) be the third derivative of r(u). Factor b(p).
-p**4*(p - 1)/3
Let f(p) be the third derivative of 0*p - 3*p**2 - 1/12*p**4 - 1/7*p**3 + 0 - 1/105*p**5. Factor f(x).
-2*(x + 3)*(2*x + 1)/7
Let b be 3/(15/(-42)*2). Let t = -4 - b. Factor 0 + t*g**2 + 0*g.
g**2/5
Factor 6*s + 784 + 106*s - 590*s**2 + 594*s**2.
4*(s + 14)**2
Let x(p) be the first derivative of 4*p**5/5 - 5*p**4 + 4*p**3 + 18*p**2 + 15. Factor x(k).
4*k*(k - 3)**2*(k + 1)
Factor 2/5*s**2 + 6/5*s - 2/5*s**4 - 6/5*s**3 + 0.
-2*s*(s - 1)*(s + 1)*(s + 3)/5
Let m = 18 + -11. Let u(p) = -p**3 + 6*p**2 + 6*p + 10. Let d be u(m). Solve 10*v**4 - d*v**5 - 4*v + 2*v**5 - 5*v**5 + 6*v + 4*v**3 + 2 - 12*v**2 = 0 for v.
-1, -1/3, 1
Let u(p) be the third derivative of 4*p**2 + 1/12*p**3 + 1/24*p**4 + 0*p + 0 + 1/120*p**5. Factor u(h).
(h + 1)**2/2
Let u(l) be the third derivative of l**8/48 + l**7/7 + 43*l**6/120 + 2*l**5/5 + l**4/6 + l**2. Factor u(h).
h*(h + 1)**2*(h + 2)*(7*h + 2)
Let q = -646 + 5816/9. Solve -q*l**3 + 2/9*l + 2/9*l**2 + 0 - 2/9*l**4 = 0.
-1, 0, 1
Let l(u) = u**2 + 6*u + 10. Let d be l(-2). Let 0 - 1/3*s + 0*s**d + 1/3*s**3 = 0. Calculate s.
-1, 0, 1
Let j(d) be the first derivative of 2 + 2*d + 3*d**2 + 1/2*d**4 + 2*d**3. Find u, given that j(u) = 0.
-1
Factor -4*d**5 + 5*d**3 - d**3 + 4*d**2 - 6*d**4 + 2*d**4.
-4*d**2*(d - 1)*(d + 1)**2
Let l = 27543/5 + -3415157/620. Let o = -1/31 + l. What is w in -1/4*w**5 + 0*w + 0 + 1/4*w**4 + o*w**3 - 1/4*w**2 = 0?
-1, 0, 1
Let b(g) = g**3 - 5*g**2 + 5*g - 2. Let q be b(3). Let i be 49/2 + q/10. Factor -i*a**4 + 8*a**4 + 11*a**3 - 2*a**2 + 7*a**5 + 0*a**3.
a**2*(a - 1)**2*(7*a - 2)
Let c = 9 + 0. Factor 32*u + 20*u**2 - 11*u**3 + 24*u**3 + 11 - c*u**3 + 5.
4*(u + 1)*(u + 2)**2
Let 0 + 0*s**2 + 3/7*s**3 - 3/7*s = 0. Calculate s.
-1, 0, 1
Let u(l) = -l**3 - 7*l**2 - 8*l - 8. Let s be u(-6). Solve -4*g - s*g**3 + 2*g + 3*g**3 + 3*g**3 = 0.
-1, 0, 1
Let l be 0/(3/(-15)*-5). Let j(w) be the third derivative of 1/60*w**5 + 0*w + l + 3*w**2 - 1/24*w**4 - 1/6*w**3 + 1/120*w**6. Factor j(k).
(k - 1)*(k + 1)**2
Let x(n) be the second derivative of -2*n**6/75 - n**5/25 + n**4/15 + 2*n**3/15 + 2*n. Determine d, given that x(d) = 0.
-1, 0, 1
Let q = 12 + -6. Suppose l + 5*x + 23 = 0, -4*l = -2*x - 11 - 7. Find w, given that 0*w**2 + l*w**3 + 2*w**2 - q*w**4 + 4*w - 10*w**3 = 0.
-1, 0, 2/3
Let d(l) be the first derivative of 1/8*l**4 + 0*l**3 + 2 + 0*l**5 - 1/12*l**6 + 0*l + 0*l**2. Factor d(i).
-i**3*(i - 1)*(i + 1)/2
Suppose 3*l + 7 + 3 = 5*f, 3*f = l + 6. Let b(z) be the first derivative of -1 - 2/45*z**5 + 2/27*z**3 + l*z + 1/18*z**4 - 1/9*z**2. Find u such that b(u) = 0.
-1, 0, 1
Factor 0 + 1/2*y**3 + 0*y**2 + 1/6*y**4 - 2/3*y.
y*(y - 1)*(y + 2)**2/6
Let i(w) be the second derivative of 3*w**5/100 + w**4/5 + 2*w**3/5 - 10*w. Factor i(b).
3*b*(b + 2)**2/5
Let o(r) = -r**3 + 5*r**2 + 7*r + 8. Let m be o(6). Let b be m/60 + (-3)/(-18). Factor b*v**3 + 0*v + 2/5*v**4 + 0 - 2/5*v**5 - 2/5*v**2.
-2*v**2*(v - 1)**2*(v + 1)/5
Let z(h) be the first derivative of h**4/10 + 2*h**3/3 + 8*h**2/5 + 8*h/5 + 1. Determine t so that z(t) = 0.
-2, -1
Let r(t) = -9*t**3 + 14*t**2 + t - 6. Let k(x) = -x**2 + x. Let a(b) = -2*k(b) - r(b). Factor a(m).
3*(m - 1)**2*(3*m + 2)
Let b(i) be the third derivative of 4/315*i**7 - 5/36*i**4 + i**2 + 0*i + 1/504*i**8 + 1/45*i**6 - 2/9*i**3 + 0 - 1/45*i**5. Factor b(h).
2*(h - 1)*(h + 1)**3*(h + 2)/3
Let j(u) be the third derivative of 3*u**8/392 + 13*u**7/245 + 2*u**6/21 + 2*u**5/35 - 17*u**2. Factor j(d).
2*d**2*(d + 3)*(3*d + 2)**2/7
Factor 0*m**2 + 0*m**4 + 0 - 2/11*m**3 + 2/11*m**5 + 0*m.
2*m**3*(m - 1)*(m + 1)/11
Let g(r) be the second derivative of -9*r**7/112 + 27*r**6/80 - 33*r**5/160 - 19*r**4/32 + r**3/2 + 3*r**2/4 + 2*r. Find v, given that g(v) = 0.
-2/3, -1/3, 1, 2
Let j(u) be the first derivative of -3/5*u**5 - 3/4*u**4 + 0*u**2 + 2 + 0*u**3 + 0*u. Find f such that j(f) = 0.
-1, 0
Let h(r) be the second derivative of r**7/126 + r**6/15 + 7*r**5/30 + 4*r**4/9 + r**3/2 + r**2/3 - 5*r. Factor h(x).
(x + 1)**4*(x + 2)/3
Suppose -b + 25 = 5*m, -6*m = -9*m - 2*b + 22. Let 0*j + 0 + 2/5*j**2 - 2/5*j**m + 6/5*j**3 - 6/5*j**5 = 0. What is j?
-1, -1/3, 0, 1
Factor 0 + 0*q + 2/7*q**5 + 0*q**4 + 0*q**2 - 2/7*q**3.
2*q**3*(q - 1)*(q + 1)/7
Let k be (3 + 1)/((-6)/(-4)). Let s(g) be the first derivative of 2*g + 4*g**2 + 3 + k*g**3. Determine l so that s(l) = 0.
-1/2
Solve -3/2*a**3 + 0 + 1/2*a**2 + 0*a + a**4 = 0.
0, 1/2, 1
Let p(s) be the third derivative of -s**5/180 + s**4/18 - 2*s**3/9 + 5*s**2. Factor p(h).
-(h - 2)**2/3
Let s(c) = c + 11. Let q be s(-8). Let a be 10/(-6)*q/(-15). Factor 4/3 + a*y**2 - 4/3*y.
(y - 2)**2/3
Let p(a) = -a**2 + a. Let j(r) = 14*r**3 + 8*r**2 - 18*r - 4. Let c(z) = -j(z) - 4*p(z). Determine d, given that c(d) = 0.
-1, -2/7, 1
Let k(w) = -w**3 - 6*w**2 + 7*w + 5. Let h be k(-7). Suppose 6*t = 2*t + 12. Factor -t + h + 2*p**4 + p**2 - 5*p**2.
2*(p - 1)**2*(p + 1)**2
Let r = 801/8 - 100. Let q(l) be the first derivative of 1/12*l**3 + 0*l - 2 - r*l**2. Find z such that q(z) = 0.
0, 1
Factor 2/5*w**3 - 2/5*w**2 + 0 + 0*w.
2*w**2*(w - 1)/5
Let h(t) = -6*t**3 - 7*t**2 + 6*t - 7. Let c = -9 + 16. Let w(u) = 2*u**3 + 3*u**3 - 3*u + 6*u**2 + 6 - 2*u. Let y(m) = c*w(m) + 6*h(m). Factor y(s).
-s*(s - 1)*(s + 1)
Determine p, given that 0 - 3/8*p**5 + 3/4*p**4 + 0*p**3 + 3/8*p - 3/4*p**2 = 0.
-1, 0, 1
Factor -4*z**2 + 13*z + 14 - 17 + 4*z - 4*z.
-(z - 3)*(4*z - 1)
Suppose 3*h = -5*a - 5, 0*a - 5*a + 5 = 5*h. Factor j**2 - j**5 - j**4 + 6*j**5 + j**3 - 6*j**h.
-j**2*(j - 1)*(j + 1)**2
Let m(r) be the second derivative of -r**5/70 + r**3/7 - 2*r**2/7 + 6*r. Solve m(j) = 0 for j.
-2, 1
Let t(z) = 9*z**2 + 12*z + 6. Let g(l) = 17*l**2 + 24*l + 13. Let q be ((-22)/4)/(1/(-2)). Let h(b) = q*t(b) - 6*g(b). Factor h(a).
-3*(a + 2)**2
Let n(v)