2*(u + 1)**2
Let h be (-6)/14*(-322)/184. Factor 0 - 1/4*p + p**3 - h*p**2.
p*(p - 1)*(4*p + 1)/4
Let y(i) be the first derivative of i**5/10 - i**4/4 + i**3/6 + 7. Factor y(m).
m**2*(m - 1)**2/2
Let n(a) be the third derivative of a**7/630 - a**6/180 - a**5/45 + a**4/36 + a**3/6 + 18*a**2. Factor n(g).
(g - 3)*(g - 1)*(g + 1)**2/3
Let n(z) be the first derivative of -z**5/150 - z**4/30 - z**2 - 4. Let s(t) be the second derivative of n(t). Factor s(g).
-2*g*(g + 2)/5
Let u(y) be the third derivative of 0*y**3 + 1/240*y**6 + 0*y**5 + 0*y + 7*y**2 + 0*y**4 + 0. Let u(v) = 0. What is v?
0
Let c(q) be the first derivative of q**4/36 - q**2/18 + 13. Let c(v) = 0. Calculate v.
-1, 0, 1
Factor 99*v**3 - 109*v**3 + 0*v**4 - 8*v + 16*v**2 + 2*v**4.
2*v*(v - 2)**2*(v - 1)
Let l(t) be the first derivative of -1/3*t**2 + 1/6*t**3 + 1/6*t - 2. Factor l(i).
(i - 1)*(3*i - 1)/6
Let b be (2/4)/(2/(-24)). Let i = 10 + b. Factor 0 - i*m + 3*m**2 + 0*m**2 - 2*m**2 + 4.
(m - 2)**2
Let w be ((-2)/(-6))/((-203)/(-63)). Let o = 79/203 - w. Determine d, given that -2/7*d**2 + o*d + 0 = 0.
0, 1
Let n(x) be the third derivative of 1/8*x**4 + 0 - 1/112*x**8 + 0*x**6 - 1/10*x**5 + 0*x**3 + 1/35*x**7 + 0*x - 5*x**2. Factor n(y).
-3*y*(y - 1)**3*(y + 1)
Suppose 9*v**2 + 6*v**3 - 3*v**3 + 8*v**2 + 18*v - 2*v**2 = 0. What is v?
-3, -2, 0
Suppose 2*r = -0*r. Suppose -2*g - t - 4 = 0, r = 5*g - 3*t - t - 16. Suppose -1/2*u**4 + g*u**2 + 0 + 0*u + 1/2*u**3 = 0. What is u?
0, 1
Let n(f) = -f**2 + 5*f - 1. Let x be n(5). Let l be x*(-2 - -1 - 1). Factor -1/3*i - 2/3*i**l + 1/3.
-(i + 1)*(2*i - 1)/3
Let h(a) = a**3 + 9*a**2 + 8*a - 3. Let z be h(-8). Let r be 2/z*(-6)/1. Find i, given that r - 11*i - 2 + 21*i**2 - 3*i**4 + 5*i**4 - 16*i**3 + 2*i**4 = 0.
1/2, 1, 2
Let b(x) be the second derivative of -x**5/60 + 2*x**4/9 - 8*x**3/9 + 7*x. Suppose b(a) = 0. What is a?
0, 4
Let y be -1 + 2 - (0 + -7). Let l = y - 6. Find p, given that -2*p**4 + 2*p**3 + 4*p**4 - l*p + 0*p**3 - 2*p**2 = 0.
-1, 0, 1
Let r be (-3)/(-9) + (-28)/(-24). Factor -r*p**2 - p - 1/2*p**3 + 0.
-p*(p + 1)*(p + 2)/2
Suppose -105 = -d - 2*d. Let 31*q**3 - 30*q**4 + d*q**3 - 9*q**4 + 13*q + 8*q + 9*q**5 - 3 - 54*q**2 = 0. What is q?
1/3, 1
Let f(r) be the first derivative of r**4/14 + 10*r**3/21 + 8*r**2/7 + 8*r/7 + 9. Factor f(g).
2*(g + 1)*(g + 2)**2/7
Let v(w) be the first derivative of 5*w**4/4 - 10*w**3/3 - 10*w**2 + 40*w - 7. Suppose v(f) = 0. What is f?
-2, 2
Let k be (-10)/(-56) - (-44)/77. Determine r, given that 3/2*r**2 - 3/4*r**3 + k*r - 3/2 = 0.
-1, 1, 2
Suppose 3*w = -2*a + 17, -3*a = 4*w - 14 - 9. Factor 0*s**3 + 0 - 2/9*s - 4/9*s**2 + 4/9*s**4 + 2/9*s**w.
2*s*(s - 1)*(s + 1)**3/9
Let i = -528 - -3699/7. Factor 0 + 0*m + 0*m**2 - 3/7*m**3 + i*m**4.
3*m**3*(m - 1)/7
Let c(d) = -3*d**2 + 3 + 4*d**2 - 2*d**2 - d**3 + d. Let p be c(0). Solve 3*r + p*r - r**3 - 5*r = 0 for r.
-1, 0, 1
Let n(u) be the second derivative of 0 + 1/12*u**3 - 1/24*u**4 + 3*u + 0*u**2. Suppose n(h) = 0. What is h?
0, 1
Let d(k) be the second derivative of -k**4/4 - 3*k**3 - 12*k**2 + k. Factor d(f).
-3*(f + 2)*(f + 4)
Let a = 977/45 - 113/5. Let m = 20/9 + a. Factor -4/3*k - k**2 + m + 2/3*k**3 + 1/3*k**4.
(k - 1)**2*(k + 2)**2/3
Let d = -129 - -133. Let i(r) be the second derivative of 1/72*r**4 - d*r + 0 + 3/4*r**2 + 1/6*r**3. Factor i(w).
(w + 3)**2/6
Suppose -2*l = 4*s, -4*l - 3*s + 4 = s. Let m(b) be the first derivative of 0*b**3 - b**2 + b**4 + 4/5*b**5 + l - 4/5*b + 1/5*b**6. Factor m(w).
2*(w + 1)**4*(3*w - 2)/5
Let d = -75 - -1126/15. Let c(m) be the second derivative of 0*m**3 + 0 + 1/50*m**5 - 3*m + 1/30*m**4 + 1/35*m**7 - d*m**6 + 0*m**2. Factor c(w).
2*w**2*(w - 1)**2*(3*w + 1)/5
Let k(m) be the second derivative of m**5/50 - 2*m**4/15 + m**3/3 - 2*m**2/5 + m + 33. Determine b, given that k(b) = 0.
1, 2
Let v(n) = 7*n**4 - 12*n**3 - 14*n**2 + 4*n + 7. Let b(a) = -a**4 + a**3 + a**2 - a - 1. Let j(m) = -24*b(m) - 3*v(m). Factor j(q).
3*(q + 1)**4
Suppose -2*j + 6 = -3*w, -4*w - w - 2*j = -6. Let h(k) be the first derivative of 1/8*k**4 + 1/3*k**3 - 2 + w*k + 1/4*k**2. Suppose h(z) = 0. Calculate z.
-1, 0
Let k(y) = -93*y**2 + 16*y - 5. Let n(z) = 140*z**2 - 24*z + 8. Let a(q) = 8*k(q) + 5*n(q). What is b in a(b) = 0?
0, 2/11
Factor 2/11*u**5 - 6/11*u**3 - 4/11*u**2 + 0*u + 0*u**4 + 0.
2*u**2*(u - 2)*(u + 1)**2/11
Solve 0*m**2 + 0*m - 2/9*m**4 + 0 - 2/9*m**5 + 0*m**3 = 0 for m.
-1, 0
Let u(o) be the second derivative of -3/20*o**5 + 0*o**2 + 1/4*o**4 + 0*o**3 + o - 1/10*o**6 + 0 + 1/14*o**7. Find x such that u(x) = 0.
-1, 0, 1
Let o = -8 - -14. Suppose 3*s = o + 3. Suppose 1/4*f + 0*f**4 + 1/4*f**5 - 1/2*f**s + 0 + 0*f**2 = 0. What is f?
-1, 0, 1
Let t(b) be the second derivative of -b**6/60 + b**5/10 - b**4/6 - 5*b. Factor t(j).
-j**2*(j - 2)**2/2
Let j(u) be the second derivative of 1/7*u**2 + 0 + u + 1/21*u**3 - 1/42*u**4 - 1/70*u**5. Suppose j(b) = 0. What is b?
-1, 1
Let y(w) be the third derivative of w**8/420 + 4*w**7/525 + w**6/150 - 11*w**2. Factor y(n).
4*n**3*(n + 1)**2/5
Let y(g) be the second derivative of -g**6/45 + g**5/15 - 2*g**3/9 + g**2/3 + 12*g. Suppose y(v) = 0. What is v?
-1, 1
Factor -6*f + 10*f + 0*f**2 - 2*f**3 + 2*f**2.
-2*f*(f - 2)*(f + 1)
Let v(h) = -6 + 1 + 6. Let x(q) = q**2 - 3. Let w(p) = -2*v(p) - x(p). Factor w(o).
-(o - 1)*(o + 1)
Let o(x) = -x**3 - 5*x**2. Let v be o(-5). Let u(q) be the third derivative of 0*q + v*q**3 - 1/300*q**5 + 0*q**4 - 2*q**2 + 0. Solve u(f) = 0 for f.
0
Let m(r) be the second derivative of 2*r**6/15 + r**5 + 3*r**4 + 14*r**3/3 + 4*r**2 - 6*r. Factor m(c).
4*(c + 1)**3*(c + 2)
Let j(b) be the first derivative of -b**4/8 - 2*b**3/3 - 3*b**2/4 + 9. Factor j(q).
-q*(q + 1)*(q + 3)/2
Suppose 3*n - 3*r = 2*r + 56, -3*r = 2*n - 12. Factor 16 + 2*f**3 + 14*f + n*f**3 + 4*f**4 - 2*f**4 + 26*f + 36*f**2.
2*(f + 1)*(f + 2)**3
Let k(w) be the third derivative of 2*w**7/315 + w**6/30 + 11*w**5/180 + w**4/24 + 42*w**2. Let k(h) = 0. Calculate h.
-3/2, -1, -1/2, 0
Let z(j) be the second derivative of 5/3*j**4 + 0 + 0*j**2 + 4/3*j**3 - 7*j. Factor z(c).
4*c*(5*c + 2)
Suppose 2*y + 25 - 9 = 0. Let v be y/(-4) + (-14)/8. Factor 1/4*g + 1/2*g**2 - v.
(g + 1)*(2*g - 1)/4
Suppose -4*x + 1 = 13. Let a = x + 5. Suppose -1/4*w + 0 + w**a - 3/4*w**3 = 0. What is w?
0, 1/3, 1
Suppose -a = t + 2, -3*a - a - 16 = 0. Let f(w) be the third derivative of 0 + 0*w**3 - 1/10*w**5 + 3*w**t + 0*w + 1/40*w**6 + 1/8*w**4. Factor f(x).
3*x*(x - 1)**2
Let u(t) = -t**3 + 11*t**2 + 11*t + 16. Let f be u(12). Suppose 5*r + 3*w + 12 = 0, -6*r + f*r + 3*w = -12. Factor -2/3*h**2 + 1/3*h + 2/3*h**4 + r - 1/3*h**3.
h*(h - 1)*(h + 1)*(2*h - 1)/3
Suppose 0 = -i - 16 + 4. Let t be 1/4 + (-33)/i. Factor 3 - t + m**2.
m**2
Let l = -43 + 43. Find r such that -2/3*r**3 - 1/3*r - r**2 + l = 0.
-1, -1/2, 0
Let b(q) be the second derivative of q**4/54 + q**3/27 - 2*q**2/9 + 9*q. Determine i, given that b(i) = 0.
-2, 1
Suppose -v = 3*v - 8. Suppose p - 2*q + 6 = 0, v*q + 0*q = -5*p + 6. Factor -1/4*k**4 + p + 1/4*k**2 - 1/4*k + 1/4*k**3.
-k*(k - 1)**2*(k + 1)/4
Let o(f) be the first derivative of -3*f**5/40 - f**4/12 + 3*f - 2. Let t(r) be the first derivative of o(r). Factor t(p).
-p**2*(3*p + 2)/2
Factor 44/7*g**3 + 8/7*g**2 + 0 + 0*g + 64/7*g**4 + 4*g**5.
4*g**2*(g + 1)**2*(7*g + 2)/7
Suppose -28*v = -33*v + 25. Factor 0 - 1/3*u**v + 0*u**2 - 2/3*u**4 + 0*u - 1/3*u**3.
-u**3*(u + 1)**2/3
Let z be 0/((-1)/1 + -1). Suppose z = 2*b - 5 - 17. Determine p, given that -3*p**2 - 5*p**3 - 14*p**2 - 16*p + 7 - b = 0.
-2, -1, -2/5
Let h(m) be the first derivative of -m**4/8 + 5*m**3/6 - m**2 + 45. Factor h(r).
-r*(r - 4)*(r - 1)/2
Suppose -1/7*x**3 + 1/7*x + 0*x**2 + 0 = 0. Calculate x.
-1, 0, 1
Let l(c) be the second derivative of 3*c**6/50 - 11*c**5/100 + c**4/30 - 7*c. Factor l(x).
x**2*(x - 1)*(9*x - 2)/5
Let h(w) be the first derivative of 1/3*w**3 + 0*w**2 - 1/1800*w**6 + 1/600*w**5 + 0*w + 0*w**4 + 3. Let r(u) be the third derivative of h(u). Factor r(m).
-m*(m - 1)/5
Let j(u) be the first derivative of -1/6*u**2 - 2/3*u + 1/9*u**3 + 5. Factor j(q).
(q - 2)*(q + 1)/3
Let c(j) = -j**2. Let u(h) = 4*h**2 + 4*h. Let l(z) = -2*c(z) - u(z). Factor l(y).
-2*y*(y + 2)
Let r(f) = 9*f**3. Let n(w) = 3*w**3. Suppose 0 