)**2/3
Let r(c) be the second derivative of c**7/14 - c**6/5 - 3*c**5/20 + c**4/2 + c. Factor r(s).
3*s**2*(s - 2)*(s - 1)*(s + 1)
Let i(x) be the second derivative of 1/20*x**5 + 1/60*x**6 + 0 + 0*x**4 - 2*x - 1/4*x**2 - 1/6*x**3. Solve i(a) = 0.
-1, 1
Let r(y) be the third derivative of 0*y**3 + 3*y**2 + 0 - 1/60*y**6 + 0*y**5 + 0*y + 0*y**4. Find i such that r(i) = 0.
0
Suppose 0 = -0*l - 3*l + 15. Determine b, given that 3*b**2 - b**4 + b + l - 2 + 2*b**3 - 3*b**3 - 5 = 0.
-2, -1, 1
Let y(q) = q**5 - 4*q**4 + 6*q**3 - 4*q**2 - q - 2. Let h(p) = p + 1. Let t(u) = 2*h(u) + y(u). Factor t(c).
c*(c - 1)**4
Let l(w) be the second derivative of -w**8/1008 + w**6/180 - w**4/72 + w**2 - 3*w. Let h(o) be the first derivative of l(o). Factor h(f).
-f*(f - 1)**2*(f + 1)**2/3
Let j(z) = -3*z - 2*z**3 + 5*z + 3*z - 5 + 2*z**2. Let d(n) = 8*n**3 + 26 - 26*n + 2*n**3 - 6*n**2 - 4*n**2 + 0*n**2. Let i(u) = -3*d(u) - 16*j(u). Factor i(a).
2*(a - 1)**2*(a + 1)
Suppose 4*l + 9 - 33 = 2*i, 2*l = -4*i - 8. Let j be (-8)/i - (-4)/(-3). Suppose -1/3*b**2 - j*b - 1/3 = 0. Calculate b.
-1
Let v be ((-162)/(-12) - 9)*20/36. Factor 3/4 + j**3 + 11/4*j**2 + v*j.
(j + 1)**2*(4*j + 3)/4
Let h(a) be the second derivative of a**7/126 - a**6/45 + a**5/60 - 12*a. Factor h(t).
t**3*(t - 1)**2/3
Factor -1/4*f + 1/4*f**2 + 0 + 1/4*f**3 - 1/4*f**4.
-f*(f - 1)**2*(f + 1)/4
Let t(q) be the second derivative of -q**7/42 - q**6/30 + q**5/5 + q**4/3 - 18*q + 1. Factor t(s).
-s**2*(s - 2)*(s + 1)*(s + 2)
Let w(u) be the second derivative of -2*u**7/21 + 2*u**6/15 + 2*u**5/5 + 28*u. Suppose w(c) = 0. Calculate c.
-1, 0, 2
Suppose -3 = -a - 0*a. Factor o + o - o**a + 0*o**2 - 3*o**2 + 2*o**2.
-o*(o - 1)*(o + 2)
Suppose 0 = -4*y + 4*u - 5 - 7, 3*y + 3*u = 15. Suppose 2*o - 3 = y. Find h such that 2*h**o - 2 - 7*h + 3*h**3 - 4*h**2 + 0*h = 0.
-1, -1/3, 2
Let b(n) be the first derivative of n**4/8 - n**3/3 + n**2/4 + 4. Find j, given that b(j) = 0.
0, 1
Let b be (3 - 10)/(-7) - (-6)/(-8). Solve -l**4 + 1/4*l**5 + 3/2*l**3 + b*l + 0 - l**2 = 0.
0, 1
Let s(x) be the third derivative of 11*x**6/120 - x**5/30 - x**4/24 - 3*x**2. Let c(r) = -r**4 - 12*r**3 + 2*r**2 + r. Let w(v) = -4*c(v) - 5*s(v). Factor w(f).
f*(f - 1)**2*(4*f + 1)
Let r(z) be the third derivative of 5*z**8/288 + 13*z**7/126 + 3*z**6/16 + z**5/18 - 5*z**4/36 - 19*z**2. Let r(l) = 0. Calculate l.
-2, -1, 0, 2/7
Let d = -3973/7 + 568. Factor -1/7*s**3 + d*s - 2/7 + 0*s**2.
-(s - 1)**2*(s + 2)/7
Let n(y) = 3*y**4 + y**3 - 2*y**2 + 2. Let x(b) be the third derivative of -b**7/210 + b**5/60 - b**3/6 - 11*b**2. Let j(i) = 3*n(i) + 6*x(i). Factor j(z).
3*z**3*(z + 1)
Let g = -47 - -10. Let k be (-16)/56 - g/7. Factor k*f**3 - 4*f**2 - 5*f**2 + 2*f**3 - 4*f + 6*f.
f*(f - 1)*(7*f - 2)
Find k such that 3/4*k**4 + 0 + 0*k - 3/4*k**3 + 1/4*k**2 - 1/4*k**5 = 0.
0, 1
Determine i so that 2/7 - 2/7*i**5 + 4/7*i**3 - 2/7*i - 4/7*i**2 + 2/7*i**4 = 0.
-1, 1
Let a = 21 + -16. Solve a*s**3 - 7*s**3 + 4*s**2 + 4*s**4 - 7*s**3 + s**3 = 0 for s.
0, 1
Let n(b) be the third derivative of b**7/10080 + b**6/1440 + b**5/480 - 3*b**4/8 + 6*b**2. Let y(h) be the second derivative of n(h). Factor y(z).
(z + 1)**2/4
Let q(o) be the third derivative of o**10/10800 - 11*o**9/75600 + o**8/16800 - o**4/24 + 3*o**2. Let d(g) be the second derivative of q(g). Factor d(b).
b**3*(2*b - 1)*(7*b - 2)/5
Let v(z) be the first derivative of -1/5*z**3 + 3/10*z**2 + 1/20*z**4 + 3 - 1/5*z. Factor v(w).
(w - 1)**3/5
Let y(v) = v**2 - 3*v - 1. Let i be y(4). Factor -5*h + 2*h + i*h - 2 + 2*h**2.
2*(h - 1)*(h + 1)
Let o = 38 + -38. Let a be 6/14 - (-5)/(-28). Find t such that 0*t - a*t**5 + 0*t**2 + o + 0*t**4 + 1/4*t**3 = 0.
-1, 0, 1
Suppose 0 = 3*c + c + 4. Let l = c - -6. Factor -3*o**4 + o**3 + 0*o**5 + o + 4*o**l - 6*o**3 + 3*o**2.
o*(o - 1)**2*(o + 1)*(4*o + 1)
Let j(m) = 2*m - 2 - m - 6*m - 3*m**2. Let t(y) = -y**2 - 2*y - 1. Let z(q) = -2*j(q) + 5*t(q). Suppose z(b) = 0. What is b?
-1, 1
Let o(j) = j**2 - 6*j + 2. Let f be o(4). Let h be (-1)/f - (-2)/4. Factor -h*p - 4/3 + 2/3*p**3 + 4/3*p**2.
2*(p - 1)*(p + 1)*(p + 2)/3
Let p(b) = b**4 + 5*b**3 - 5*b**2 + 7*b + 4. Let w(l) = -2*l**4 - 4*l**3 + 4*l**2 - 8*l - 5. Let u(x) = 5*p(x) + 4*w(x). Solve u(n) = 0 for n.
0, 1
Let r(p) = -p - 3. Let q be r(-5). Factor -2*m**q - 2*m**2 + 6*m**2.
2*m**2
Let d be 1 - (3 + -2) - -5. Suppose -h = -d*f + 19, -13 + 1 = -4*f + 4*h. Factor f*r - 2*r + 1 + 5*r**2 - 4*r - 4*r**2.
(r - 1)**2
Let a be 16/(-24)*3/(-5). Let j(l) be the second derivative of 2*l - l**2 - a*l**5 - 4/3*l**3 + 0 - 1/15*l**6 - l**4. Suppose j(f) = 0. What is f?
-1
Let j(f) be the second derivative of -f**4/3 + 16*f**3/3 - 32*f**2 - 10*f. Find g such that j(g) = 0.
4
Let f(u) be the third derivative of -2*u**7/189 + 2*u**6/45 - 4*u**5/135 - 66*u**2. Factor f(g).
-4*g**2*(g - 2)*(5*g - 2)/9
Suppose -1 = g - 4. Factor -9*j - 3*j**2 - g - 3*j - 12 + 3.
-3*(j + 2)**2
Suppose 13 = 5*t + 4*g - 31, 4*g + 4 = -t. Factor -4*x**2 - 12 - 6 + 4*x**2 - 2*x**2 - t*x.
-2*(x + 3)**2
Suppose 3*i = 2*i + c + 2, -3*i - 4 = 2*c. Suppose i = 4*s - 4. Find p such that 2*p**4 - 1 - 4*p - p**2 - s + p**2 + 4*p**3 = 0.
-1, 1
What is w in -16 - 8*w**3 - 8*w - 5*w**3 + 4*w**2 + 15*w**3 = 0?
-2, 2
Suppose 0 = -3*v - 0*v - 12. Let g = v + 6. Determine u, given that 2 + 2*u - u**g - 5*u + 4*u = 0.
-1, 2
Let c = -9/4 + 7/3. Let g(w) be the first derivative of 0*w**2 - c*w**3 + 0*w + 2. Let g(p) = 0. What is p?
0
Let h = 38/3 + -112/9. Factor -16/9 - 4/3*b**2 - 8/3*b - h*b**3.
-2*(b + 2)**3/9
Let b(w) = w - 3. Let i be b(4). Let u = 4 + i. Suppose -3/2*o**3 + 3/2*o**4 + 0*o + 0 - 1/2*o**u + 1/2*o**2 = 0. Calculate o.
0, 1
Let k(o) be the second derivative of o**7/14 - o**6/10 - 3*o**5/20 + o**4/4 - 10*o. What is u in k(u) = 0?
-1, 0, 1
Factor -4772*s**3 - 4 + 32208*s**3 - 8664*s**2 - 33 + 912*s + 5.
4*(19*s - 2)**3
Let k be (-9)/(-3) + (1 - 1). Let y(a) = 4*a**3 + 10*a**2 - a - k*a - 3*a**2 + 7. Let i(z) = 2*z**3 + 3*z**2 - 2*z + 3. Let q(d) = 7*i(d) - 3*y(d). Factor q(x).
2*x*(x - 1)*(x + 1)
Solve 415*n**3 - 5*n - 5*n - 4 - 417*n**3 - 8*n**2 = 0 for n.
-2, -1
Let s(f) be the first derivative of -3*f**7/140 - f**6/60 + f**5/12 - f**4/12 + f**3/3 - 3. Let r(h) be the third derivative of s(h). Let r(j) = 0. Calculate j.
-1, 1/3
What is r in 101*r**4 - 2*r**2 - 52*r**4 + 3*r**3 - 50*r**4 = 0?
0, 1, 2
Let w = 5 - 1. Let i = 15 - 11. Factor 0*t**i - 5*t**4 + 2*t**2 + 3*t**w.
-2*t**2*(t - 1)*(t + 1)
Let u(g) be the third derivative of g**7/5040 + g**6/720 + g**5/240 + g**4/12 - 7*g**2. Let c(s) be the second derivative of u(s). Factor c(b).
(b + 1)**2/2
Let o = 161/2 + -79. Factor -o*s**2 + 0*s + 2 + 1/2*s**3.
(s - 2)**2*(s + 1)/2
Let j(u) be the second derivative of -u**5/5 - 5*u**4/6 - 17*u**3/24 - u**2/4 + 24*u. Factor j(l).
-(l + 2)*(4*l + 1)**2/4
Let u(h) be the second derivative of 5*h**4/48 - 5*h**3/12 - 14*h. Solve u(z) = 0 for z.
0, 2
Let r = 699/4 + -174. Let 3/4*f**3 - 3/4*f - 3/4*f**2 + r = 0. Calculate f.
-1, 1
Suppose 2*k**2 - 8*k**2 - 8*k**3 - 4*k**2 - 2*k**4 - 4*k = 0. What is k?
-2, -1, 0
Let s(a) be the third derivative of a**7/1050 + a**6/600 - 19*a**2. Suppose s(i) = 0. What is i?
-1, 0
Let j be (-1)/(2 + -4 - -4)*-10. Factor 1/2*s**2 + 1/4*s**3 + 0 - 3/4*s**j + 0*s - s**4.
-s**2*(s + 1)**2*(3*s - 2)/4
Suppose -9 = -5*z + 6. Suppose 7 = z*g - 2. Factor 0*o + o + g*o**2 - 2*o**2.
o*(o + 1)
Let m(j) = 0*j**2 - 5*j**2 + 4*j**2 - 6*j. Let c be m(-5). Determine l, given that c*l**2 - 5*l**2 + 2*l**2 + 3 - 5 = 0.
-1, 1
Factor -3*h**2 + 2*h**4 + 6*h**3 + 9*h**2 - 4*h**2 - 4 - 6*h.
2*(h - 1)*(h + 1)**2*(h + 2)
Factor 4/7 - 6/7*k + 2/7*k**2.
2*(k - 2)*(k - 1)/7
Let q be 3/(-12) + (-21)/(-4). What is d in d + d - 3*d**2 - 3*d**2 - 1 + q*d**2 = 0?
1
Let o be ((-3)/6)/1*-2. Suppose 3*a - 11 = o. Factor 0*f**3 + 0*f**3 - a*f**2 - 2*f**3 - 2*f.
-2*f*(f + 1)**2
Let r(f) be the third derivative of 0*f - f**2 - 1/60*f**4 - 1/30*f**3 + 0 - 1/300*f**5. Factor r(t).
-(t + 1)**2/5
Factor 18/7*p**4 + 12/7*p + 0 - 10*p**2 + 96/7*p**3.
2*p*(p + 6)*(3*p - 1)**2/7
Factor -39*v**2 - 36*v**3 - 3*v**4 + 18*v - 16*v**3 + 76*v**3.
-3*v*(v - 6)*(v - 1)**2
Let l be 2/(-2)*-753 - 3. Let b be (10/6)/(5/l). Factor 3125/4*j**5 + 100*j**2 + 20*j - b*j**3 - 625/2*j*