in r(f) = 0?
-1, 1
Let y be (-1)/(48/(-52)) - (-7)/28. Factor -2/3 - y*r + 2*r**2.
2*(r - 1)*(3*r + 1)/3
Let g(f) be the first derivative of -1 - 1/6*f**2 + 1/18*f**4 - 1/90*f**6 + 0*f**5 - 2*f + 0*f**3. Let u(q) be the first derivative of g(q). Factor u(s).
-(s - 1)**2*(s + 1)**2/3
Let r(u) be the third derivative of 0*u**4 + 0 - 1/1155*u**7 + u**2 + 0*u**3 + 0*u + 1/330*u**5 + 0*u**6. Factor r(v).
-2*v**2*(v - 1)*(v + 1)/11
Let c(b) be the second derivative of -2*b + 0 + 1/6*b**3 + 0*b**4 + 1/60*b**5 + 1/180*b**6 + 0*b**2. Let z(f) be the second derivative of c(f). Factor z(p).
2*p*(p + 1)
Let f be (-8)/(-6) + (30/6 - 6). Let c(t) be the third derivative of 1/30*t**5 + 0 + 0*t + f*t**3 - 3*t**2 - 1/6*t**4. Determine z so that c(z) = 0.
1
Factor -4/3*v**2 - 4/3*v + 8/3.
-4*(v - 1)*(v + 2)/3
Factor 2/9*h**3 + 0*h + 2/9*h**2 + 0 - 2/9*h**4 - 2/9*h**5.
-2*h**2*(h - 1)*(h + 1)**2/9
Let y(t) be the second derivative of -1/42*t**3 + 0*t**2 + t + 0*t**4 + 0 + 1/140*t**5. Suppose y(x) = 0. Calculate x.
-1, 0, 1
Factor -16*z + 108 + 46*z + 2*z**2 + 18*z + 180.
2*(z + 12)**2
Let j(k) be the first derivative of -k**4/9 - 8*k**3/27 + 2*k**2/9 + 8*k/9 + 7. Factor j(z).
-4*(z - 1)*(z + 1)*(z + 2)/9
Let z(r) be the first derivative of r**5/40 + 5*r**4/24 + r**3/4 - 9*r**2/4 - 3*r + 3. Let i(o) be the first derivative of z(o). Factor i(k).
(k - 1)*(k + 3)**2/2
Let p(f) be the third derivative of f**6/180 + f**5/90 - 14*f**2. Factor p(v).
2*v**2*(v + 1)/3
Let q(i) be the third derivative of -i**6/60 + i**5/30 + i**4/12 - i**3/3 - 29*i**2. Factor q(k).
-2*(k - 1)**2*(k + 1)
Let 27/4 - 1/4*p**4 + 2*p**3 - 9/2*p**2 + 0*p = 0. Calculate p.
-1, 3
Let r be -3 - ((-301)/60 + 2). Let i(u) be the third derivative of 0*u**4 + 0*u**3 + 0 - r*u**5 - u**2 + 0*u. Solve i(q) = 0 for q.
0
Let w be (-5738)/(-5740) + 6/21. Let c = -7/82 + w. Factor -4/5*q - 4/5*q**3 - c*q**2 - 1/5*q**4 - 1/5.
-(q + 1)**4/5
Factor 1/4*j**2 + 0*j - 1/4.
(j - 1)*(j + 1)/4
Let 5*h**2 - 2*h**2 + 3*h + 9 + 3*h - 18 = 0. Calculate h.
-3, 1
Let w = -9508/3 - -2992. Let v = w - -180. Factor -2/3*i**4 - 2/3 - v*i**3 - 8/3*i - 4*i**2.
-2*(i + 1)**4/3
Factor 4*c**4 - 4*c**5 - 15*c**4 - c**4 - 4*c**2 - 12*c**3.
-4*c**2*(c + 1)**3
Let h = 1052/9 - 116. Solve 4/9*o**3 + 2/9*o - 8/9*o**4 - 2/3*o**5 + h*o**2 + 0 = 0.
-1, -1/3, 0, 1
Let g be (-68)/(-72) - 5/10. Factor -2/9*k**4 + 4/9*k + 0*k**2 + 2/9 - g*k**3.
-2*(k - 1)*(k + 1)**3/9
Let a(y) be the second derivative of 1/6*y**5 + 2/9*y**2 - 1/54*y**4 - 2*y - 7/27*y**3 - 1/15*y**6 + 0. Let a(d) = 0. Calculate d.
-2/3, 1/3, 1
Suppose -9 = 3*y - 6*y. Let t(r) be the first derivative of 1 + 0*r**2 - 2/3*r**y + 0*r. Factor t(h).
-2*h**2
Let r = -81 + 84. Factor -18/7*p**2 - 54/7 - 54/7*p - 2/7*p**r.
-2*(p + 3)**3/7
Factor 2/3 - 1/3*q - 1/3*q**2.
-(q - 1)*(q + 2)/3
Suppose 2*v + 2*m = 4, -5*v + 2*v - 4*m + 8 = 0. Let w be v/(4/4 + 1). Factor w*z + 2*z**5 + 6/7*z**3 - 24/7*z**4 + 4/7*z**2 + 0.
2*z**2*(z - 1)**2*(7*z + 2)/7
Let x be (-6)/(-315)*14/6. Let z(g) be the first derivative of -1/9*g**2 + 0*g + 2/27*g**3 + 1/18*g**4 + 2 - x*g**5. Factor z(a).
-2*a*(a - 1)**2*(a + 1)/9
Let s be 2/4 + (-99)/(-22). Let q(x) = 28*x**3 + 58*x**2 - 32*x. Let o(i) = 11*i**3 + 23*i**2 - 13*i. Let t(j) = s*q(j) - 12*o(j). Determine l so that t(l) = 0.
-2, 0, 1/4
Suppose -2/5 + 1/5*s + 1/5*s**2 = 0. Calculate s.
-2, 1
Let t = -25 + 25. Let b(h) be the second derivative of -1/15*h**4 + 1/50*h**5 + 0 + 0*h**3 + t*h**2 - 3*h. Solve b(c) = 0 for c.
0, 2
Let p(r) be the second derivative of -3*r**4/2 - 2*r**3 - r**2 + 16*r. Factor p(j).
-2*(3*j + 1)**2
Factor -4/3*b - 2/3 - 2/3*b**2.
-2*(b + 1)**2/3
Let x(o) be the third derivative of 0*o**4 - 1/168*o**8 - 1/105*o**7 + 0 + 1/30*o**5 + 1/60*o**6 + 0*o + 0*o**3 - 3*o**2. Suppose x(h) = 0. What is h?
-1, 0, 1
Let t(w) = w**2 + 4*w - 2. Let k be t(-5). Let b(r) = -7*r - 117. Let d be b(-17). What is g in 0*g**k + 0*g**d + 1/2*g**4 + 0*g - 1/2*g**5 + 0 = 0?
0, 1
Factor -7/5*o**3 + o**2 + 0 - 1/5*o + 3/5*o**4.
o*(o - 1)**2*(3*o - 1)/5
Let b = -1 + 4. Suppose -2*h + 3*l = -14 + 5, -h + l + 4 = 0. Factor i**h - 2*i - 6*i**b + 2*i**2 - 9*i**2.
-i*(i + 1)*(5*i + 2)
Let r = -1/237 - -132/79. Suppose -2/3*v + 0 + r*v**2 = 0. What is v?
0, 2/5
Let b be (-6)/(-4)*(-8)/(-3). Solve 5*l**b - 6*l**4 + 0*l**4 = 0.
0
Let i(w) = -22*w**4 + 15*w**3 + 23*w**2. Let y(a) = 15*a**4 - 10*a**3 - 15*a**2. Let x(t) = -5*i(t) - 7*y(t). Factor x(h).
5*h**2*(h - 2)*(h + 1)
Let n(a) = 3*a**2 - 7*a + 2. Let u(o) = o**2 - o. Let w(c) = -c**2 - 3*c + 3. Let b(x) = 5*u(x) + w(x). Let f(i) = -4*b(i) + 5*n(i). Factor f(v).
-(v + 1)*(v + 2)
Suppose -5*z = j + 1, 0 = 3*j + 2 + 1. Factor -2*f - 2*f - 2*f**2 + 0*f + z*f.
-2*f*(f + 2)
Let t(l) = l - 5. Let f be t(7). Suppose -8 = -f*s - 2*s. Factor 0*b + 2/5*b**s - 2/5.
2*(b - 1)*(b + 1)/5
Let q(t) be the second derivative of -t**4/32 - t**3/8 + 9*t**2/16 + 11*t. Let q(x) = 0. What is x?
-3, 1
Let h(o) be the first derivative of o**6/900 - o**5/100 + 8*o**3/3 + 9. Let r(m) be the third derivative of h(m). Find a such that r(a) = 0.
0, 3
Let c be (0*(1 - 0))/(-2 - 0). Find d such that 0*d**2 + c*d - 1/4*d**3 - 1/4*d**5 + 0 - 1/2*d**4 = 0.
-1, 0
Let i be (-7)/2*(4 - 2). Let d(u) = u**2 + 7*u + 5. Let g be d(i). Factor 8*r**4 + 6*r**3 - 3*r**2 - r**2 - 4*r**3 - 6*r**g.
-2*r**2*(r - 1)**2*(3*r + 2)
Suppose 0 = 2*f - 6*f. Let z be (f + (-3)/6)*-4. Factor -3*w**4 - 7*w**3 - 5*w**z + 6 - 6 - w.
-w*(w + 1)**2*(3*w + 1)
Suppose -l + 4*b = 14, -b + 4*b = l + 10. Let j be (-3)/l + 18/4. Suppose -3*d**2 - 4*d**j - d - d**4 + d**3 + 0*d**4 = 0. Calculate d.
-1, 0
Let j be (4/(-6))/((-4)/(-42)). Let w(c) = -2*c - 10. Let d be w(j). Factor 2*m**4 - 2*m**2 + d*m**2 - 4*m**4.
-2*m**2*(m - 1)*(m + 1)
Let f be ((-2)/6)/((-3)/342). Let a = 192/5 - f. Factor -8/5*n**3 + a - 2/5*n**2 + 8/5*n.
-2*(n - 1)*(n + 1)*(4*n + 1)/5
Let o be 6/4*(-4)/(-390). Let v = o - -5/13. Factor 8/5*t + v + 8/5*t**3 + 12/5*t**2 + 2/5*t**4.
2*(t + 1)**4/5
Suppose 2*t - t - 2*l = -6, l = 4*t - 4. Determine h so that 4 - 60*h + 28*h**t - 5 - 4*h**3 + 7 + 30 = 0.
1, 3
Suppose 0 = -5*z + 6*z. Let v be z/(-4) + 2/8. Factor 0 + v*s**3 + 1/4*s**2 + 0*s.
s**2*(s + 1)/4
Suppose -4*r - 3*s = -0*r - 3, 3*s = -3*r. Find o such that 1 - 4*o - 1 - 3*o**3 + 6*o**2 + o**r = 0.
0, 1, 2
Let w(x) be the second derivative of -x**4/24 + x**3/6 + 2*x**2 + 19*x. Factor w(k).
-(k - 4)*(k + 2)/2
Let u be (3/6)/(9/(-6)). Let m = u + 5/6. Factor 1/2*x**2 - 1/2 + m*x - 1/2*x**3.
-(x - 1)**2*(x + 1)/2
Let k(a) be the second derivative of a**4/36 - 5*a**3/18 - a**2 + 54*a. Let k(p) = 0. What is p?
-1, 6
Let t be (11/((-44)/6))/(-3). Factor -t*p**2 + 0 - 1/2*p.
-p*(p + 1)/2
Let i(l) be the first derivative of -1/4*l**2 - 3 + 0*l - 1/2*l**4 - 5/6*l**3. Find y, given that i(y) = 0.
-1, -1/4, 0
Let d = -428 + 3004/7. Factor d*k**3 + 4/7*k**2 + 4/7 + 2/7*k**5 - 10/7*k - 8/7*k**4.
2*(k - 2)*(k - 1)**3*(k + 1)/7
Suppose -16*g = -8*g - 16. Factor -14/9*f**3 + 4/9*f**g + 8/9*f**4 + 2/9*f + 0.
2*f*(f - 1)**2*(4*f + 1)/9
Let h = -2 + 2. Suppose p - 3*c - 2 - 10 = 0, -3*p + 5*c = -24. Factor 0 + 0*m**4 - 1/3*m**5 + 2/3*m**p + h*m**2 - 1/3*m.
-m*(m - 1)**2*(m + 1)**2/3
Determine m so that 2/3*m + 8/9*m**2 + 2/9*m**3 + 0 = 0.
-3, -1, 0
Let t(q) = -8*q - 45. Let i be t(-6). Solve 0*p - 2/7*p**2 + 4/7*p**i + 8/7*p**5 + 2*p**4 + 0 = 0 for p.
-1, 0, 1/4
Let j(x) = -x**3 + x**2 - x - 1. Let l(z) = -z**2 + 1. Let q(g) = j(g) + l(g). Let s(c) = 2*c**3 - 2*c**2 + 2*c. Let f(n) = 3*q(n) + s(n). Factor f(r).
-r*(r + 1)**2
Let d(t) = -5*t**2 + 3*t. Let u(w) = 6*w**2 - 4*w. Suppose 0 = 2*f - 4*f. Suppose f = -3*g - 0*g - 15. Let y(m) = g*d(m) - 4*u(m). Factor y(l).
l*(l + 1)
Suppose -2*i - 5 = -4*j + 13, -21 = -5*j + i. Let z = j + -2. Find k such that z*k**5 - 8 - 4*k**4 + 2*k**3 + 8 = 0.
0, 1
Let u(g) be the second derivative of 1/16*g**4 + 2*g + 3/80*g**5 + 0 + 0*g**2 + 1/120*g**6 + 1/24*g**3. Factor u(j).
j*(j + 1)**3/4
Let -3/4 + 3/4*u**2 + 3/4*u - 3/4*u**3 = 0. Calculate u.
-1, 1
Let z = -646572/4375 - -46/625. Let n = z - -148. Factor 4/7*u**3 - 6/7*u**2 + 0 + n*u.
2*u*(u - 1)*(2*u - 1)/7
Let l(p) = -p**2 + p. Let r(c) = 7*c**2 - 7*c. Let y(x) = -5*l(x) - r(x). Factor y(w).
-2*w*(w - 1)
Let i(r) be the second derivative o