(r) = 0.
1
Let t(h) be the second derivative of 9*h**5/20 - 7*h**4/2 + 25*h**3/6 - 2*h**2 - 6*h - 3. Factor t(c).
(c - 4)*(3*c - 1)**2
Factor 13*m - 73*m + 33 - 1 + 24*m**2 - 64*m**3 + 68*m**3.
4*(m - 1)**2*(m + 8)
Let z(o) = o**3 + 7*o**2 - o - 3. Let b be z(-7). Suppose 4*x - 2*x - 4 = 4*l, b*l = -2*x + 4. What is q in -5*q**4 - 8*q**3 - 2*q**3 + 0*q**3 + 15*q**x = 0?
-3, 0, 1
Suppose 6*t - 17 + 5 = 0. Solve 3*c + 51*c**t + 0*c**3 + c**3 - 57*c**2 + 2*c**3 = 0.
0, 1
Let q = -15977 + 575123/36. Let i = 19/12 + q. Factor 0 + 10/9*n**2 - i*n.
2*n*(5*n - 1)/9
Suppose 58*l**2 + 517*l + 2*l**2 + 2*l**3 + 83*l + 2000 = 0. What is l?
-10
Factor -10/9*m - 44/3 + 2/9*m**2.
2*(m - 11)*(m + 6)/9
Let x = -87511/7 - -12502. Factor x*y**4 - 3/7*y**3 - 33/7*y - 12/7 - 27/7*y**2.
3*(y - 4)*(y + 1)**3/7
Let u(f) be the third derivative of 0*f**3 - 3/80*f**6 - 1/105*f**7 - 1/20*f**5 + 0*f - 1/48*f**4 - 15*f**2 + 0. Solve u(q) = 0 for q.
-1, -1/4, 0
Let f(h) = 0 - 3*h - 2 + 1. Let x be f(-1). Let 1 + x*p - 3*p + p**2 + 2*p + p = 0. What is p?
-1
Let b(k) be the second derivative of k**7/147 + 32*k**6/105 + 128*k**5/35 - 238*k - 2. Factor b(n).
2*n**3*(n + 16)**2/7
Factor -4/7*i**2 - 10/7*i + 2/7*i**3 + 12/7.
2*(i - 3)*(i - 1)*(i + 2)/7
Let v be (4/20)/(3/45). Let n(w) be the first derivative of 1/3*w**4 + 0*w + 1/6*w**2 + 5/9*w**v - 6. What is u in n(u) = 0?
-1, -1/4, 0
Let j(p) be the second derivative of p**7/490 - p**6/140 - 3*p**5/140 + 5*p**2/2 - 12*p. Let q(x) be the first derivative of j(x). Suppose q(t) = 0. What is t?
-1, 0, 3
Factor -2/11*g**2 - 1568/11 - 112/11*g.
-2*(g + 28)**2/11
Let v(p) be the first derivative of 5*p**3/3 + 5*p**2 - 50. Suppose v(s) = 0. What is s?
-2, 0
Suppose 5 + 35 = 23*q - 6. Factor -1/4*z**4 + q + 5/4*z**3 - 3/2*z**2 - z.
-(z - 2)**3*(z + 1)/4
Suppose -5*w + 4 = -4*q, 2*q - 8 = w - q. Let s(t) be the third derivative of 3/10*t**5 + 0*t + 0*t**3 - 1/6*t**4 - w*t**2 - 7/60*t**6 + 0. Solve s(b) = 0.
0, 2/7, 1
Let p(z) be the second derivative of 0 - 1/6*z**6 + 3/4*z**5 - 27*z - 5/4*z**4 + 0*z**2 + 5/6*z**3. Factor p(l).
-5*l*(l - 1)**3
Let v(u) = -3*u**2 + 9*u. Suppose -4*h = 2*h - 36. Let q(o) = 4*o**2 - 8*o. Let z(x) = h*v(x) + 5*q(x). Factor z(i).
2*i*(i + 7)
Let g = -23 - -25. Factor d**2 - 5*d**2 + 3*d**3 - g*d + 4 - d**3.
2*(d - 2)*(d - 1)*(d + 1)
Let b(i) be the second derivative of 0 - 16*i - 1/8*i**5 - 5/4*i**3 - 5/4*i**2 - 5/8*i**4. Factor b(d).
-5*(d + 1)**3/2
Suppose -21 = -0*q - 3*q + 5*x, -3*q - 3*x = 3. Factor -6*j**2 + 152*j + 2*j**q - 89*j - 16 - 83*j.
-4*(j + 1)*(j + 4)
Find k such that -545*k - 613*k + 37010 + 4*k**2 + 74737 - k**2 = 0.
193
Let j = 5 + -1. Let t = j - 1. What is o in 1 + 1 - o**t - 3*o**3 - 5*o**4 + 3*o**4 + 4*o = 0?
-1, 1
Let s(c) be the first derivative of 7 - 1/10*c**4 - 128/5*c - 8/5*c**3 - 48/5*c**2. Let s(q) = 0. What is q?
-4
Factor -2/17*y**4 - 126/17*y**2 - 122/17*y - 40/17 - 46/17*y**3.
-2*(y + 1)**3*(y + 20)/17
Let o = 3 + 17. Let x(i) = 16*i**3 + 15*i**2 - 35*i**2 + 0*i**3 + o*i**4 - 16. Let w(q) = -q**4 - q**3 + q**2 + 1. Let d(j) = -16*w(j) - x(j). Factor d(h).
-4*h**2*(h - 1)*(h + 1)
Let z(t) be the third derivative of t**6/280 - 3*t**4/56 - t**3/7 + 3*t**2 - 22*t. Let z(n) = 0. Calculate n.
-1, 2
Factor 12 - 9*g**2 - 48*g - 99 - 61 - 104*g + 5*g**2.
-4*(g + 1)*(g + 37)
Let r(a) be the second derivative of a**5/10 - 7*a**4/6 - a**3/3 + 7*a**2 - a - 29. Factor r(y).
2*(y - 7)*(y - 1)*(y + 1)
Let z(b) be the first derivative of b**4/48 - b**3/12 + b**2/8 + 13*b + 7. Let r(i) be the first derivative of z(i). Determine n, given that r(n) = 0.
1
Let j(q) = 2*q**3 - 4*q**2 + 21*q - 38. Let d be j(2). Let -5*k - 5/2*k**2 + 5*k**3 + 15/4*k**d - 5/4 = 0. Calculate k.
-1, -1/3, 1
Factor -35*h**4 + 10 + 55*h + 10*h**2 + 15 + 153*h**3 - 5*h**5 - 203*h**3.
-5*(h - 1)*(h + 1)**3*(h + 5)
Let v = 168 - 166. Let z(p) be the first derivative of 6*p + 2 + p**3 + 9/2*p**v. Factor z(g).
3*(g + 1)*(g + 2)
Let v(o) be the third derivative of o**5/12 - 25*o**4/24 + 42*o**2 - 2. Factor v(s).
5*s*(s - 5)
Let u be (-26)/(-117) + (104/18 - 2). Factor 0*s - 4/7*s**2 + 4/7*s**u + 0*s**3 + 0.
4*s**2*(s - 1)*(s + 1)/7
Suppose o - 345 = -2*o. Let v = 231/2 - o. Find y such that 0*y**2 + y**4 + v*y**5 + 1/2*y**3 + 0*y + 0 = 0.
-1, 0
Suppose 9*d = 4*d - 190. Let g be 10/2 + d/8. Find s such that -1/4*s**4 - g - 1/4*s**5 + 1/2*s**2 + 1/2*s**3 - 1/4*s = 0.
-1, 1
Let r(k) be the second derivative of -5*k**8/336 + k**6/12 - 5*k**4/24 - 6*k**2 - 13*k. Let x(z) be the first derivative of r(z). Factor x(c).
-5*c*(c - 1)**2*(c + 1)**2
Let q(x) = -4*x**2 + 4*x + 3. Let k(g) = 2*g**2 - 2*g - 1. Let s(j) = 5*k(j) + 3*q(j). Factor s(t).
-2*(t - 2)*(t + 1)
Factor 22/3*o**2 + 304/9*o - 232/9.
2*(3*o - 2)*(11*o + 58)/9
Let r(i) = i + 1. Let n be r(2). Suppose -25 = -2*l - 5*d, 4*l - n*d + 20 = d. Factor 0*u - 16/5*u**2 + 4/5*u**4 + 0*u**3 + l.
4*u**2*(u - 2)*(u + 2)/5
Let j(y) be the third derivative of -1/60*y**6 + 1/210*y**7 + 0 + 0*y - 2*y**2 + 0*y**3 + 1/60*y**5 + 0*y**4. Factor j(v).
v**2*(v - 1)**2
Let k(q) be the first derivative of 2*q**5/55 - 7*q**4/22 + 12*q**3/11 - 20*q**2/11 + 16*q/11 - 27. Determine w, given that k(w) = 0.
1, 2
Let n(k) be the third derivative of -k**6/240 + 121*k**5/120 - 239*k**4/48 + 119*k**3/12 - 225*k**2. Factor n(q).
-(q - 119)*(q - 1)**2/2
Let o = -4 + 8. Find z, given that -6*z**3 - 6*z**5 - 3 + 13*z**2 + 9*z + 3*z**5 - 19*z**2 + 9*z**o = 0.
-1, 1
Suppose 127 = -4*p + 135. Factor 3/4*i**p - 9/2 - 15/4*i.
3*(i - 6)*(i + 1)/4
Let q(g) = -g**2 + 22*g + 18. Let o(r) = -22*r - 20. Let n(k) = -3*o(k) - 4*q(k). Factor n(m).
2*(m - 6)*(2*m + 1)
Factor 16 + 8/3*j + 2/3*j**5 + 4/3*j**4 - 6*j**3 - 44/3*j**2.
2*(j - 3)*(j - 1)*(j + 2)**3/3
Factor -18/5*a + 36/5 - 2/5*a**3 - 16/5*a**2.
-2*(a - 1)*(a + 3)*(a + 6)/5
Factor 13359 + 2*v**2 - 364*v + 6176 - 2973.
2*(v - 91)**2
Let q be -2 - (-1 + (-12)/3). Suppose -k + q - 1 = 0. Factor 6 - 8*z**3 - 7*z**k + 13*z**2 + 28*z**2 - 32*z.
-2*(z - 3)*(z - 1)*(4*z - 1)
Let d(s) be the first derivative of -s**4/14 - 4*s**3/7 - 9*s**2/7 - 106. Factor d(k).
-2*k*(k + 3)**2/7
Let q be 95/8 + 7038/(-612). Factor 3/8*p**2 + 0*p + 0 - 9/8*p**3 - q*p**5 + 9/8*p**4.
-3*p**2*(p - 1)**3/8
Let h(m) = -m**2 - 10*m - 14. Let j be h(-8). Suppose j*u = -4*u + 4*u. Let u + 1/4*q**3 + 0*q + 1/4*q**4 - 1/4*q**2 - 1/4*q**5 = 0. Calculate q.
-1, 0, 1
Let n(m) be the first derivative of -5*m**4/12 - 25*m**3/3 + 60*m**2 - 380*m/3 + 106. Factor n(q).
-5*(q - 2)**2*(q + 19)/3
Suppose 3*q**3 - 10*q - 3*q**2 + 27*q - 11*q - 12*q = 0. Calculate q.
-1, 0, 2
Suppose -5*c + 16 = -29. Suppose 2*t - 9 = -3*u - 2*u, 3*u = 3*t + 18. Factor 2 + u*y - 4*y**3 + 6 + c*y.
-4*(y - 2)*(y + 1)**2
Let g(f) be the second derivative of f**7/42 + 8*f**6/15 + 21*f**5/5 + 12*f**4 + 6*f + 1. Factor g(k).
k**2*(k + 4)*(k + 6)**2
Let h(r) be the second derivative of -r**7/84 + r**6/30 + 13*r**5/40 + 5*r**4/12 - 30*r - 2. Let h(u) = 0. Calculate u.
-2, -1, 0, 5
Factor 5*c**4 + 5*c**5 + 37492 - 37492 + 2*c**3 + 2*c**4.
c**3*(c + 1)*(5*c + 2)
Let y = 1401/104 + 3/104. Factor -9*p**2 - 6 - 3/2*p**3 - y*p.
-3*(p + 1)**2*(p + 4)/2
Suppose -55 = -3*d - 5*r + 18, 0 = 3*d + 3*r - 63. Let b be (18 - d)*(-2)/(-24). Factor 0 + 0*v + 0*v**2 - 1/3*v**3 - b*v**4.
-v**3*(v + 2)/6
Let -1/2*p**3 - 23/2*p + 9/2*p**2 + 15/2 = 0. Calculate p.
1, 3, 5
Suppose 0 = 5*l - 14*l + 45. Determine z, given that -7*z + l*z - 6*z + 5*z**3 + z**3 - 8*z**2 = 0.
-2/3, 0, 2
Let a(x) be the first derivative of -5*x**3 - 5*x**4 + 16 + 0*x + 5/2*x**2. Determine r so that a(r) = 0.
-1, 0, 1/4
Suppose i + 1 - 3 = 0. Let t be 48/126 - i/(-7). Factor 1/3*p**2 + 1/3 - t*p.
(p - 1)**2/3
Let f(u) be the third derivative of 0*u - 2*u**2 + 1/7*u**7 - 5/8*u**4 + 0 - 1/2*u**6 + 0*u**3 - 5/336*u**8 + 5/6*u**5. Determine x, given that f(x) = 0.
0, 1, 3
Factor 81*p - 3/4*p**4 - 54*p**2 + 45/4*p**3 + 0.
-3*p*(p - 6)**2*(p - 3)/4
Let v be 112/330 - 174/(-2871). Factor 7/5*i**3 - v*i**2 + 0 + 0*i - i**4.
-i**2*(i - 1)*(5*i - 2)/5
Let x(l) be the third derivative of -1/40*l**6 - 1/210*l**7 + l**2 + 0 + 0*l + 0*l**3 + 1/336*l**8 + 1/12*l**4 + 1/60*l**5. Factor x(n).
n*(n - 2)*(n - 1)*(n + 1)**2
Let m(h) = 3*h**5 - 13*h**4 - 3*h**3 + 3*h**2 + 5*h - 5. Let w(x) = -4*x