Let v(s) be the second derivative of s**4/6 - 64*s**3/3 + 1024*s**2 - 2*s + 73. Factor v(x).
2*(x - 32)**2
Let g = 20407/5 - 4079. Factor -g*c**2 + 3*c + 3/5*c**3 - 6/5.
3*(c - 2)*(c - 1)**2/5
Let s(w) be the first derivative of w**7/105 - 7*w**6/240 + w**5/60 + w**4/48 - 15*w**2/2 + 7. Let n(l) be the second derivative of s(l). Factor n(m).
m*(m - 1)**2*(4*m + 1)/2
Let j(i) be the first derivative of i**6/180 + i**5/30 + i**4/24 - i**3/9 - i**2/3 + 3*i - 1. Let t(s) be the first derivative of j(s). Factor t(a).
(a - 1)*(a + 1)*(a + 2)**2/6
Let z(d) be the first derivative of -6*d - 2*d**2 + 5*d - 12 + 2*d - 4*d. Let w(x) = x**2. Let a(v) = -w(v) + z(v). Factor a(b).
-(b + 1)*(b + 3)
Let h(g) be the second derivative of 0 - 5/6*g**4 - 5/21*g**7 + 0*g**2 - 5*g - 1/4*g**5 + 0*g**3 + 5/6*g**6. Determine l, given that h(l) = 0.
-1/2, 0, 1, 2
Suppose -n + 4*l = -24 + 4, -11 = -n - 5*l. Suppose -3*c = -5*c - 8, 0 = -t + 4*c + n. Let -5/2*f**4 + 4*f**3 + 0*f + t + 2*f**2 = 0. What is f?
-2/5, 0, 2
Let h(s) be the second derivative of s**7/441 - 2*s**6/315 - s**5/70 + 2*s**4/63 + 4*s**3/63 + 91*s. Suppose h(f) = 0. Calculate f.
-1, 0, 2
Let j = -98 - -113. Suppose 10*r - j = 5*r. Factor 1 - 15/4*t**2 + t**3 + r*t.
(t - 2)**2*(4*t + 1)/4
Let f(y) be the first derivative of y**4/4 + 160*y**3/3 + 3200*y**2 + 105. Suppose f(t) = 0. Calculate t.
-80, 0
Let h be (-38)/(-209) + 856/11. Let n be (-8)/2 - h/(-18). Factor 0*r + 1/3*r**3 + 0 - n*r**4 + 0*r**2.
-r**3*(r - 1)/3
Let d = -43 + 48. Let v(b) be the third derivative of 0*b**3 - 1/20*b**d + 0 - 1/120*b**6 + 0*b**4 + b**2 + 0*b. Factor v(y).
-y**2*(y + 3)
Let a = -686 + 686. Let w(g) be the second derivative of a*g**6 - 1/40*g**5 + 0*g**3 + 0*g**2 - g - 1/36*g**4 + 1/252*g**7 + 0. Find x such that w(x) = 0.
-1, 0, 2
Let l(o) = -12*o**2 + 20*o. Let v(w) be the third derivative of 2*w**5/15 - 13*w**4/24 + 6*w**2. Let s(m) = 5*l(m) + 8*v(m). Factor s(z).
4*z*(z - 1)
Let q(d) = -2*d**2 - 3*d + 2. Let m be q(-4). Let u be 153/34*(-2)/m. What is t in u*t**2 + 1/2 - t = 0?
1
Let f(r) = 11*r**2 + 5*r - 6. Let l(n) = -10*n**2 - 5*n + 5. Let m = -97 - -103. Let s(p) = m*l(p) + 5*f(p). Solve s(t) = 0.
-1, 0
Let q(w) be the first derivative of -w**5/20 + w**4/12 + 2*w**3/3 - 2*w**2 - 10*w - 3. Let y(g) be the first derivative of q(g). Factor y(b).
-(b - 2)*(b - 1)*(b + 2)
Let d(m) be the second derivative of -3*m + 1/12*m**4 + 0 + 0*m**2 + 0*m**3 + 1/5*m**6 - 5/84*m**7 - 9/40*m**5. Let d(k) = 0. Calculate k.
0, 2/5, 1
Let j(c) be the third derivative of 0*c - 1/1512*c**8 + 0 + 1/12*c**4 - 2/135*c**6 + 0*c**3 - 1/45*c**5 + 2/315*c**7 - 21*c**2. Suppose j(m) = 0. Calculate m.
-1, 0, 1, 3
Let v(m) be the second derivative of -m**6/1620 + m**5/540 - 13*m**3/3 - 23*m. Let p(i) be the second derivative of v(i). Factor p(x).
-2*x*(x - 1)/9
Let i(j) be the first derivative of -3*j**4/28 - 8*j**3/7 - 27*j**2/14 + 54*j/7 - 147. Let i(q) = 0. What is q?
-6, -3, 1
Let z(q) be the third derivative of q**6/60 + q**5/15 - 8*q**4/3 - 32*q**3 + 2*q**2 - 395. Let z(t) = 0. What is t?
-4, 6
Let q = -25 - -27. Factor -3*h**2 - h**2 + q*h + 8 + 2*h.
-4*(h - 2)*(h + 1)
Let g(k) = -3*k**2 + 4*k + 5. Let t(v) = -10*v - 16 + 7*v**2 + v + 5. Suppose -6 = b - 0*b. Let z(d) = b*t(d) - 15*g(d). Determine x, given that z(x) = 0.
-1, 3
Find y such that -3/10*y**3 - 2/5 + 7/5*y**2 - 7/10*y = 0.
-1/3, 1, 4
Let j be (4/(120/9))/((-201)/(-268)). Solve 4/5*a + j*a**4 + 8/5*a**3 + 0 + 2*a**2 = 0 for a.
-2, -1, 0
Let w be 2*6/(-4) - (-6)/2. What is v in 16 + w - v**3 + 9*v**2 + 0*v**3 - 24*v = 0?
1, 4
Let q(g) = -8*g + 58. Let t(n) = -n**3 - 17*n**2 - 2*n - 27. Let j be t(-17). Let y be q(j). Factor -5/3*c + 1/3*c**4 - 2/3 - c**y + 1/3*c**3.
(c - 2)*(c + 1)**3/3
Factor -9*y**2 + 3/7*y**3 - 3/7*y + 9.
3*(y - 21)*(y - 1)*(y + 1)/7
Let j(a) be the first derivative of a**6/105 - 3*a**5/70 + a**4/42 + a**3/7 - 2*a**2/7 + 13*a + 8. Let d(v) be the first derivative of j(v). Factor d(t).
2*(t - 2)*(t - 1)**2*(t + 1)/7
Let o(v) be the second derivative of -v**7/21 + v**6/15 + 3*v**5/10 - v**4/6 - 2*v**3/3 + 74*v. Suppose o(m) = 0. What is m?
-1, 0, 1, 2
Suppose 52*c - 622 = 47*c - 4*f, -386 = -3*c + 4*f. Let w be ((-12)/(-9))/(357/c). What is k in 4/17 - 10/17*k + 8/17*k**3 - w*k**4 + 2/17*k**5 + 4/17*k**2 = 0?
-1, 1, 2
Let p(y) be the second derivative of 1/10*y**6 - 3/4*y**4 + 2*y**3 + 0 - 3/10*y**5 + 6*y**2 + 42*y. Factor p(l).
3*(l - 2)**2*(l + 1)**2
Suppose -3*j - 82 = -j. Let r = 44 + j. Let -t**2 + 9/2*t**r + 0 - 7/2*t**4 + 0*t = 0. Calculate t.
0, 2/7, 1
Let g be (3 + -6)/((-3)/2). Factor -45*p**2 + p**4 + g*p**4 - 49 - 69*p + 19 - 3*p**3.
3*(p - 5)*(p + 1)**2*(p + 2)
Let f(q) = q**2 + 20*q + 40. Let v be f(-18). Factor 1 - 3*p**4 - p + 2*p**3 + v*p - 4*p**3 - p**5 + 2*p**2 + 0*p.
-(p - 1)*(p + 1)**4
Let q be (-2*(-2)/312)/(195/20). Let h = q + 15196/10647. Factor 8/7*g + 12/7*g**2 + 2/7*g**4 - 16/7 - h*g**3.
2*(g - 2)**3*(g + 1)/7
Let q = -735 + 2206/3. Let n(r) be the first derivative of 0*r + q*r**3 + 0*r**2 + 7 + 1/4*r**4. Factor n(j).
j**2*(j + 1)
Let d(k) be the third derivative of 5*k**8/336 + k**7/7 + k**6/6 - k**5/2 - 25*k**4/24 + 18*k**2. Factor d(r).
5*r*(r - 1)*(r + 1)**2*(r + 5)
Factor 12/5*c - 1/10*c**2 - 22/5.
-(c - 22)*(c - 2)/10
Suppose 5*t - 4*t - 8 = 0. Factor -20*i**4 + 2*i - 2*i - t*i**3 - 4*i**2 + 16*i**4.
-4*i**2*(i + 1)**2
Let w(o) be the first derivative of o**4/2 - 8*o**3/3 - 35*o**2 + 300*o + 373. Factor w(l).
2*(l - 5)**2*(l + 6)
Let g(q) be the third derivative of -q**7/75 - q**6/24 + q**5/6 - q**4/24 - q**3/5 + 20*q**2 - 1. Suppose g(k) = 0. Calculate k.
-3, -2/7, 1/2, 1
Let b be -10*3/3*53/(-265). Let t(o) be the first derivative of -12*o**b + 3/2*o**4 - 3*o**3 - 12*o - 6 + 3/5*o**5. Let t(q) = 0. What is q?
-2, -1, 2
Let z be 15/(-4) + 12/16. Let c be (z + 3)*(16/6 + -3). Factor c*k + 0 + 0*k**2 + 1/2*k**4 - 1/2*k**5 + k**3.
-k**3*(k - 2)*(k + 1)/2
Suppose 0 = -4*n - 3*m + 33, -4*n - 5*m + 134 - 111 = 0. Let t(r) be the second derivative of 0 - 5/12*r**4 + 0*r**2 - 5/6*r**3 - n*r. Factor t(b).
-5*b*(b + 1)
Let o be (-14)/((-392)/21) + 3/(-4). Let s = 47 + -43. Factor 0 + 0*p + 0*p**3 - 1/6*p**s + 1/6*p**5 + o*p**2.
p**4*(p - 1)/6
Let h(p) be the third derivative of -p**5/78 - 7*p**4/39 - 5*p**3/13 - 46*p**2 + 2. Solve h(k) = 0 for k.
-5, -3/5
Let q(y) be the first derivative of y**5/10 + 2*y**4/3 + 5*y**3/3 + 2*y**2 + 24*y - 2. Let m(r) be the first derivative of q(r). Factor m(a).
2*(a + 1)**2*(a + 2)
Suppose -3*x + j + 16 = x, 4 = -j. Factor 5 - 9*o - x*o**2 - 1 + 8.
-3*(o - 1)*(o + 4)
Let h(v) be the second derivative of -v**7/63 - 4*v**6/45 - v**5/5 - 2*v**4/9 - v**3/9 - 66*v. Factor h(k).
-2*k*(k + 1)**4/3
Let l = 49 + -32. Factor -12*a**2 - 13*a**4 + a**3 + l*a**4 + 3*a**3 - 4*a + 8.
4*(a - 1)**2*(a + 1)*(a + 2)
Let d = -259/30 - -59/6. Let y(n) be the first derivative of 1/10*n**4 - d*n - 10 - n**2 - 2/15*n**3. Factor y(z).
2*(z - 3)*(z + 1)**2/5
Suppose -2*i + 10 = 14. Let z(v) = -v**3 + v**2 + v - 1. Let x(o) = -6*o**4 + 13*o**3 - 5*o**2 - 13*o + 11. Let h(m) = i*x(m) - 22*z(m). Solve h(s) = 0.
-1, 0, 1/3, 1
Let t(p) be the second derivative of 1/45*p**3 + 0*p**6 + 0*p**2 + 0*p**4 + 1/315*p**7 + 0 + 2*p - 1/75*p**5. Suppose t(o) = 0. What is o?
-1, 0, 1
Suppose -2*h - h + 3*c + 33 = 0, 0 = 5*h - 2*c - 52. Factor -h*g**2 + 20*g**2 + 12 + 37*g - 3*g.
2*(g + 3)*(5*g + 2)
Suppose 3*k = -a + 13, -7*k + 2*k = -2*a - 29. Factor 3/5*u**k + 12/5*u**4 + 0 - 6/5*u**3 - 36/5*u**2 + 27/5*u.
3*u*(u - 1)**2*(u + 3)**2/5
Let x(j) = -2*j**2 + 15*j - 7. Let k be x(7). Suppose k = p + p - 10. Factor 10*r - 9*r + p*r**2 - 6*r.
5*r*(r - 1)
Solve -190/3*y + 185/3 + 5/3*y**2 = 0 for y.
1, 37
Factor 1352/7 + 2/7*w**2 + 104/7*w.
2*(w + 26)**2/7
Solve 16/9 + 2/9*p**2 + 4/3*p = 0 for p.
-4, -2
Let r(p) be the third derivative of -p**7/42 - 11*p**6/24 - 13*p**5/4 - 245*p**4/24 - 50*p**3/3 + 8*p**2 - 5*p. Factor r(m).
-5*(m + 1)**2*(m + 4)*(m + 5)
Let b(m) be the second derivative of -1/72*m**4 + 1/180*m**6 - 1/3*m**2 - 1/252*m**7 + m + 1/24*m**5 - 2/9*m**3 + 0. Factor b(i).
-(i - 2)**2*(i + 1)**3/6
Let y(d) be the second derivative of -d**5/60 + 2*d**4/9 - 13*d**3/18 + d**2 - 206*d. Factor y(r).
-(r - 6)*(r - 1)**2/3
Let x(t) = t**2 + t