). Let j(k) = 0. Calculate k.
-1, 0, 2
Suppose -42 = 3*j - 57. Let l(r) be the third derivative of 0 + 0*r**3 + 0*r - 3*r**2 - 4/15*r**j - 7/120*r**6 - 1/6*r**4. Find y such that l(y) = 0.
-2, -2/7, 0
Let p(u) be the first derivative of -u**3/15 - 3*u**2/10 - 2*u/5 - 27. Factor p(m).
-(m + 1)*(m + 2)/5
Find m, given that 0 - 1/5*m**2 - 1/5*m = 0.
-1, 0
Let o(z) be the first derivative of -z**6/60 + z**5/40 + z**4/8 - z**3/12 - z**2/2 - z + 2. Let n(b) be the first derivative of o(b). Factor n(d).
-(d - 2)*(d - 1)*(d + 1)**2/2
Let l(h) be the second derivative of 2*h**7/21 - h**6/5 + h**4/6 - 7*h. Factor l(o).
2*o**2*(o - 1)**2*(2*o + 1)
Let j(q) = -2*q**3 - 5*q**2 - 4*q + 2. Suppose 0 = -2*b + 5*b - 21. Let i(k) = -5*k**3 - 11*k**2 - 9*k + 4. Let d(f) = b*j(f) - 3*i(f). Factor d(h).
(h - 2)*(h - 1)*(h + 1)
Factor 2/7*n**3 + 24/7*n + 12/7*n**2 + 16/7.
2*(n + 2)**3/7
Let k(u) = u**4 + u**3 + u**2 + 1. Let c(r) = r**3 - 1. Let w(d) = -3*c(d) - 3*k(d). Factor w(h).
-3*h**2*(h + 1)**2
Solve -64/17 - 116/17*g**2 - 14/17*g**3 - 256/17*g = 0 for g.
-4, -2/7
Let w = 17 - 8. Let d = w + -4. Factor -5 + 2*s - 2*s**3 + d.
-2*s*(s - 1)*(s + 1)
Let a(f) be the first derivative of -5*f**4/4 + 5*f**3/3 + 18. Factor a(r).
-5*r**2*(r - 1)
Let i(v) = 4*v**2 - 4*v + 6. Let y(u) be the third derivative of -3*u**5/20 + 7*u**4/24 - 13*u**3/6 + 2*u**2. Let k(l) = -5*i(l) - 2*y(l). Factor k(g).
-2*(g - 2)*(g - 1)
Suppose -v + 32 = 5*f + 7, -3*v - 3*f = -15. Let l(k) be the third derivative of v + 0*k + 1/21*k**3 - 1/210*k**5 + 0*k**4 - 2*k**2. Factor l(u).
-2*(u - 1)*(u + 1)/7
Let w = 1088 + -1085. Factor 2/11*s**2 + 2/11*s**w + 0 - 2/11*s - 2/11*s**4.
-2*s*(s - 1)**2*(s + 1)/11
Factor 16*n - 16 + 5*n**2 - 4*n**3 + 4*n**4 - 12*n**3 + 10*n**2 - 3*n**2.
4*(n - 2)**2*(n - 1)*(n + 1)
Let a = 239582/583791 - 2/14969. Let u = a - 2/195. Factor -80*g**3 + 50*g**4 + 36*g**2 - 32/5*g + u.
2*(g - 1)*(5*g - 1)**3/5
Let r(j) be the third derivative of 0 + 0*j**5 + 3*j**2 + 0*j + 1/660*j**6 - 1/132*j**4 + 0*j**3. Factor r(c).
2*c*(c - 1)*(c + 1)/11
Let h = 15359/1935 - 305/43. Let a = -4/9 + h. Solve -2/5 - 2/5*s + 2/5*s**3 + a*s**2 = 0 for s.
-1, 1
Let k be (-3)/(30/(-21) + 1). Let t(m) be the second derivative of m - 1/2*m**2 + 1/42*m**k - 1/30*m**6 + 1/6*m**4 + 1/6*m**3 - 1/10*m**5 + 0. Factor t(p).
(p - 1)**3*(p + 1)**2
Let o be (-10)/12*(-24)/80. Factor -o*c**3 - 1/4*c + 0 - 1/2*c**2.
-c*(c + 1)**2/4
Suppose 4*u + 5*y - 21 = 0, -2*u = u - 5*y - 7. Let l(f) = -f**3 + 3*f**2 + 5*f + 2. Let g be l(u). Factor -g*a - 2*a**2 + 8*a + a**2.
-a*(a - 2)
Let f(s) be the first derivative of -1/9*s**3 + 1 - 1/6*s**2 - s - 1/36*s**4. Let t(v) be the first derivative of f(v). Suppose t(h) = 0. What is h?
-1
Factor -8/9*s**2 + 2/9*s**3 - 4/9 + 10/9*s.
2*(s - 2)*(s - 1)**2/9
Let l be (-70)/22 - 4/(-22). Let w(i) = -2*i - 4. Let a be w(l). Factor 1 - 2*z + 9*z**2 - 2*z - 3*z**a - 3*z**3 - z**3 + z**4.
(z - 1)**4
Let q(m) be the second derivative of -1/600*m**6 - 3/200*m**5 + 1/3*m**3 - 2*m + 0 - 1/20*m**4 + 0*m**2. Let l(z) be the second derivative of q(z). Factor l(o).
-3*(o + 1)*(o + 2)/5
Let l(w) be the third derivative of -w**6/40 - w**5/12 - 7*w**4/72 - w**3/18 + 6*w**2. What is b in l(b) = 0?
-1, -1/3
Suppose -7*a = -3*a. Let r(p) be the second derivative of 0*p**3 + 1/120*p**6 + 0*p**5 - p + a*p**2 + 0 + 0*p**4. Factor r(n).
n**4/4
Let y = 2392/19 - 126. Let p = y + 25/57. Factor -p*s - 1/3*s**4 + 0 + 1/3*s**3 + 1/3*s**2.
-s*(s - 1)**2*(s + 1)/3
Factor 0 + 0*a + 1/5*a**3 - 2/5*a**2.
a**2*(a - 2)/5
Let l be 4 + 136/(-36) + 272/72. Factor 0*c**l + 0*c + 0 + 1/4*c**3 + 0*c**2 - 1/4*c**5.
-c**3*(c - 1)*(c + 1)/4
Let y(z) be the second derivative of 1/70*z**6 - 1/28*z**4 + 0 + 1/14*z**3 + 5*z - 3/140*z**5 + 0*z**2. Find a, given that y(a) = 0.
-1, 0, 1
Let s = 21104/4521 + -2/1507. Find o, given that -s*o**2 - 6 + 2/3*o**3 + 10*o = 0.
1, 3
Let b(z) be the second derivative of z**4/3 + 8*z**3/3 + 8*z**2 - 5*z. Factor b(d).
4*(d + 2)**2
Let p(r) be the first derivative of 2 + 3/4*r**4 + r**3 - 3/2*r**2 - 3*r. Suppose p(f) = 0. What is f?
-1, 1
What is g in g**2 - 361 + 361 = 0?
0
Let y(p) = p + 9. Let o be y(-5). Suppose o*c = -5*g + 7, 2 = -2*g - c - 3*c. Factor 0 + 0*w + 0*w**g + 2/3*w**2 - 2/3*w**4.
-2*w**2*(w - 1)*(w + 1)/3
Let -2/7*a**2 + 0*a + 4/7*a**3 - 2/7*a**4 + 0 = 0. What is a?
0, 1
Let n(w) be the second derivative of 2*w**7/15 - w**6/10 + w**5/50 - 5*w. Factor n(p).
p**3*(4*p - 1)*(7*p - 2)/5
Let u(q) be the second derivative of -5*q**4/12 + 35*q**3/6 - 25*q**2 + 49*q. Determine n, given that u(n) = 0.
2, 5
Let r(v) be the third derivative of -v**8/7 + 4*v**7/35 + 7*v**6/40 + v**5/20 + 3*v**2. Find t, given that r(t) = 0.
-1/4, 0, 1
Let w be 4 + 2*(1 + -2). Factor -2*q**3 + w*q**3 - q**3 + 2*q - q**3 - 2 + 2*q**2.
-2*(q - 1)**2*(q + 1)
Let y = 29 + -27. Suppose -3*v + v = 0. Suppose -2/11*w**y - 2/11*w + v = 0. What is w?
-1, 0
Let v be (6/(-10))/(-2*(-4)/(-40)). Let i(x) be the first derivative of 1/5*x**2 - 2/15*x**v + 0*x + 1. Factor i(a).
-2*a*(a - 1)/5
Let s be 1/(1*(-3)/(-12)). Suppose -l = s*l. Factor 0*a + 1/4*a**2 - 1/4*a**3 + l.
-a**2*(a - 1)/4
Let g(i) be the first derivative of -19*i**3/2 - 11*i**2 - 2*i + 16. Determine k so that g(k) = 0.
-2/3, -2/19
Factor -2*x**2 - 24*x**3 - 27*x + 47*x - x**2 + 4*x**5 + 16*x**4 - 13*x**2.
4*x*(x - 1)**2*(x + 1)*(x + 5)
Let m(a) be the first derivative of a**5/10 + a**4 + 5*a**3/2 - 2*a**2 - 8*a + 25. Find t such that m(t) = 0.
-4, -1, 1
Let v(t) be the third derivative of -t**4/24 + 12*t**2. Let y(g) = -5*g + g**3 - g**2 - 2*g**3 + 3*g. Let k(a) = -4*v(a) + y(a). Factor k(f).
-f*(f - 1)*(f + 2)
Let j = 85/114 + -3/38. Suppose n = 10*n - n. Factor 0*p + n - 2/3*p**4 - 2/3*p**3 + 2/3*p**5 + j*p**2.
2*p**2*(p - 1)**2*(p + 1)/3
Let n(o) be the first derivative of o**9/12096 - o**7/840 - o**6/720 + o**5/160 + o**4/48 + o**3 - 1. Let v(t) be the third derivative of n(t). Factor v(z).
(z - 2)*(z - 1)*(z + 1)**3/4
Let s(u) = -u**2 - 14*u + 37. Let b be s(-16). Let a(c) be the third derivative of 0*c + 1/60*c**b + 0 + 1/30*c**6 + 0*c**3 + 0*c**4 - c**2. Factor a(h).
h**2*(4*h + 1)
Let v be (-1 + 1)/(2/2). Let w(p) be the first derivative of -2 + 0*p + 1/6*p**3 - 1/16*p**4 + v*p**2. Factor w(m).
-m**2*(m - 2)/4
Let r = -46 - -277/6. Let v(w) be the third derivative of 0 + 0*w - 1/3*w**3 - 1/30*w**5 - 2*w**2 + r*w**4. Factor v(f).
-2*(f - 1)**2
Let a(m) be the third derivative of m**8/11200 + m**7/1400 - m**5/50 + m**4/8 + 2*m**2. Let d(r) be the second derivative of a(r). Factor d(i).
3*(i - 1)*(i + 2)**2/5
Suppose f - 17 = -3*o, 2*f = o - 2 + 8. Factor 0*n**2 + 2/11*n**f + 2/11*n**3 + 4/11*n**4 + 0*n + 0.
2*n**3*(n + 1)**2/11
Suppose 0 = 3*w + 5*z - 6, 4*w - 7 = 3*z + 1. Let h(k) be the first derivative of 0*k + 1/6*k**3 + 0*k**w + 1/8*k**4 - 3. Factor h(d).
d**2*(d + 1)/2
Let u = 4 - 2. Let v = u - 0. Determine b, given that -4*b - 8/3 - 2*b**v - 1/3*b**3 = 0.
-2
Determine w, given that -8/3*w**2 + 4/3*w**4 + 10/3*w**5 + 10/3*w + 4/3 - 20/3*w**3 = 0.
-1, -2/5, 1
Let t be 0 - (1 + 1 + 0). Let k be 2 + ((-30)/(-9))/t. Suppose 0 - k*r**2 - 2/3*r = 0. What is r?
-2, 0
What is c in 10/7*c - 2/7*c**2 - 6/7 - 2/7*c**3 = 0?
-3, 1
Let p be (-2)/11 + 658/2772. Let a(y) be the second derivative of 3*y - 1/3*y**2 + 0*y**3 + 0 + p*y**4. Determine v, given that a(v) = 0.
-1, 1
Let g(l) be the third derivative of -l**9/83160 + l**7/6930 - l**5/660 + l**4/8 - 6*l**2. Let c(h) be the second derivative of g(h). Find x such that c(x) = 0.
-1, 1
Let p be 2/4 - (-28)/8. Factor 3*y + p - 2 + 5*y**2 - 4*y**2.
(y + 1)*(y + 2)
Suppose -3*w + 3 + 54 = 0. Let x = w - 17. Determine p, given that -1/2*p**5 - 1/2*p**4 + p**3 + p**x - 1/2 - 1/2*p = 0.
-1, 1
Let b(x) be the first derivative of 7/10*x**5 + 0*x - x**3 - 5/8*x**4 - 1 + 1/5*x**6 + 1/2*x**2. Let d(g) be the second derivative of b(g). Solve d(k) = 0.
-2, -1/4, 1/2
Let l(c) = -7*c**3 - 27*c**2 - 18*c - 2. Let i(x) = 120*x**3 + 460*x**2 + 305*x + 35. Let f(g) = 2*i(g) + 35*l(g). Factor f(y).
-5*y*(y + 1)*(y + 4)
Let w = -21 + 6. Let z be 6*(-10)/w - 2. Factor 1/5*j**z - 2/5*j + 1/5.
(j - 1)**2/5
Let y be 44/(-286) + 56/26. Let k(w) be the first derivative of 1/12*w**4 + 0*w**y + 0*w - 1/9*w**3 - 3. Determin