) = 0.
-1, 1
Let l = 59 + -56. Let d(r) be the first derivative of -21/5*r**5 - 69/4*r**4 - 39/2*r**2 - 4 - 27*r**l - 6*r. Determine k, given that d(k) = 0.
-1, -2/7
Let z be (-30)/4*72/(-90). Let w = z - 11/2. Factor w*s**3 - 1/2*s**2 - 1/2*s + 1/2.
(s - 1)**2*(s + 1)/2
Let p(u) be the third derivative of u**8/33600 - u**6/3600 + u**4/24 + 7*u**2. Let i(y) be the second derivative of p(y). Factor i(g).
g*(g - 1)*(g + 1)/5
Let x(j) = 2*j - 3. Let q be x(3). Let 4*f**3 - f**5 - 2*f**3 + 3*f**q - 4*f**3 = 0. Calculate f.
-1, 0, 1
Let b = 1 + 0. Suppose 3 = 2*s - b. Factor -s*w**4 - 2*w**3 + 3*w**5 - w**5 - w**2 + 3*w**2.
2*w**2*(w - 1)**2*(w + 1)
Suppose -4*c - c + 3*p = -13, 11 = 3*c - 5*p. What is a in 2*a**4 + 0 + c*a**3 + 2/3*a**2 + 2/3*a**5 + 0*a = 0?
-1, 0
Let a(p) be the first derivative of -1/3*p - 1/15*p**5 + 1 + 2/9*p**3 + 0*p**2 + 0*p**4. What is j in a(j) = 0?
-1, 1
Suppose 1/2 + n + 1/2*n**2 = 0. Calculate n.
-1
Factor -1/2 + 3/4*q + 0*q**2 - 1/4*q**3.
-(q - 1)**2*(q + 2)/4
Find g such that 24/7 - 20/7*g + 4/7*g**2 = 0.
2, 3
Let q(l) be the first derivative of -1/20*l**5 + 2 - 1/12*l**4 + 0*l**2 + 0*l**3 + l. Let d(a) be the first derivative of q(a). Solve d(b) = 0 for b.
-1, 0
Let x be 0 + (-28)/(-24) + -1. Let d(n) be the first derivative of x*n**3 - 2 + 1/2*n - 1/2*n**2. Find o, given that d(o) = 0.
1
Let z(l) = 4*l**2 - l + 4. Let t(y) = -8*y**2 + y - 9. Let f = -2 - 4. Let d(r) = f*t(r) - 13*z(r). Suppose d(u) = 0. What is u?
-1/4, 2
Let p be 95/4 + (-3)/4. Let -m**2 - 6*m - p + 23 - 2*m**2 = 0. Calculate m.
-2, 0
Let j(y) be the first derivative of y**5/40 + y**4/8 - y**3/24 - y**2/4 + 27. Let j(d) = 0. What is d?
-4, -1, 0, 1
Factor -2/13*f**2 + 0 - 2/13*f + 2/13*f**3 + 2/13*f**4.
2*f*(f - 1)*(f + 1)**2/13
Let b be 4*2*(-3)/(-6). Factor b*o**3 + 8*o**2 + 35*o - 35*o.
4*o**2*(o + 2)
Let h = -1 + 3. Factor 1 + 4*f - h*f + f**2 - f**2 + f**2.
(f + 1)**2
Let a(t) = t**3 + 4*t**2. Let h(s) = -2*s**2. Let y(l) = 4*a(l) + 10*h(l). Suppose y(v) = 0. What is v?
0, 1
Let k(i) be the first derivative of i**4/32 + i**3/6 + 5*i**2/16 + i/4 + 6. Factor k(s).
(s + 1)**2*(s + 2)/8
Let h(v) be the second derivative of 0*v**2 - 1/3*v**3 + 3*v - 1/2*v**4 + 0 - 1/15*v**6 - 3/10*v**5. Factor h(u).
-2*u*(u + 1)**3
Let i(y) be the second derivative of y**6/150 - 3*y**5/50 + y**4/5 - 4*y**3/15 + 7*y. Factor i(h).
h*(h - 2)**3/5
Let q = 401 - 3605/9. Determine w so that 0 + 2/9*w**2 - q*w = 0.
0, 2
Suppose 5*n + 4*r - 29 = 3*r, -3*r = -4*n + 8. Suppose d - 9 = -2*d. Suppose -z**4 + 0*z**5 + 7*z**4 + 2*z**2 + 6*z**d + 2*z**n = 0. What is z?
-1, 0
Let z(a) be the third derivative of -a**6/300 - a**5/50 - a**4/20 - a**3/15 + 4*a**2. Let z(v) = 0. What is v?
-1
Let a(c) be the second derivative of c**7/7 - 3*c**6/4 + 93*c**5/80 - c**4/8 - 9*c**3/8 + 3*c**2/4 - 19*c. Let a(k) = 0. What is k?
-1/2, 1/4, 1, 2
Let d be 5 + 2 + 2 + -4 + 0. Suppose 4/7*y**4 + 0*y + 10/7*y**d - 10/7*y**3 - 4/7*y**2 + 0 = 0. What is y?
-1, -2/5, 0, 1
Factor 1/2*n**2 + 1/4*n**3 + 0 + 1/4*n.
n*(n + 1)**2/4
Suppose 7 - 1 = -2*a. Let d(t) = 4*t**2 + t - 3. Let v(y) = 5*y**2 + y - 4. Let k(s) = a*v(s) + 4*d(s). Suppose k(r) = 0. Calculate r.
-1, 0
Let s be 4/(-16) - 25/(-4). Let d(j) = j - 4. Let z be d(s). Factor 2/7*k**3 + 8/7 + 10/7*k**z + 16/7*k.
2*(k + 1)*(k + 2)**2/7
Factor 1/2*y**3 + 1/2*y**2 - 1/2*y**4 + 0 - 1/2*y.
-y*(y - 1)**2*(y + 1)/2
Let 1/2*s**5 - 11/4*s**4 + 0 + 21/4*s**3 - 4*s**2 + s = 0. What is s?
0, 1/2, 1, 2
Let w = 80 - 117. Let x = -35 - w. Let 1/2*v**4 + 9/4*v**3 + v + 0 + 3*v**x = 0. Calculate v.
-2, -1/2, 0
Factor -1/5*w + 1/5*w**2 - 1/5*w**4 + 0 + 1/5*w**3.
-w*(w - 1)**2*(w + 1)/5
Let s(y) be the second derivative of -y**6/30 + 3*y**5/20 - y**4/12 - y**3/2 + y**2 - 2*y. Suppose s(a) = 0. Calculate a.
-1, 1, 2
Let o be 3 - (-32)/(-12) - -1. Let z(r) be the first derivative of o*r**3 + 2 - 2*r**2 - 4/5*r**5 + 1/6*r**6 + 3/4*r**4 + 0*r. Factor z(i).
i*(i - 2)**2*(i - 1)*(i + 1)
Let b(k) be the second derivative of -5*k - 5/27*k**3 - 1/3*k**2 + 0 - 1/27*k**4. Let b(v) = 0. What is v?
-3/2, -1
Let g = -2/65 + 144/455. Factor 0*x - 2/7 + g*x**2.
2*(x - 1)*(x + 1)/7
Let d(y) be the first derivative of 2/35*y**5 + 0*y + 3/28*y**4 + 0*y**3 - 1/14*y**2 + 7. Determine w so that d(w) = 0.
-1, 0, 1/2
Let f(o) be the first derivative of -2*o**6/15 + 11*o**5/25 - 9*o**4/20 + o**3/15 + o**2/10 - 6. Let f(s) = 0. What is s?
-1/4, 0, 1
Let c = 41 - 16. Let z = c - 73/3. What is t in -2/3*t**2 - 2/3*t + z*t**4 + 0 + 2/3*t**3 = 0?
-1, 0, 1
Let t(z) be the second derivative of 0*z**2 - z - 7/36*z**4 + 0 - 1/9*z**3. Solve t(m) = 0 for m.
-2/7, 0
Solve 48 - 60*k**2 + 27*k**2 + 29*k**2 - 16*k = 0.
-6, 2
Let i(k) be the first derivative of 3*k**5/20 + 3*k**4/4 + 3*k**3/2 + 3*k**2/2 + 3*k/4 - 1. Solve i(q) = 0.
-1
Let x(y) = y**2 - 12*y - 24. Let o be x(14). Let r(p) be the third derivative of 0 + 0*p + 1/54*p**o + 1/270*p**5 + 3*p**2 - 1/540*p**6 + 0*p**3. Factor r(a).
-2*a*(a - 2)*(a + 1)/9
Factor -5*d**5 + 3*d**5 - 2*d**4 + d**3 + d**3 + 2*d**2.
-2*d**2*(d - 1)*(d + 1)**2
Let j(n) = -n**5 - 8*n**4 - 4*n**2 - 5*n. Let o(u) = -2*u**5 - 15*u**4 - 7*u**2 - 9*u. Let l(v) = -11*j(v) + 6*o(v). Determine w, given that l(w) = 0.
-1, 0, 1
Let q(m) be the third derivative of m**6/1440 - m**5/480 + m**3/2 - m**2. Let z(i) be the first derivative of q(i). Let z(p) = 0. Calculate p.
0, 1
Suppose 0 = -2*g - 0*g + 16. Suppose -o - 5*a - g = 0, a = 4*o + 6*a + 2. Factor -2*x**3 - 3*x**o + 2*x**3 + 4 + x**3.
(x - 2)**2*(x + 1)
Let f be 4 + (-19)/4 + 1. Find r, given that f*r**2 + 0 + 1/4*r = 0.
-1, 0
Suppose -3*x + 27 = -21. Let y = x - 12. What is v in -24/5*v**y - 18/5*v**5 + 8/5*v + 24/5*v**2 + 0 + 2*v**3 = 0?
-1, -2/3, 0, 1
Let h = 989/5 - 197. Let c(k) be the first derivative of -1/5*k**2 - h*k + 4/15*k**3 - 3 + 1/10*k**4. Suppose c(b) = 0. What is b?
-2, -1, 1
Let o = -48 + 146/3. Find x, given that 0*x - 2/3 + o*x**2 = 0.
-1, 1
Determine a so that 20*a**2 + 10*a**3 - 15/2*a - 45/2 = 0.
-3/2, 1
Let q = -20 + 19. Let y be (0/3)/(3/q). Factor 1/3*u**3 + 0 + 1/3*u**4 + 0*u**2 + y*u.
u**3*(u + 1)/3
Let c(b) be the first derivative of -2*b**3/51 + 2*b**2/17 + 12. Factor c(t).
-2*t*(t - 2)/17
Suppose -4*y + 5*y = 5. Suppose 4*t + s - 2*s = 4, -3*t - y*s = -26. Factor -392*n**2 - 184*n + 686*n**4 - 4 + 20 + 1148*n**t - 1274*n**3.
2*(n - 1)*(7*n - 2)**3
Let u be 2 - (-9)/((-108)/16). Let 0 + 0*d - 1/3*d**3 - u*d**2 = 0. Calculate d.
-2, 0
Let i(m) = m**4 + m**2 - m + 1. Let l(h) = -h**5 - 9*h**3 + 2*h**2 + 3*h - 5. Let x(w) = 5*i(w) + l(w). Factor x(z).
-z*(z - 2)*(z - 1)**3
Suppose 3*s + 30 = -r - 3*r, -5*s - 2*r - 50 = 0. Let b be (-5)/10 + s/(-4). Find h, given that -2*h**2 - 3*h**b + 5*h**2 + 4 + 4*h + h**2 = 0.
-2
Let g(j) be the third derivative of -j**10/12600 + j**8/2240 - j**7/1680 + j**5/12 - 4*j**2. Let x(y) be the third derivative of g(y). Factor x(i).
-3*i*(i + 1)*(2*i - 1)**2
Let o(d) = 6*d**4 + 42*d**3 + 50*d**2 + 38*d + 12. Let q(p) = -11*p**4 - 85*p**3 - 99*p**2 - 77*p - 25. Let x(v) = 9*o(v) + 4*q(v). Factor x(n).
2*(n + 1)**3*(5*n + 4)
Let m = -3 - -2. Let s be (1/(-5))/(m/2). Factor 2/5*v**3 - 2/5 + s*v**2 - 2/5*v.
2*(v - 1)*(v + 1)**2/5
Let t(d) be the first derivative of d**5/10 + d**4/3 - 2*d + 4. Let w(p) be the first derivative of t(p). Solve w(h) = 0 for h.
-2, 0
Let b(i) be the first derivative of -i**3/21 + 5. Suppose b(u) = 0. What is u?
0
Let r be 4/(-24)*(3 + -5). Let v(o) be the first derivative of 0*o + r*o**3 - 1/8*o**4 + 1 - 2/5*o**5 + 0*o**2 + 1/4*o**6. Factor v(d).
d**2*(d - 1)**2*(3*d + 2)/2
Let k(z) = z**2 + 2*z - 4. Let x be k(-3). Let u be x*3*4/(-20). Suppose -2/5*d**2 - 1/5 - u*d = 0. What is d?
-1, -1/2
Let i(g) be the first derivative of 3/7*g + 3/35*g**5 + 0*g**4 - 2/7*g**3 + 0*g**2 + 4. Factor i(a).
3*(a - 1)**2*(a + 1)**2/7
Let p(w) be the third derivative of 0*w + 5*w**2 - 28/75*w**5 - 16/15*w**3 + 8/75*w**6 + 4/5*w**4 + 1/840*w**8 - 3/175*w**7 + 0. Let p(r) = 0. What is r?
1, 2
Let q = 15 + -13. Factor 6*l**2 - l**3 - 3*l**q - 3*l**2 + 2*l**2.
-l**2*(l - 2)
Let q be -1*(0 + -3)/3. Let z(d) be the first derivative of 4/3*d + 1/9*d**3 + q - 2/3*d**2. Factor z(u).
(u - 2)**2/3
Let w(v) = -8*v - 5. Let f be w(-4). Let -84*h + f*h**3 - 6*h**2 - 21*h**