 1)/5
Let h = -37 + 37. Let b(f) be the second derivative of 2*f + h + 1/4*f**2 - 1/8*f**3 + 1/48*f**4. Determine a, given that b(a) = 0.
1, 2
Suppose -9*v + 4*v - 180 = 0. Let p = -36 - v. Factor 2*s**3 + 1/3*s**5 - 4/3*s**2 + p - 4/3*s**4 + 1/3*s.
s*(s - 1)**4/3
Let q(c) = -3*c**2 - 8*c - 8. Let w(v) = -8*v**2 - 23*v - 23. Let b(z) = 11*q(z) - 4*w(z). Let o be b(4). Factor 0*k**3 + 2*k**o + 4*k**3 - k**4 - 3*k**3.
k**3*(k + 1)
Let t be 16 - 12 - 112/30. Let w(b) be the first derivative of -t*b**3 + 1/5*b**2 + 0*b + 1/10*b**4 - 2. Find i, given that w(i) = 0.
0, 1
Let f(y) be the third derivative of -y**6/180 - y**5/10 - 3*y**4/4 + y**3/6 + y**2. Let n(u) be the first derivative of f(u). Factor n(x).
-2*(x + 3)**2
Let y(a) be the second derivative of 0*a**2 - 1/42*a**7 + 1/6*a**4 - 1/15*a**6 - 3*a + 1/6*a**3 + 0*a**5 + 0. Determine n so that y(n) = 0.
-1, 0, 1
Let v(z) be the second derivative of -z**5/10 + 5*z**4/12 - z**3/3 - 4*z. Factor v(q).
-q*(q - 2)*(2*q - 1)
Factor -6/5*b**2 + 2/5*b - 8/5*b**3 + 0.
-2*b*(b + 1)*(4*b - 1)/5
Let r(x) be the second derivative of -x**9/60480 + x**8/4480 - x**7/1120 - x**4/2 + 3*x. Let h(t) be the third derivative of r(t). Factor h(b).
-b**2*(b - 3)**2/4
Let m(f) = -3*f - 1. Let q be m(-1). Factor 7*b**3 + b**2 + b**q - 5*b**3.
2*b**2*(b + 1)
Let n(b) be the first derivative of 9*b**5/10 + 2*b**4 - 13*b**3/6 - 4*b**2 + 2*b + 4. Determine o, given that n(o) = 0.
-2, -1, 2/9, 1
Let q = 3/53 - -26/477. Let l(p) be the first derivative of 0*p**2 + q*p**3 - 1/3*p - 3. Factor l(k).
(k - 1)*(k + 1)/3
Suppose -15 = -4*g + 1. Factor -3*z**g + 121*z**3 - 121*z**3 + 3*z**5.
3*z**4*(z - 1)
Let p(q) be the first derivative of q**4/4 + q**3 + 3*q**2/2 + q + 5. Let n(l) be the first derivative of p(l). Factor n(z).
3*(z + 1)**2
Let h be 1/(-2) - (-28)/8. Factor 2 - h + 3 + 2*b**2 + 4*b.
2*(b + 1)**2
Let m(h) be the first derivative of 0*h**4 + 1/3*h**3 + 0*h + 2 + 1/300*h**5 + 0*h**2 + 1/1800*h**6. Let p(v) be the third derivative of m(v). Factor p(c).
c*(c + 2)/5
Let z(n) = -n**2 + 3*n + 4. Let l be z(4). Suppose l = 2*h - 4*h + 6. Determine x, given that 0 - 2/3*x**5 + 2*x**h + 4/3*x**4 - 8/3*x**2 - 8/3*x = 0.
-1, 0, 2
Let q(v) be the second derivative of v**9/280 - v**7/70 - v**6/45 - v**5/60 - 7*v**4/12 - 2*v. Let p(a) be the third derivative of q(a). Solve p(g) = 0 for g.
-1/3, 1
Let f = -245/2 + 2707/22. Let v(w) = w**2 - 7*w - 6. Let s be v(8). Determine m, given that 2/11*m**4 + f*m**s + 0 + 6/11*m**3 + 2/11*m = 0.
-1, 0
Factor -1/6*r**4 + 0*r**2 + 0 + 0*r + 0*r**3.
-r**4/6
Let c = 28 + -16. Factor 10*g**5 - 12*g**5 - 2*g + 8*g**2 + 4*g**4 - c*g**3 + 4*g**4.
-2*g*(g - 1)**4
Let p(c) be the first derivative of c**6/36 + c**5/15 + c**4/24 - 3. Suppose p(k) = 0. What is k?
-1, 0
Let t be 184/44 - (-1 + 5). What is y in -2/11*y**3 + 0 + 0*y + t*y**4 + 0*y**2 = 0?
0, 1
Suppose -u + 0*u + 19 = -2*x, -67 = -4*u + 5*x. Suppose -5*j = q - u, j - 17 = -2*q - 3*q. Factor -q*l**4 - 6*l**3 - l - 3*l**5 + 11*l**4 + 2*l.
-l*(l - 1)**3*(3*l + 1)
Suppose -7 = r - 3*o, -3*r = -2*o - 2*o + 6. Factor 4*j**r - j**3 - j**2 - 3*j**3 + 5*j**2.
-4*j**2*(j - 2)
Let d(z) = -z**2 - z + 1. Let q(b) = -3*b**2 + 21*b - 7. Let s(g) = 22*d(g) + 2*q(g). Suppose s(j) = 0. Calculate j.
-2/7, 1
Factor -i + 8*i - 3*i + 5*i**2 + 11*i.
5*i*(i + 3)
Let h be (-5)/15*0 - (-20)/3. Let -h*c**2 + 0 + 23/3*c**3 + 4/3*c - 7/3*c**4 = 0. What is c?
0, 2/7, 1, 2
Let r(k) be the second derivative of -1/30*k**6 + 0 + 7/40*k**5 + 0*k**2 - 4*k + 1/12*k**4 + 0*k**3 - 1/12*k**7. Determine z, given that r(z) = 0.
-1, -2/7, 0, 1
Factor 1 + 7/2*o + 19/4*o**2 + o**4 + 1/8*o**5 + 25/8*o**3.
(o + 1)**2*(o + 2)**3/8
Suppose -4*p + 5*l + 18 = 0, -24 = -2*p + l - 18. Let 1/3*u**p + 1 + 4/3*u = 0. Calculate u.
-3, -1
Let k(g) be the third derivative of -g**7/1155 + 7*g**6/660 - g**5/22 + 13*g**4/132 - 4*g**3/33 + 8*g**2 + 2*g. Find h, given that k(h) = 0.
1, 4
Let a(o) be the first derivative of 1/4*o**4 - o**3 - 2 + o**2 + 0*o. Let a(z) = 0. What is z?
0, 1, 2
Let d(g) be the third derivative of 0*g**3 - 1/80*g**6 + 1/120*g**5 - 1/420*g**7 + 0*g - g**2 + 0 + 1/672*g**8 + 1/24*g**4. Factor d(n).
n*(n - 2)*(n - 1)*(n + 1)**2/2
Let d(r) be the third derivative of -3/14*r**4 - 1/70*r**5 - 2*r**2 + 0 + 0*r + 3/280*r**6 - 4/7*r**3 + 1/490*r**7. Factor d(x).
3*(x - 2)*(x + 1)*(x + 2)**2/7
Find d, given that 0 - 1/3*d - d**2 - d**3 - 1/3*d**4 = 0.
-1, 0
Suppose 155 = -2*m + 23. Let d be 2/(-11) + (-166)/m. Factor 2/3*u + 0 - d*u**2 - 2/3*u**3 + 7/3*u**4.
u*(u - 1)*(u + 1)*(7*u - 2)/3
Factor -20*j**3 + 25*j**4 + 100*j - 8*j**2 - 100*j + 3*j**4.
4*j**2*(j - 1)*(7*j + 2)
Suppose -4/5*b**2 - 28/5*b**3 - 8/5 + 12/5*b**4 + 28/5*b = 0. Calculate b.
-1, 1/3, 1, 2
Let -5*o**2 - 10*o**3 + 20 + o + 21 - 36 + 9*o = 0. What is o?
-1, -1/2, 1
Let s(c) be the third derivative of -2*c**2 + 0*c**3 - 1/5*c**5 + 0 - 1/2*c**4 - 1/112*c**8 + 0*c + 3/40*c**6 + 1/35*c**7. Find p, given that s(p) = 0.
-1, 0, 2
Let q(t) = t + 4. Let v be q(0). Suppose o = -o + v. Factor -2*d + 3*d + 3*d**2 + d**o - 3*d.
2*d*(2*d - 1)
Let w(n) = -n**3 - 18*n**2 - 74*n. Let u(r) = -r. Let g(f) = 14*u(f) + 2*w(f). Factor g(s).
-2*s*(s + 9)**2
Solve 3/7*c**3 + 0*c**2 + 0 - 3/7*c = 0 for c.
-1, 0, 1
Let s(q) be the first derivative of -q**7/105 - q**6/25 - q**5/25 + q**4/15 + q**3/5 + q**2/5 - 9*q - 3. Let v(p) be the first derivative of s(p). Factor v(k).
-2*(k - 1)*(k + 1)**4/5
Factor d**3 - 2*d**3 + 4*d**4 - d**4 - 2*d**4.
d**3*(d - 1)
Suppose -77 = 13*k - 90. Factor -1/4*r**2 - k - r.
-(r + 2)**2/4
Let d = 13 + -10. Let d*w + w - w - 3*w**2 = 0. What is w?
0, 1
Let n be (4 - -4)*(-1)/(-2). Let -5*f**n + f**2 - 5*f**2 - 3*f**3 + 0*f**2 + 15*f**3 = 0. Calculate f.
0, 2/5, 2
Let r(n) be the second derivative of -n**5/240 - n**4/144 + n**3/12 + 3*n. Suppose r(w) = 0. What is w?
-3, 0, 2
Let m(y) be the second derivative of 1/15*y**3 + 1/25*y**5 - 1/10*y**2 + 7/60*y**4 - 3*y + 0. Determine i, given that m(i) = 0.
-1, 1/4
Suppose -5 = -3*v + 1. Determine k so that 9*k**3 + 6*k**v + 4*k**2 + 3*k**4 - 4*k**2 = 0.
-2, -1, 0
Let k = 1/141 - -29182/705. Let m = k + -41. Factor 0*n**3 - 2/5*n**4 + m*n**2 + 1/5*n**5 - 1/5*n + 0.
n*(n - 1)**3*(n + 1)/5
Determine p, given that -3/2*p - 3/2*p**2 + 3 = 0.
-2, 1
Suppose -5*l - 5*g = 75, -4*l + 4*g - 53 = g. Let t be (12/21)/((-4)/l). What is b in b + b**2 + 0*b + b**2 - 3*b**t = 0?
0, 1
Let k(g) be the second derivative of -1/20*g**5 + 1/30*g**6 + 0 + 2*g + 0*g**2 + 0*g**3 + 0*g**4. Let k(w) = 0. What is w?
0, 1
Let a(u) = -45*u**3 + 72*u**2 + 48*u + 9. Let w(k) = 46*k**3 - 72*k**2 - 47*k - 8. Let f(y) = 2*a(y) + 3*w(y). Let f(i) = 0. Calculate i.
-1/4, 2
Let l(n) = n + 4. Let w(r) = r**2 - 7*r + 4. Let t be w(6). Let v be l(t). Factor q - q**v - q + 0*q.
-q**2
Let r(m) be the third derivative of 7*m**5/60 + m**4/8 - 2*m**3/3 + 2*m**2. Let g(w) = w**2 + 1. Let j(b) = -2*g(b) - r(b). Factor j(h).
-(3*h - 1)*(3*h + 2)
Let l be (43 + 1)*(-8)/(-16). Suppose 3*k + 0*c - 4*c = l, -k - 2 = c. What is m in -3*m**k + 2 + 4*m**2 - 2*m**2 - 5*m + 4*m**2 = 0?
2/3, 1
Let f(p) be the third derivative of -p**6/320 - p**5/160 + p**4/32 + 26*p**2. Factor f(q).
-3*q*(q - 1)*(q + 2)/8
Suppose 5 = -3*t + c + 18, 5*t + 4*c = 33. What is o in 6/5*o**t + 2/5 - 12/5*o**3 + 6/5*o - 4/5*o**2 + 2/5*o**4 = 0?
-1, -1/3, 1
Let m(t) = 12*t**3 + 16*t**2 + 6*t - 8. Let k(v) be the third derivative of -v**6/120 - v**5/60 + v**3/6 - 4*v**2. Let g(i) = 10*k(i) + m(i). Factor g(d).
2*(d + 1)**3
Let u = -6 + 12. Suppose 5*z + 4*n = u, -3*z - 4 = -2*n - 12. Solve -16/3*t**3 + 0 + 10/3*t**4 - 2/3*t**5 + 8/3*t**z + 0*t = 0 for t.
0, 1, 2
Let b(v) = v + 3. Let t be b(7). Let x be 4/t + (-80)/(-175). Factor 0*h**2 - x*h + 4/7 + 2/7*h**3.
2*(h - 1)**2*(h + 2)/7
Let g(l) be the first derivative of l**4/28 - 2*l**2/7 + 2. Let g(k) = 0. Calculate k.
-2, 0, 2
What is t in -2/15 + 2/15*t + 2/5*t**3 + 2/3*t**2 = 0?
-1, 1/3
Suppose -6 + 0 = 2*n. Let b be (-6)/(-9) - 7/n. Solve -49*s**b + 29*s**4 + 20*s**4 + 0*s**2 - 4*s**2 + 4*s = 0 for s.
-2/7, 0, 2/7, 1
Let j(f) be the first derivative of -f**6/40 - f**5/20 + f**4/8 + f**3/2 - 5*f**2/2 + 5. Let u(i) be the second derivative of j(i). What is o in u(o) = 0?
-1, 1
Suppose 3 - 11 = -4*k. Let 