 t. Factor 1/4 + g*f - 1/4*f**2.
-(f - 1)*(f + 1)/4
Determine v, given that -16*v**3 + 0*v**3 - 4*v**2 + 14*v**3 = 0.
-2, 0
Let p be (-4 - -4) + 0/1. Let s(k) be the first derivative of 4/3*k**6 + 16/5*k**5 + 1/8*k**2 + 21/8*k**4 + 2 + p*k + 11/12*k**3. Suppose s(d) = 0. What is d?
-1, -1/2, -1/4, 0
Let v(k) = -2*k - 4. Let c(r) = -r - 6. Let u be c(-3). Let w be v(u). Solve -3 - 2*m + 2*m**w + 3 = 0 for m.
0, 1
Let y(q) be the first derivative of -2*q**3/15 + 12*q**2/5 - 72*q/5 - 42. Determine v, given that y(v) = 0.
6
Let d(s) be the second derivative of -5*s**7/42 + s**6/6 + 3*s**5/4 - 5*s**4/12 - 5*s**3/3 - 5*s. Let d(x) = 0. Calculate x.
-1, 0, 1, 2
Let d(p) be the third derivative of 1/60*p**6 + 0*p**3 + 0*p**4 + p**2 + 0 + 1/60*p**5 + 0*p + 1/210*p**7. Factor d(f).
f**2*(f + 1)**2
Suppose 0 = 14*j - 5*j - 36. Let z(q) be the first derivative of -3/4*q**j - 1 + 2/3*q**3 + 3/2*q**2 - 2*q. Suppose z(k) = 0. Calculate k.
-1, 2/3, 1
Factor -13*s**4 + 0*s**5 - 3*s**5 + 13*s**4 + 3*s**3.
-3*s**3*(s - 1)*(s + 1)
Let a(n) be the first derivative of 3/5*n**5 + 0*n - 5 - 3/4*n**4 + 3/2*n**2 - n**3. Factor a(j).
3*j*(j - 1)**2*(j + 1)
Let w(m) be the third derivative of 1/315*m**7 - 1/180*m**6 + 0*m**4 - 1/90*m**5 + 0*m + 0 + 1/504*m**8 + 0*m**3 + 3*m**2. Factor w(h).
2*h**2*(h - 1)*(h + 1)**2/3
Let a(s) be the second derivative of s**7/14 + 2*s**6/5 + 3*s**5/5 - s**4/2 - 5*s**3/2 - 3*s**2 - 6*s. Factor a(d).
3*(d - 1)*(d + 1)**3*(d + 2)
Let y(h) = 3*h**3 + 2*h**2 - h - 2. Let u(t) = t**3 + t**2 - 1. Let p(a) = -2*u(a) + y(a). Let k(n) = n**3 - n. Let c(x) = 5*k(x) - 3*p(x). Factor c(b).
2*b*(b - 1)*(b + 1)
Let m = -4 + 4. Suppose -5*w - 5 = 5*i, -2*w + 0*w - i + 1 = m. Factor y + 1 + 1/4*y**w.
(y + 2)**2/4
Let c(t) = t**3 - 3*t**2 - 4*t + 5. Let m(n) = -4*n**3 + 16*n**2 + 20*n - 24. Let x(v) = 24*c(v) + 5*m(v). Let x(z) = 0. What is z?
-1, 0
Let q(n) be the second derivative of 2/3*n**2 - 3*n + 1/18*n**4 + 0 - 1/3*n**3. Solve q(h) = 0.
1, 2
Let r(w) be the third derivative of 0*w**3 + 0*w + 0 - 1/42*w**4 + w**2 - 1/210*w**5 + 1/140*w**6. Find t, given that r(t) = 0.
-2/3, 0, 1
Let s(c) be the third derivative of -2*c**7/35 - 11*c**6/30 - c**5 - 3*c**4/2 - 4*c**3/3 + 13*c**2. Determine p so that s(p) = 0.
-1, -2/3
Let k = -9/31 + 297/62. Let l = 25/4 - 6. Solve -l - 7/4*i - 11/2*i**3 - 3/4*i**5 - k*i**2 - 13/4*i**4 = 0.
-1, -1/3
Let y(x) be the second derivative of -x**6/75 - 2*x**5/75 + 2*x**4/45 - 6*x. Factor y(i).
-2*i**2*(i + 2)*(3*i - 2)/15
Let b(c) be the first derivative of -2/5*c**5 + 4/3*c**3 - 4 - 2/3*c**6 + 2*c**4 - 2*c - 2*c**2. Solve b(x) = 0 for x.
-1, -1/2, 1
Let d(g) be the third derivative of -g**2 + 0*g - 1/420*g**6 - 1/84*g**4 - 1/105*g**5 + 0 + 0*g**3. Determine t so that d(t) = 0.
-1, 0
Let r = -42 + 46. Let v(f) be the second derivative of 3*f + 9/5*f**5 + 2/3*f**3 + 0 + 0*f**2 - 13/6*f**r. Factor v(q).
2*q*(2*q - 1)*(9*q - 2)
Let v(s) be the second derivative of -s**5/100 + s**3/30 - 10*s. Factor v(c).
-c*(c - 1)*(c + 1)/5
Let r(v) be the third derivative of 0 + 1/45*v**5 - 1/36*v**4 + 0*v**3 + 0*v - 3*v**2 - 1/180*v**6. Let r(t) = 0. What is t?
0, 1
Let i(a) be the first derivative of -3*a**4/14 + 4*a**3/21 + a**2/7 - 8. Factor i(r).
-2*r*(r - 1)*(3*r + 1)/7
Let v(j) be the second derivative of 3*j**8/2240 - j**7/105 + 13*j**6/720 - j**5/60 - j**4/12 - 4*j. Let x(i) be the third derivative of v(i). Factor x(r).
(r - 2)*(3*r - 1)**2
Let w(t) be the first derivative of t**6/180 + t**5/60 - 2*t**3/3 - 3. Let x(b) be the third derivative of w(b). Suppose x(g) = 0. What is g?
-1, 0
Let r(f) be the second derivative of -f**5/4 - 5*f**4/3 - 5*f**3/2 - 10*f. Let r(i) = 0. What is i?
-3, -1, 0
Suppose -2*r + 1 = 5*l - 0, -3*r - 3*l = -6. Let s(m) be the first derivative of -3 + 0*m + 1/6*m**6 + 3/5*m**5 + 1/3*m**r + 3/4*m**4 + 0*m**2. Factor s(n).
n**2*(n + 1)**3
Solve -4/9*p**5 - 52/9*p + 56/9*p**3 - 40/9 + 32/9*p**2 + 8/9*p**4 = 0 for p.
-2, -1, 1, 5
Let f(d) be the third derivative of 0 + 1/30*d**5 - 1/4*d**4 + 0*d - 2*d**2 - 1/540*d**6 + d**3. What is k in f(k) = 0?
3
Suppose -1/2 - 1/4*y**2 - 3/4*y = 0. Calculate y.
-2, -1
Factor -32/7*u - 128/7 - 2/7*u**2.
-2*(u + 8)**2/7
Let b(g) be the second derivative of -2*g + 1/15*g**5 + 1/60*g**6 + 0*g**3 - 3/2*g**2 + 0*g**4 + 0. Let q(f) be the first derivative of b(f). Factor q(n).
2*n**2*(n + 2)
Let k(c) be the second derivative of 1/4*c**2 - 1/60*c**6 + 0 - c - 1/20*c**5 + 1/6*c**3 + 0*c**4. Suppose k(h) = 0. What is h?
-1, 1
Let q(l) be the first derivative of -1/4*l**2 - 2 + 0*l**3 + 1/20*l**5 + 1/8*l**4 - 1/4*l. Solve q(y) = 0.
-1, 1
Let w(z) be the third derivative of -z**9/5040 - z**8/2240 + z**7/420 + z**4/4 - 7*z**2. Let c(v) be the second derivative of w(v). Factor c(q).
-3*q**2*(q - 1)*(q + 2)
Let u(i) be the first derivative of 0*i + 6/55*i**5 + 0*i**2 + 3/22*i**4 + 2 + 1/33*i**6 + 2/33*i**3. Let u(x) = 0. Calculate x.
-1, 0
Suppose h = 43*h. Solve 4/5*m**5 + 0*m**2 + 0*m**4 + h*m - 4/5*m**3 + 0 = 0 for m.
-1, 0, 1
Let i(g) be the second derivative of 0*g**2 + 1/80*g**5 + 1/24*g**3 - 1/24*g**4 + 0 - 2*g. Factor i(n).
n*(n - 1)**2/4
Let g(b) be the third derivative of b**7/945 - b**6/540 - b**5/270 + b**4/108 - 4*b**2. Factor g(i).
2*i*(i - 1)**2*(i + 1)/9
Let h = -53 - -74. Let n be h/9 + (-1)/3. Factor -1 + 4*d**2 + 2*d**3 - 2*d**n - 2*d - 1.
2*(d - 1)*(d + 1)**2
Let w be 10/12 + (-12)/16. Let c(y) be the first derivative of w*y**3 + 2 - 1/8*y**4 + 0*y + 0*y**2 + 1/20*y**5. Factor c(p).
p**2*(p - 1)**2/4
Let z(g) be the third derivative of 1/560*g**8 - 1/600*g**6 + 0*g**4 + 0*g**3 + 0 + 6*g**2 - 1/525*g**7 + 0*g + 0*g**5. Factor z(a).
a**3*(a - 1)*(3*a + 1)/5
Let d be 2/8 - 45/(-12). Let h(v) be the second derivative of 7/10*v**6 + 0 - 1/12*v**d + v - 11/10*v**5 + 1/3*v**3 + 0*v**2. Let h(a) = 0. What is a?
-2/7, 0, 1/3, 1
Determine x, given that 6 - 9*x + 4*x**2 + 0*x**2 - x**2 + 0*x**2 = 0.
1, 2
Let m(s) be the first derivative of 5 + 1/3*s**3 + 0*s + s**2. Factor m(q).
q*(q + 2)
Let i(f) be the third derivative of 0*f + 0 - 1/140*f**7 + 3/32*f**4 + 7/240*f**6 + 1/1344*f**8 - 2*f**2 - 1/12*f**3 - 1/15*f**5. Let i(r) = 0. Calculate r.
1, 2
Factor 3*l**2 + l**3 + 14 - 14 + 0*l**2 + 2*l.
l*(l + 1)*(l + 2)
Let r be (-2)/(-3) - 1830/45. Let g = r - -124/3. Let 2/3*x**3 - 2/3 + 2*x**2 - g*x**4 - 2/3*x = 0. What is x?
-1, -1/2, 1
Let q(r) = 4*r**3 + 2*r**2 - 1. Let m be q(-1). Let a be 2 + (10/m)/2. Factor -4/3*d**2 + a*d + 0.
-d*(4*d - 1)/3
Let k(s) be the first derivative of -s**7/2100 + s**6/900 + 2*s**3 - 3. Let t(c) be the third derivative of k(c). Factor t(r).
-2*r**2*(r - 1)/5
Let b(x) = -x**2 + 3*x + 3. Let o be b(3). Solve 42*k - 6 + 30*k**o + 54*k**3 + 9*k + 25*k**2 - 154*k**2 = 0.
1/4, 2/7, 1
Let b(l) = 15*l**3 + 85*l**2 + 101*l - 49. Let h(f) = 15*f**3 + 85*f**2 + 100*f - 50. Let n(s) = -5*b(s) + 4*h(s). Let n(u) = 0. Calculate u.
-3, 1/3
Suppose -3*w + w + 5*i = 14, 3*w - 4*i = -7. Suppose 2*b = w + 3. Factor -14/3*u**2 + 2/3 + 4/3*u + 8/3*u**b.
2*(u - 1)**2*(4*u + 1)/3
Let m(n) be the second derivative of -6*n + 0*n**2 + 1/150*n**6 + 0 + 0*n**3 + 0*n**5 + 0*n**4 - 1/210*n**7. Factor m(b).
-b**4*(b - 1)/5
Let c = -15 + 16. Let i(o) = o**2 + o + 1. Let b(d) = -4*d**2 - 13*d + 11. Let p(h) = c*b(h) + 5*i(h). Factor p(k).
(k - 4)**2
Let c = -355/4 - -89. Factor c*s**2 + 0 + 3/4*s.
s*(s + 3)/4
Let k(u) be the second derivative of -u**4/18 - 4*u**3/9 - u**2 - 5*u. Determine o so that k(o) = 0.
-3, -1
Let u be 2/24 + 3/12. Let h(q) be the first derivative of u*q**3 + 0*q**2 + 0*q - 2. Solve h(l) = 0.
0
Let o = 72 + -431/6. Let d(n) be the first derivative of 0*n + 1/16*n**4 + 1/8*n**2 + 1 + o*n**3. Factor d(z).
z*(z + 1)**2/4
Let c be (21/(-36))/((-15)/(-200)). Let y = c + 8. Determine b so that 0 + 0*b**4 + 0*b + 0*b**2 + y*b**3 - 2/9*b**5 = 0.
-1, 0, 1
Let o(r) = r**4 - r**3 + r**2 + r. Let s(i) = 10*i**4 - 12*i**3 + 8*i**2 + 12*i - 2. Let h be (-2 - 1)*(-1)/(-3). Let k(n) = h*s(n) + 8*o(n). Factor k(a).
-2*(a - 1)**3*(a + 1)
Let f = -4 - -5. Let v(s) = -3*s**3 + 6*s + 3. Let w(q) = q**2 - 1. Let b(u) = f*v(u) + 3*w(u). Factor b(a).
-3*a*(a - 2)*(a + 1)
Let i be (-4)/(-2 - (-7)/6). Determine m so that 12/5*m - i*m**2 + 0 - 3*m**3 = 0.
-2, 0, 2/5
Suppose 5*z - t = 