tive of 0 + 4/15*n**2 + 1/90*n**4 + 8*n + 4/45*n**3. Factor g(w).
2*(w + 2)**2/15
Let i(y) be the first derivative of y**5/70 + y**4/21 - 2*y + 6. Let h(q) be the first derivative of i(q). Solve h(f) = 0 for f.
-2, 0
Let w(h) = -12*h**3 + 28*h**2 - 2*h - 2. Let d(x) = -25*x**3 + 55*x**2 - 5*x - 5. Let b(c) = 3*d(c) - 5*w(c). Factor b(s).
-5*(s - 1)**2*(3*s + 1)
Let i(v) be the third derivative of 0*v + 1/30*v**4 + 0 - 8*v**2 + 2/75*v**5 - 1/525*v**7 - 1/150*v**6 - 1/5*v**3. Determine g so that i(g) = 0.
-3, -1, 1
Factor 2/9*o**2 + 0 + 2/9*o - 2/9*o**4 - 2/9*o**3.
-2*o*(o - 1)*(o + 1)**2/9
Let r(u) be the second derivative of u**7/21 - 2*u**6/9 + 13*u**5/90 + 10*u**4/27 + 4*u**3/27 + 7*u. Solve r(c) = 0.
-1/3, 0, 2
Let h = -6 - -4. Let b = h - -4. Factor -3*s**4 - s**3 + 5*s**2 - b*s**3 - 2*s + 4*s**5 - 2*s**4 + s.
s*(s - 1)**2*(s + 1)*(4*s - 1)
Factor -8 + 27783/2*t**4 + 240*t - 2268*t**2 + 5292*t**3.
(3*t + 2)*(21*t - 2)**3/2
Let r(z) be the third derivative of -z**8/1848 + z**6/220 + z**5/165 - z**2. Factor r(m).
-2*m**2*(m - 2)*(m + 1)**2/11
Let v = 41 - 39. Solve 1/3*z**v + 1/3 + 2/3*z = 0.
-1
Suppose -5*w = -4 - 6. Let o(k) be the second derivative of -2*k + 37/6*k**4 - 4/5*k**5 - 16/5*k**6 + 2*k**w + 17/3*k**3 + 0. What is t in o(t) = 0?
-2/3, -1/4, 1
Suppose 3/2*v**4 + 0 - 3/2*v**2 + 9/2*v**3 - 9/2*v = 0. Calculate v.
-3, -1, 0, 1
Let a(u) = 28*u**5 + 8*u**4 - 67*u**3 + 11*u**2 + 21*u - 8. Let i(w) = -w**5 + w**2 + w. Let m(b) = 5*a(b) + 35*i(b). Let m(y) = 0. What is y?
-2, -2/3, 2/7, 1
Let k be (-4 + 5)*((-36)/(-15) - 2). Suppose 0*f**3 - 2/5*f**4 + 0 + k*f**2 + 0*f = 0. Calculate f.
-1, 0, 1
Factor 0*n**3 - 2/5*n**2 + 0 + 0*n + 2/5*n**4.
2*n**2*(n - 1)*(n + 1)/5
Factor 0*p - 3/2*p**4 + 0 - 9/2*p**2 + 6*p**3.
-3*p**2*(p - 3)*(p - 1)/2
Let f(a) = 0*a + 3*a + 1 - 4*a. Let h be f(-1). Factor 1 - l - 1 + l**2 + h*l**3.
l*(l + 1)*(2*l - 1)
Factor -20/7*o**3 - 10/7*o - 2/7*o**5 - 2/7 - 10/7*o**4 - 20/7*o**2.
-2*(o + 1)**5/7
Suppose n + 4*n = 0. Suppose n = -3*h + h + 4. Factor -4*k**2 - 4*k**h - k**3 + 3*k**4 + 5*k**2 + k.
k*(k - 1)*(k + 1)*(3*k - 1)
Let a(p) be the third derivative of -1/16*p**4 + 1/40*p**5 - 7*p**2 + 0*p + 0 - 1/240*p**6 + 1/12*p**3. Factor a(d).
-(d - 1)**3/2
Suppose 0 = r - 3*s - 0*s, -3*s = 2*r - 9. Find m, given that m**r + 5*m**2 - 3*m**2 + 2 + 2*m - 4*m**2 - 3*m**3 = 0.
-1, 1
Let i(y) = -9*y**4 - 6*y**3 + 9*y**2 + 6*y - 3. Let d(n) = -9*n**4 - 6*n**3 + 9*n**2 + 6*n - 2. Let t(f) = 3*d(f) - 2*i(f). Factor t(h).
-3*h*(h - 1)*(h + 1)*(3*h + 2)
Let r(x) = x**3 - 9*x**2 - 11*x + 12. Let o be r(10). Factor -3*f**2 + o*f - 5*f**2 + 2*f + 7*f**2 - 3.
-(f - 3)*(f - 1)
Suppose 3*q = 7 + 5. Let k(n) = -5*n**5 - 26*n**4 + n**3 - n**2 + 15*n + 5. Let l(j) = -j**5 - 5*j**4 + 3*j + 1. Let c(g) = q*k(g) - 22*l(g). Factor c(u).
2*(u - 1)*(u + 1)**4
Suppose f = -3*f. Let l(b) be the third derivative of f*b + 0*b**3 + 1/18*b**5 + 2*b**2 - 1/45*b**6 - 1/36*b**4 + 0. Factor l(q).
-2*q*(q - 1)*(4*q - 1)/3
Let g(a) be the first derivative of -1/2*a**3 - 1/2*a**2 + 3/10*a**5 + 1/8*a**4 + 0*a - 6 + 1/12*a**6. Determine c, given that g(c) = 0.
-2, -1, 0, 1
Let h(q) be the third derivative of 1/35*q**7 - 1/15*q**5 + 1/60*q**6 + 2*q**2 + 0*q**3 + 0*q + 0*q**4 + 0. Factor h(l).
2*l**2*(l + 1)*(3*l - 2)
Let -2/5*v**5 + 0*v + 2/5*v**2 + 0 + 6/5*v**4 - 6/5*v**3 = 0. What is v?
0, 1
Let q(a) = -4*a**3 + 6*a**2 - 12*a + 8. Let n(p) = 5*p**3 - 6*p**2 + 12*p - 8. Let g(o) = -3*n(o) - 4*q(o). Let g(y) = 0. Calculate y.
2
Let j(n) be the second derivative of -1/30*n**5 + 0 + 2/3*n**2 - 2/3*n**3 + 1/4*n**4 + n. Determine u so that j(u) = 0.
1/2, 2
Let k(l) be the third derivative of l**5/40 - 10*l**2. Factor k(f).
3*f**2/2
Let v = 678/13 + -52. Determine d so that v*d - 4/13*d**2 + 0 - 8/13*d**4 - 14/13*d**3 = 0.
-1, 0, 1/4
Let i = -1178/45 - -132/5. Determine z, given that 0*z + 0 + i*z**2 = 0.
0
Let b = 3047/7 - 435. Determine c, given that -2/7 + b*c**2 - 2/7*c**3 + 2/7*c = 0.
-1, 1
Let l = 2/2555 - -834/365. Factor 4/7*w**4 - 16/7*w**3 - l*w + 4/7 + 24/7*w**2.
4*(w - 1)**4/7
Suppose 4*p + 3*n + 5 = 3*p, 0 = 5*p + 5*n + 15. Let r = p + 5. Factor 4/5*v**r - 2/5*v + 0*v**2 - 2/5*v**5 + 0 + 0*v**4.
-2*v*(v - 1)**2*(v + 1)**2/5
Suppose 3*d - 3 = 6. Let k be 2/d - 6/9. Factor -2*f**4 + k*f**5 + 6*f**4 + 2*f**5 - 4*f**2 - 2*f.
2*f*(f - 1)*(f + 1)**3
Let y(x) be the second derivative of -x**7/840 + x**6/360 + x**3/3 - x. Let p(d) be the second derivative of y(d). Factor p(l).
-l**2*(l - 1)
Let m(g) be the second derivative of -g**5/210 - g**4/42 + g**2/2 + 4*g. Let c(l) be the first derivative of m(l). Let c(u) = 0. Calculate u.
-2, 0
Suppose 36 = -5*z - 24. Let i be (-5)/(45/z) - 1. Let -1/3*n**4 - i*n - n**3 + 0 - n**2 = 0. Calculate n.
-1, 0
Let i(z) = 3*z**2 - 3*z - 2. Let c be (-222)/8 - 1/4. Let a = -17 - c. Let j(u) = -16*u**2 + 16*u + 11. Let f(b) = a*i(b) + 2*j(b). Factor f(p).
p*(p - 1)
Let n(o) be the third derivative of -o**5/100 + o**4/20 - o**3/10 + 2*o**2. Find s such that n(s) = 0.
1
Factor -14/11*p + 8/11 + 4/11*p**2 + 2/11*p**3.
2*(p - 1)**2*(p + 4)/11
Let b(k) be the second derivative of -k**8/2520 + k**7/1260 + k**6/540 - k**5/180 + k**3/3 + 4*k. Let o(s) be the second derivative of b(s). Factor o(y).
-2*y*(y - 1)**2*(y + 1)/3
Let n(f) be the second derivative of 0*f**3 + f**2 - f + 0 - 1/6*f**4. What is x in n(x) = 0?
-1, 1
Let c(s) be the first derivative of -2*s**3/15 - 3*s**2/5 + 11. Factor c(t).
-2*t*(t + 3)/5
Let i(b) be the second derivative of b**5/30 - 5*b**4/18 + b. Solve i(r) = 0.
0, 5
Let s(m) be the third derivative of m**9/15120 - m**8/5040 + m**5/12 - 2*m**2. Let v(l) be the third derivative of s(l). Find u such that v(u) = 0.
0, 1
Let z(w) be the third derivative of -w**5/12 - w**4/12 + w**3/2 - w**2. Factor z(d).
-(d + 1)*(5*d - 3)
Let a = -4 + 2. Let u = a + 5. Suppose 1/3 + 2/3*r**2 - r**4 + r - 1/3*r**5 - 2/3*r**u = 0. What is r?
-1, 1
Let s(z) be the first derivative of -z**4/6 - 4*z**3/3 + z**2/3 + 4*z + 52. Factor s(v).
-2*(v - 1)*(v + 1)*(v + 6)/3
Suppose -20 = -2*x - 5*o, 3*x = -x - o + 76. Suppose -2*q + 0*d = -d - 9, 4*d + x = 0. Find n, given that -q*n**4 + n**4 - n**3 + 0*n**4 = 0.
-1, 0
Let n = -170 + 174. Factor 4/3*w**3 + 2/3 - 2/3*w**5 + 2/3*w**n - 2/3*w - 4/3*w**2.
-2*(w - 1)**3*(w + 1)**2/3
Solve 0*v**2 + 10*v - 5*v**2 - 30*v**3 + 5*v**4 + v**5 + 4*v**5 + 15*v**3 = 0.
-2, -1, 0, 1
Let y(r) be the third derivative of 1/105*r**7 + 0*r**5 + 6*r**2 - 1/60*r**6 + 0 + 0*r**3 + 0*r + 0*r**4. Factor y(h).
2*h**3*(h - 1)
Let k(m) be the third derivative of m**7/1470 + m**6/84 + 3*m**5/35 + 9*m**4/28 + 9*m**3/14 + 22*m**2. Find i such that k(i) = 0.
-3, -1
Solve 27 + 2*s**2 + 0*s**2 - 10 - 11 - 8*s = 0 for s.
1, 3
Let x(z) be the first derivative of z**5/300 - z**3/30 - z**2 + 4. Let l(t) be the second derivative of x(t). What is h in l(h) = 0?
-1, 1
Find w such that -6/5*w + 27/5*w**2 - 21/5*w**3 + 0 = 0.
0, 2/7, 1
Let u(w) = w**2 + w + 1. Let y be u(3). Suppose 5*c - 173 = -y. Determine q so that 42*q**3 - c*q + 12 + 2*q**2 + 5 - 9 = 0.
-1, 2/7, 2/3
Let n = -3 - -5. Suppose -w**n + w**3 - 3*w**4 - 2*w**2 - 2*w**3 + 7*w**3 = 0. What is w?
0, 1
Suppose c = -c. Let r(z) be the third derivative of c*z + 0 + 1/30*z**5 - 1/12*z**4 + 0*z**3 - z**2. Solve r(x) = 0 for x.
0, 1
Suppose -4*v - 4*p + 3*p = -12, 2*v + 4*p + 8 = 0. Suppose v*u + 22 = 5*n, 2*u + 12 - 4 = n. Factor 0*t - 2/7*t**n + 0*t**3 + 0 + 2/7*t**4.
2*t**2*(t - 1)*(t + 1)/7
Let t(o) = 2*o + 7. Let u be t(-5). Let a be (-8)/(-40) + u/(-35). Solve -a*c + 2/7*c**3 + 0 + 0*c**2 = 0 for c.
-1, 0, 1
Let w(g) be the second derivative of -g**6/40 + 3*g**4/8 - g**3 - 7*g**2/2 - 7*g. Let f(p) be the first derivative of w(p). Factor f(i).
-3*(i - 1)**2*(i + 2)
Let v = -34/5 - -38/5. Let 6/5*h + v + 2/5*h**2 = 0. Calculate h.
-2, -1
Let g(n) = -3*n**4 - 3*n**3 - 3*n**2 - 3*n. Let h(b) = b**2 + b. Let x(o) = g(o) + 6*h(o). Determine m, given that x(m) = 0.
-1, 0, 1
Suppose j = -4 + 2. Let k be ((-1)/j)/(3/2). Find a, given that 0*a**2 + k*a**4 + 1/3*a**3 + 0 + 0*a = 0.
-1, 0
Let m(y) be the third derivative of -y**6/30 + 7*y**5/45 - y**4/9 - 8*y**2. Factor m(g).
-4*g*(g - 2)*(3*g - 1)/3
Let y(j) be the third derivative of -j**7/350 - j**6/100 - j**5/100 + 2*j**2. 