33. Let q be o(7). Let a(m) be the second derivative of -1/9*m**3 - 1/3*m**q + 4/45*m**6 + 1/2*m**4 - 2*m - 11/30*m**5 + 0. Factor a(n).
2*(n - 1)**3*(4*n + 1)/3
Let a be ((-6)/(-4) + -2)*0. Factor -3*z**3 + z + 0*z**4 + 2*z**5 - z**2 + z**4 + a*z**5.
z*(z - 1)*(z + 1)**2*(2*z - 1)
Let d = 68 - 200/3. Suppose -d*y**2 + 0*y**3 + 0*y + 2/3*y**4 + 2/3 = 0. What is y?
-1, 1
Let m(u) be the first derivative of -u**3/3 - 4*u**2 - 7*u - 8. What is c in m(c) = 0?
-7, -1
Factor 3/2*x**2 + 0*x - 3/4 - 3/4*x**4 + 0*x**3.
-3*(x - 1)**2*(x + 1)**2/4
Let z be ((-320)/(-140))/(1/1). Solve 4/7*g - 6/7*g**4 + 0 + z*g**3 - 2*g**2 = 0 for g.
0, 2/3, 1
Let w = 29/26 - 8/13. Suppose -w*l**3 + 1/2*l - 1/2 + 1/2*l**2 = 0. What is l?
-1, 1
Suppose -14*s**4 - 2*s**4 - 50*s**2 + 60*s**3 - 19*s**4 + 5*s**4 + 15*s + 5*s**5 = 0. What is s?
0, 1, 3
Let s(m) be the third derivative of 4*m**7/2205 + m**6/180 + m**5/315 - m**4/252 + 21*m**2. Factor s(w).
2*w*(w + 1)**2*(4*w - 1)/21
Let t(a) = -a**2 + 3*a + 1. Let p be t(4). Let u = p + 5. Find f, given that f - 3*f + 4*f - 2*f**2 - u*f**3 + 2 = 0.
-1, 1
Let q(r) = 4*r**4 + 7*r**3 + 17*r**2 - 7. Let l(j) = j**4 + 2*j**3 + 5*j**2 - 2. Let z(m) = 7*l(m) - 2*q(m). Factor z(h).
-h**2*(h - 1)*(h + 1)
Let w(b) be the second derivative of b**6/540 - b**5/90 - b**3/3 - 3*b. Let s(k) be the second derivative of w(k). Factor s(m).
2*m*(m - 2)/3
Suppose 0 = 11*x + 14*x. Let 2/9*r**3 + 0*r**2 + x + 2/9*r**4 + 0*r = 0. What is r?
-1, 0
Let a(c) = -8*c - 3*c**4 - c**2 + 9*c - c**3 + 2*c**4. Let j(k) = -k**5 + 5*k**4 + 5*k**3 + 3*k**2 - 4*k. Let x(u) = -4*a(u) - j(u). Factor x(q).
q**2*(q - 1)**2*(q + 1)
Let i(f) be the second derivative of f**4/54 + 8*f**3/27 + 16*f**2/9 - 9*f. Factor i(o).
2*(o + 4)**2/9
Let q(k) be the second derivative of k**6/30 + 3*k**5/20 + k**4/6 - 18*k. Factor q(l).
l**2*(l + 1)*(l + 2)
Let f(o) be the first derivative of 0*o - 1/2*o**6 - 6*o**2 + 5 - 12*o**3 - 18/5*o**5 - 39/4*o**4. Factor f(s).
-3*s*(s + 1)**2*(s + 2)**2
Find r such that 0*r - 8/5 + 2/5*r**3 + 6/5*r**2 = 0.
-2, 1
Let f(r) be the second derivative of -r**7/105 - r**6/75 + 11*r**5/200 + r**4/30 - r**3/12 - r**2/10 + 10*r. Let f(k) = 0. Calculate k.
-2, -1/2, 1
Let h(g) = 26*g**3 + 60*g**2 + 120*g + 80. Let n(p) = 5*p**3 + 12*p**2 + 24*p + 16. Let s(w) = -3*h(w) + 16*n(w). Factor s(o).
2*(o + 2)**3
Let w(k) = k - 4. Let r be w(6). Solve 12*i + 5*i**2 + 18 - 3*i**2 - 2*i**2 + 2*i**r = 0 for i.
-3
Factor 2/3*t - 2/15*t**3 + 4/5 - 4/15*t**2.
-2*(t - 2)*(t + 1)*(t + 3)/15
Let s(a) = -8*a**2 - 4*a - 6. Let k(h) = -12*h**2 - 3. Let b(v) = -13*v**2 + v - 2. Let j(w) = -3*b(w) + 4*k(w). Let t(y) = -5*j(y) + 6*s(y). Factor t(q).
-3*(q + 1)*(q + 2)
Let k(g) be the first derivative of g**6/240 - g**5/120 - g**2 - 1. Let o(r) be the second derivative of k(r). Factor o(d).
d**2*(d - 1)/2
Let z(i) be the second derivative of i**5/8 + i**4/8 - 2*i. Factor z(n).
n**2*(5*n + 3)/2
Solve -4/19*x - 2/19*x**2 - 2/19 = 0.
-1
Find o, given that -o**2 + 0 - 1/5*o**4 + 2/5*o + 4/5*o**3 = 0.
0, 1, 2
Suppose 3*i - 7*i + 5*s = -8, -3*s = -12. Suppose -5*l + 3 = -i. Factor 2*q**2 - l*q**2 + 2*q**2.
2*q**2
Let p = 4/13 - 3/52. Factor 1/4*c**2 + 0 + p*c.
c*(c + 1)/4
Suppose o = -4*f + 15, 5*f + 2*o = 4*f + 9. Factor 2/5*q**f + 8/5*q**2 + 0 + 8/5*q.
2*q*(q + 2)**2/5
Let i(c) = -3*c**3 - 2*c**2 + 1. Let h be i(-1). Let a(l) be the first derivative of -5/8*l**h - 2 + 1/4*l + 1/3*l**3. What is q in a(q) = 0?
1/4, 1
Suppose 0 = -4*o - k + 6*k, 3*o - 4*k = 0. Suppose -6*y**3 + o*y - 3*y**4 + 0 - 4*y**2 - 1/2*y**5 = 0. What is y?
-2, 0
Suppose 0*g**3 + 0*g + 3*g**2 - 3/2 - 3/2*g**4 = 0. What is g?
-1, 1
Let w = 41 + -163/4. Factor -w + o - o**2.
-(2*o - 1)**2/4
Let q(h) be the first derivative of h**4/4 + 2*h**3 + 9*h**2/2 + 4*h - 31. Factor q(c).
(c + 1)**2*(c + 4)
Factor 1/4*a - 1/4*a**2 + 0.
-a*(a - 1)/4
Let c(t) be the first derivative of -t**6/12 + 3*t**5/40 + t**4/12 - 3*t + 3. Let a(i) be the first derivative of c(i). Factor a(y).
-y**2*(y - 1)*(5*y + 2)/2
Find f such that -3/2*f**3 + 3/2*f**2 + 6*f - 6 = 0.
-2, 1, 2
Let s(o) be the first derivative of 7*o**3/30 - 47*o**2/20 - 7*o/5 + 1. Factor s(f).
(f - 7)*(7*f + 2)/10
Suppose 0 = -0*c + 5*c - 25. Factor -5*z**4 + c*z**2 + z**4 - z**2.
-4*z**2*(z - 1)*(z + 1)
Let l(y) be the first derivative of 3*y**5/5 - 9*y**4/4 + 2*y**3 - 1. Suppose l(g) = 0. What is g?
0, 1, 2
Let x(t) be the first derivative of t**6/2 + t**5/5 - 9*t**4/4 - 3*t**3 - t**2 + 9. Factor x(n).
n*(n - 2)*(n + 1)**2*(3*n + 1)
Let j(u) be the third derivative of -u**8/1008 - u**7/630 + u**6/180 + u**5/90 - u**4/72 - u**3/18 + 6*u**2. Factor j(m).
-(m - 1)**2*(m + 1)**3/3
Suppose -3/8*s**3 - 105/8*s + 75/8 + 33/8*s**2 = 0. Calculate s.
1, 5
Let u(b) = -b**3 + 8*b**2 - 8*b + 9. Let s be u(7). Factor s - 7*y + 0*y**2 + 3*y**3 - y**2 + 3*y**2 + 0.
(y - 1)*(y + 2)*(3*y - 1)
Factor -4/19*q + 6/19 - 2/19*q**2.
-2*(q - 1)*(q + 3)/19
Suppose -n - 31 = -5*u, -6 = -2*n + 2. Let v(g) = 3*g**3 - 9*g. Let p(x) = x**4 + 5*x**3 - 19*x - 1. Let t(a) = u*v(a) - 3*p(a). Solve t(q) = 0.
-1, 1
Factor 0*t**2 + t**2 + t**4 - 32*t**3 + 34*t**3.
t**2*(t + 1)**2
Let h(v) = 12*v**4 + 21*v**3 - 18*v**2 + 15*v. Let j(q) = q**4 + q**3 - q**2 + q. Let z(f) = 2*f - 5. Let x be z(-5). Let k(u) = x*j(u) + h(u). Factor k(w).
-3*w**2*(w - 1)**2
Let v(y) be the second derivative of 0 + 1/6*y**4 + 1/3*y**3 - 2*y**2 - 4*y. Suppose v(a) = 0. What is a?
-2, 1
Let w be ((-8)/6)/((-2)/(-9)). Let v be (w/9)/((-8)/9). Let -v*f**4 + 0 + 3/4*f**3 + 1/4*f**5 + 0*f - 1/4*f**2 = 0. Calculate f.
0, 1
Let t be 32/464 + 316/464. Find r, given that 0 + 3/4*r**2 + 3/4*r**3 - t*r**4 - 3/4*r = 0.
-1, 0, 1
Let j be 2/(-8) - (-3)/(-17). Let f = -3/17 - j. Suppose -1/4 - f*b + 1/4*b**2 + 1/4*b**3 = 0. Calculate b.
-1, 1
Let j(a) be the third derivative of a**6/30 - a**4/2 - 4*a**3/3 + 26*a**2. Factor j(o).
4*(o - 2)*(o + 1)**2
Let f(l) be the second derivative of 1/7*l**6 - 135/7*l**3 + 2*l + 45/7*l**4 - 9/7*l**5 + 0 - 1/147*l**7 + 243/7*l**2. Factor f(k).
-2*(k - 3)**5/7
Suppose -2*n = -n + 5*p - 2, 5*n - 4*p - 10 = 0. Find i such that -4/5*i + 0 - 2/5*i**n + 2/5*i**3 = 0.
-1, 0, 2
Let k be (148/28 - 4)/(10/35). Factor 15/2*v**2 + 1/2 + 7/2*v + k*v**3.
(v + 1)*(3*v + 1)**2/2
Factor -3/2*c + 9/4 + 1/4*c**2.
(c - 3)**2/4
Let l(q) be the second derivative of -q**6/30 + q**4/12 - 6*q. Factor l(t).
-t**2*(t - 1)*(t + 1)
Let m(b) be the first derivative of -b**3/12 + 3*b**2/8 - b/2 + 2. Factor m(t).
-(t - 2)*(t - 1)/4
Suppose -p - 5*u = -4*p + 18, -11 = 4*p + 5*u. Let v be 1 - 0 - (p - 2). Factor 2*l**v - 1 + 3 + 2*l**4 - 6*l**2.
2*(l - 1)**2*(l + 1)**2
Let d(q) be the first derivative of -1/120*q**4 + 0*q - 1 + 1/300*q**5 - 3/2*q**2 + 0*q**3. Let x(i) be the second derivative of d(i). Factor x(k).
k*(k - 1)/5
Suppose -2*b**4 + 11/2*b - 3/2*b**5 + 1 + 4*b**3 + 9*b**2 = 0. Calculate b.
-1, -1/3, 2
Let w = 3/38 + 347/418. Let 8/11*j**2 + 2/11 + w*j = 0. What is j?
-1, -1/4
Let q(s) be the second derivative of -s**6/60 + s**5/20 + 7*s**4/24 - 5*s**3/3 + 3*s**2 - 14*s + 3. Suppose q(x) = 0. Calculate x.
-3, 1, 2
Factor -4/9*w - 2/9*w**2 + 16/9.
-2*(w - 2)*(w + 4)/9
Let s(m) be the second derivative of m**7/1260 - m**6/360 - m**4/4 + 2*m. Let u(h) be the third derivative of s(h). Factor u(y).
2*y*(y - 1)
Let a(f) be the second derivative of f**5/200 + f**4/120 - 21*f. Find d such that a(d) = 0.
-1, 0
Let z(w) be the third derivative of -w**9/20160 - w**8/20160 + w**7/2520 + w**5/12 - 2*w**2. Let q(m) be the third derivative of z(m). Factor q(u).
-u*(u + 1)*(3*u - 2)
Let m(d) be the first derivative of -33*d**5/20 + d**4/2 + 11*d**3/2 - 3*d**2 + 2*d - 1. Let j(o) be the first derivative of m(o). Factor j(p).
-3*(p - 1)*(p + 1)*(11*p - 2)
Suppose 4*f - 10 = 2*f. Factor 3*p + 4*p + p**2 + 2 - f*p - 5*p.
(p - 2)*(p - 1)
Let y(b) = 10*b**2 - 60*b + 18. Let w(s) = 21*s**2 - 121*s + 36. Let i(z) = -4*w(z) + 9*y(z). Factor i(m).
2*(m - 9)*(3*m - 1)
Suppose 3*v - q - 12 = 0, -2*v - 8 = -6*v + 4*q. Solve y**3 + 7*y**v + 3*y**4 - 3*y**5 - 7*y**3 - y**5 = 0.
-2, 0, 1
Let m = -152 - -313/2. Solve m*h**2 + 2 + 7/4*h**3 + 1/4*h**4 + 5*h = 0 for h.
-2, -1
Let t(d) be the third derivative of d**8/10080 + d**7/2520 - d**5/15 - d**2. Let q(f) be th