 - 32. Factor b(t).
(t - 2)*(t + 2)/4
Let p = 8 - 8. Let a(b) be the second derivative of 0*b**3 + 2*b + 7/80*b**5 + p - 1/24*b**4 + 0*b**2. Find n such that a(n) = 0.
0, 2/7
Suppose 2*t = -6*p + p + 43, 0 = 2*p + 3*t - 15. Let h(r) = r**2 - 8*r - 6. Let z be h(p). Let -5 - 10*k**4 + 7 - 2 - 14*k**z - 4*k**2 = 0. Calculate k.
-1, -2/5, 0
Suppose -3*h - f + 6 = 2*f, 2*h - 5*f = -10. Suppose 4*a + 8 = h, -u + 3*a + 6 = 4*u. Find x such that 0 + 0*x**4 + u*x**2 + 1/3*x**3 - 1/3*x**5 + 0*x = 0.
-1, 0, 1
Let f(l) be the third derivative of -l**7/70 - 7*l**6/40 - 3*l**5/4 - 9*l**4/8 + 6*l**2. Factor f(k).
-3*k*(k + 1)*(k + 3)**2
Let r(h) = -h**2 + 12*h + 13. Let m be r(13). Let u(x) be the first derivative of 1/3*x**3 + x**2 + m*x + 2. Factor u(d).
d*(d + 2)
Let a(q) = 12*q - 118. Let c be a(10). Find n such that 1/2 - 1/2*n**c + 0*n = 0.
-1, 1
Let q(f) be the third derivative of 0*f**3 + 0*f - 1/10*f**5 - 1/168*f**8 - 11/315*f**7 + 0 - 5*f**2 - 1/18*f**4 - 1/12*f**6. Suppose q(x) = 0. Calculate x.
-1, -2/3, 0
Let v be ((-13)/(-65))/((-1)/(-2)). Factor -1/5*y + 1/5*y**5 + v*y**2 - 2/5*y**4 + 0*y**3 + 0.
y*(y - 1)**3*(y + 1)/5
Let c(i) be the first derivative of i**5/60 - i**4/24 + 3*i**2/2 - 3. Let n(b) be the second derivative of c(b). Solve n(r) = 0 for r.
0, 1
Determine w so that -2/5*w**5 + 0 + 2/5*w**4 + 2/5*w**3 + 0*w - 2/5*w**2 = 0.
-1, 0, 1
Let w(z) be the third derivative of -z**9/15120 - z**8/1260 - z**7/315 + 2*z**5/45 - z**4/24 + z**2. Let j(d) be the second derivative of w(d). Factor j(m).
-(m + 2)**3*(3*m - 2)/3
Let h(b) = 5*b**4 + 18*b**3 + 17*b**2 + b - 5. Let x(j) = 3*j + 4*j - j - 5*j - 1. Let p(g) = -h(g) + x(g). Find l such that p(l) = 0.
-2, -1, 2/5
Factor 0*w + 9/5*w**3 + 6/5*w**2 + 3/5*w**4 + 0.
3*w**2*(w + 1)*(w + 2)/5
Let g(x) be the first derivative of x**6/3 - x**4 + x**2 + 28. Find q such that g(q) = 0.
-1, 0, 1
Let y(p) be the first derivative of 0*p**2 - 4 - 1/54*p**6 + 1/36*p**4 + 0*p**3 + 0*p**5 + 0*p. Let y(u) = 0. Calculate u.
-1, 0, 1
Let l = -3 + 18. Suppose -2*q = 0, 0*i + 5*i - l = -5*q. Determine u, given that -2*u**2 + 3*u**2 - i*u**2 + 4*u**2 = 0.
0
Suppose -i = -w - 2*w + 14, 2*w = -i + 6. Factor 2*s**2 + 3*s**3 + 2*s**2 - 2*s**w + 2*s**3 - 7*s**3.
-2*s**2*(s - 1)*(s + 2)
Let -1/3*c - 1/3*c**5 + 0 + 2/3*c**3 + 0*c**4 + 0*c**2 = 0. What is c?
-1, 0, 1
Let g(c) be the second derivative of c**5/150 - 7*c**4/90 - c**3/9 + 5*c**2 + 15*c + 2. Factor g(b).
2*(b - 5)**2*(b + 3)/15
Let u(j) = j**3 + 6*j**2 + 2*j - 6. Let g be u(-5). Let n be 34/g + 10/45. Solve 4*t**5 - 4*t**2 - 6*t**n - 2*t**5 + 2*t**2 + 6*t**3 = 0 for t.
0, 1
Let z(l) = 4*l. Let g(s) = -s + 1. Let y(n) = -g(n) - z(n). Let j be y(-1). Factor 0 + 4/3*p**j - 1/3*p - 1/3*p**5 - 2*p**3 + 4/3*p**4.
-p*(p - 1)**4/3
Let h = 4 - 3. Factor 2*d**2 + h + 2 + 1 - 6.
2*(d - 1)*(d + 1)
Let k(u) = 6*u**2 - 4*u - 1. Let x(z) = 7*z**2 - 4*z - 2. Let i(v) = 5*k(v) - 4*x(v). Let d be i(2). Factor 2*l + 2/3 - 2*l**4 + 4/3*l**2 - 2/3*l**5 - 4/3*l**d.
-2*(l - 1)*(l + 1)**4/3
Let k = -2 + 4. Suppose 0 = -5*q + 2 + 13, a - k*q = -2. Factor 13*w**3 + w**5 - 6*w**4 + a*w + 0*w + 0*w**5 - 12*w**2.
w*(w - 2)**2*(w - 1)**2
What is z in 30/7*z**2 - 18/7*z**3 + 64/7*z + 24/7 = 0?
-2/3, 3
Factor 73*w**2 + 4 + 7*w**3 - 77*w**2 - 2*w**5 + w**3 - 6*w.
-2*(w - 1)**3*(w + 1)*(w + 2)
Let o(s) = -21*s**3 - 21*s**2 - 15*s + 3. Let j(t) = -2*t + 2*t + t**2 + t**3 + t. Let r(a) = -18*j(a) - o(a). Factor r(f).
3*(f - 1)*(f + 1)**2
Let f(z) = 5*z**4 + 13*z**3 + 5*z**2 - 13*z + 4. Let k(t) = 3*t**4 + 7*t**3 + 3*t**2 - 7*t + 2. Let u(d) = 4*f(d) - 7*k(d). Factor u(v).
-(v - 2)*(v - 1)**2*(v + 1)
Suppose -2*i + 19 = 3*r, -5*r - 4*i + 37 = -2*i. Let d = r + -5. Determine z, given that z**4 + 2*z + 2*z**4 - 2*z**5 + z**d - 4*z**2 = 0.
-1, 0, 1
Let u(y) = 37*y**2 + 13*y. Let z(q) = 92*q**2 + 32*q. Let i(p) = 12*u(p) - 5*z(p). What is l in i(l) = 0?
-1/4, 0
Let u(y) be the third derivative of y**7/525 - y**6/300 - 42*y**2. Solve u(a) = 0 for a.
0, 1
Let n(k) be the second derivative of k**7/63 + k**6/45 - k**5/30 - k**4/18 + k. Suppose n(w) = 0. Calculate w.
-1, 0, 1
Let y be (-104)/(-20) + (-2)/10. Suppose -5*c + 27 - 7 = 0. Factor 0 - l**c - l**3 + 0*l - 1/3*l**y - 1/3*l**2.
-l**2*(l + 1)**3/3
Let l(w) = -w**3 + 5*w**2 + 7*w. Let g be l(6). Suppose 3*x**2 - g*x**2 + x**3 + 0*x + x + 5*x**2 = 0. Calculate x.
-1, 0
Factor -8/3*l + 2 + 2/3*l**2.
2*(l - 3)*(l - 1)/3
Suppose -1 + 9 = -3*n - 4*j, 2*n + j = -2. Factor n + 6/7*l - 2/7*l**2.
-2*l*(l - 3)/7
Suppose 0 = 4*u - 0*u - 32. Suppose 4*m - 2*m = 2*v - u, 4*v = 5*m + 16. Let 9/4*a + 7/4*a**v - 1/2 - 5/4*a**2 - 9/4*a**3 = 0. What is a?
-1, 2/7, 1
Factor 22*a**2 - 24*a**3 - 2654 + 2654 + 12*a - 10*a**4.
-2*a*(a - 1)*(a + 3)*(5*a + 2)
Let s = 8/7 + -25/28. Let u(m) be the first derivative of -1/6*m**2 - 2 + 2/3*m + s*m**4 - 4/9*m**3. Suppose u(t) = 0. Calculate t.
-2/3, 1
Let u(i) be the third derivative of i**6/160 + i**5/80 - i**4/16 - 4*i**2. Factor u(g).
3*g*(g - 1)*(g + 2)/4
Let y(z) be the third derivative of z**8/2240 + z**4/8 + 7*z**2. Let w(p) be the second derivative of y(p). Factor w(x).
3*x**3
Let l = 1 - -1. Find v, given that -8*v**4 - 3*v**l - 8*v + 4*v**4 + 7*v**2 + 8*v**3 = 0.
-1, 0, 1, 2
Let y = 36 - 28. Let q(h) be the first derivative of -y*h + 4*h**2 - 1 - 2/3*h**3. Suppose q(v) = 0. Calculate v.
2
Let d = 1 + 3/11. Let 6/11*b**3 + 14/11*b**4 + 4/11*b - d*b**2 - 10/11*b**5 + 0 = 0. What is b?
-1, 0, 2/5, 1
Let r(t) = 11*t**2 - 9*t + 1. Let c(f) = -f**2 + f - 1. Let l(a) = 18*c(a) + 2*r(a). Factor l(u).
4*(u - 2)*(u + 2)
Factor 4*n**3 - 8*n**2 + 10 - 11 + 1 - 32*n.
4*n*(n - 4)*(n + 2)
Let x(h) be the first derivative of h**3/4 - 13*h**2/4 - 9*h/4 + 50. Factor x(z).
(z - 9)*(3*z + 1)/4
Let a = -31/44 + 16/11. Let z(x) be the first derivative of -1/5*x**5 + 1 + a*x**4 + 3/4*x**2 - 13/12*x**3 - 1/4*x. Factor z(u).
-(u - 1)**2*(2*u - 1)**2/4
Let u = 224/117 + -22/13. Suppose -2*a + 6*a = -16, -8 = 2*d + 2*a. Factor 0*c + 0*c**2 + d*c**3 - u*c**4 + 0.
-2*c**4/9
Let c(v) be the first derivative of 2 + 1/2*v**4 - 2/3*v**3 + 2*v - v**2. Factor c(o).
2*(o - 1)**2*(o + 1)
Let q(g) be the third derivative of -1/48*g**4 - 3*g**2 + 0 + 0*g**6 - 1/210*g**7 + 1/672*g**8 + 1/60*g**5 + 0*g**3 + 0*g. Let q(d) = 0. What is d?
-1, 0, 1
Suppose 0*n - 3*n + 12 = 0. Factor 2*q**3 + q**5 - 2*q**2 + 5*q**4 + 3*q**3 - 9*q**n.
q**2*(q - 2)*(q - 1)**2
Solve -6*p**2 - 4*p**3 - 2 + 2 + 2*p**2 = 0.
-1, 0
Let v be (3 + -3)/(0 + -4). Determine q so that v*q - 6/5*q**2 - 2/5*q**5 + 0 + 6/5*q**4 + 2/5*q**3 = 0.
-1, 0, 1, 3
Let j be (1 + 0)/(2/6). Solve 24 + 18 + 3*y**2 - 54 + j*y**3 - 12*y = 0.
-2, -1, 2
Let u(i) be the second derivative of -i**5/20 + i**3/6 - i. Let n(t) = t**3 - t. Let j(z) = 2*n(z) + 4*u(z). Factor j(y).
-2*y*(y - 1)*(y + 1)
Let y(n) be the second derivative of n**7/252 - n**6/60 + n**5/40 - n**4/72 - 26*n. Factor y(a).
a**2*(a - 1)**3/6
Suppose 5*t - 4*t = 18. Let f = -35/2 + t. What is m in -f*m**2 + 1/2 + 0*m = 0?
-1, 1
Let v be (-6)/(-4)*(-11 + 13). Find g, given that 2*g**v - 4*g**3 + 0*g**3 - 2*g + 4*g**2 = 0.
0, 1
Let a = 8 - 3. Let q(j) be the second derivative of -j - 1/6*j**4 + 1/20*j**a + 1/6*j**3 + 0*j**2 + 0. Determine b, given that q(b) = 0.
0, 1
Let s = -71/120 - 3/40. Let x = 0 - s. Factor 2/3 + x*l**2 - 4/3*l.
2*(l - 1)**2/3
Let i(u) be the first derivative of -u**9/12096 + u**8/6720 + u**7/3360 - u**6/1440 - 4*u**3/3 + 1. Let p(s) be the third derivative of i(s). Factor p(x).
-x**2*(x - 1)**2*(x + 1)/4
Let m(w) be the third derivative of w**7/11340 + w**6/810 + w**5/135 + w**4/24 - 2*w**2. Let p(f) be the second derivative of m(f). Factor p(a).
2*(a + 2)**2/9
Factor 1/7*z**5 + 1/7*z**3 + 0*z**2 + 2/7*z**4 + 0 + 0*z.
z**3*(z + 1)**2/7
Suppose 4*q = -q + 10. Factor 12*k - q*k**3 + 0*k - 4*k.
-2*k*(k - 2)*(k + 2)
Let w = 4 + -6. Let x be 12/(-10) - (0 + w). Factor -2/5*n**2 + 2/5*n + x.
-2*(n - 2)*(n + 1)/5
Let r(k) = 10*k**2 - 7*k + 4. Let b(n) = -9*n**2 + 6*n - 3. Let f(q) = 7*b(q) + 6*r(q). Let f(h) = 0. Calculate h.
-1, 1
Let n(k) be the second derivative of -2*k**6/135 - k**5/9 - 2*k**4/9 + 9*k. Determine i so that n(i) = 0.
-3, -2, 0
Let w(a) = -2*a - 29. Let n be w(-17). Let u(r) be the second derivative of -1/24*r**3 - 