e c.
0, 1
Let t(z) = -8*z**4 - 8*z**3 + 8*z**2 + 13*z + 5. Let v(u) = 4*u**4 + 4*u**3 - 4*u**2 - 6*u - 2. Let l(h) = 2*t(h) + 5*v(h). Determine s, given that l(s) = 0.
-1, 0, 1
Determine r, given that -2/9*r**3 + 4/9*r**2 - 4/9 + 2/9*r = 0.
-1, 1, 2
Let m be 9*6/9 - 3. Factor -12*o - 6*o**m + 2 + 4*o**4 + 2 + 13*o**2 - 3*o**4.
(o - 2)**2*(o - 1)**2
Let h(i) = i + i - 4*i - 13*i**2 - 13*i**3 - 2*i**4 + 5 + 2. Let k(y) = y**3 + y**2 - 1. Let w(u) = -2*h(u) - 14*k(u). Suppose w(o) = 0. Calculate o.
-1, 0
Let o(d) be the third derivative of 0 + 0*d**3 + 2*d**2 - 2/45*d**6 + 1/105*d**7 - 1/18*d**4 + 0*d + 7/90*d**5. Factor o(n).
2*n*(n - 1)**2*(3*n - 2)/3
Suppose -2*w + 4*i = 3*w + 16, 16 = 4*w + 4*i. Let a(t) be the third derivative of w*t**3 - 1/270*t**5 + 4*t**2 + 0 + 1/108*t**4 + 0*t. Factor a(p).
-2*p*(p - 1)/9
Suppose 3*k - 4*n + 3*n = 1109, -2 = n. Determine a so that 134*a**3 - 46*a**2 + k*a**4 - 5 - 28*a + 98*a**5 - 131*a**4 - 4*a + 13 = 0.
-1, 2/7
Let x(s) be the first derivative of -s**8/2520 + s**7/1260 + s**6/270 + 2*s**3/3 + 2. Let t(o) be the third derivative of x(o). Solve t(g) = 0.
-1, 0, 2
Let k(w) = w**3 + 7*w**2 + 8*w + 12. Let f be k(-6). Find y such that -2/3*y + f + 4/3*y**2 = 0.
0, 1/2
Let b be (-1 + (-10)/(-4))*2. Let j be 85/68*16/10. Determine r so that -3/4*r + 3*r**b + 9/4*r**j + 0 = 0.
-1, 0, 1/4
Let a(b) = -b**3 + 19*b**2 - 18*b**2 + 2*b**3. Let y(o) = o**4 - 3*o**3 - 3*o**2. Let q(g) = 3*a(g) + y(g). Solve q(v) = 0 for v.
0
Suppose -g - 5*d + 20 = 0, 3 = 2*g + 2*d - 5. Factor 1/2 + p**3 - 1/2*p**4 + g*p**2 - p.
-(p - 1)**3*(p + 1)/2
Find h, given that -2/9*h**3 + 2/9*h - 4/9*h**2 + 4/9 = 0.
-2, -1, 1
Let d be -3*2*7/(-14). Factor -5*g + 3*g - g + 6*g**2 - 5*g**3 + 2*g**d.
-3*g*(g - 1)**2
Factor 2/5*l**4 - 4/5 + 2/5*l**2 + 6/5*l**3 - 6/5*l.
2*(l - 1)*(l + 1)**2*(l + 2)/5
Let z = 9 - 37/5. Factor 0*v + 2/5*v**2 - z.
2*(v - 2)*(v + 2)/5
Suppose 3*m = 14*m - 22. Factor 0 - 6/5*i**3 + 6/5*i**4 + 2/5*i**m + 0*i - 2/5*i**5.
-2*i**2*(i - 1)**3/5
Let p(o) = o**2 + o - 3. Let d be p(-3). Let t = 3 - 1. Suppose -3*u**2 - t*u**3 + u - u**3 - u**4 + u - d*u = 0. Calculate u.
-1, 0
Let r be 2/6 - 238/(-51). Let h(d) be the third derivative of -2*d**2 + 0 + 0*d**3 - 1/360*d**6 + 1/72*d**4 - 1/60*d**r + 1/210*d**7 + 0*d. Factor h(p).
p*(p - 1)*(p + 1)*(3*p - 1)/3
Let i be (80/(-56))/((-4)/7) - 2. Let c = -59/2 + 30. Let -i*n**3 + n - c*n**2 + 0 = 0. Calculate n.
-2, 0, 1
Factor 2/15*r**3 - 4/15*r**2 + 2/15*r + 0.
2*r*(r - 1)**2/15
Suppose 4*a + 8*a - 8 + 6*a**2 - 20*a + 2*a**4 + 8*a**3 = 0. What is a?
-2, -1, 1
Let c be (3 + 4 + 3 + -8)/1. Factor 2/3*a**5 + 0*a + 2*a**3 - 2/3*a**c - 2*a**4 + 0.
2*a**2*(a - 1)**3/3
Let q(r) be the first derivative of -1/2*r**6 - 99/14*r**4 - 12/7*r**2 - 44/7*r**3 + 1 + 0*r - 111/35*r**5. Determine s, given that q(s) = 0.
-2, -1, -2/7, 0
Solve -2/3 + 5/3*s - 4/3*s**2 + 1/3*s**3 = 0 for s.
1, 2
Let t(c) be the third derivative of 0 - c**2 + 1/120*c**6 + 0*c**4 + 0*c**3 + 1/60*c**5 + 0*c. Solve t(x) = 0.
-1, 0
Let b(k) be the first derivative of -k**6/40 + k**5/20 + k**4/8 - k**3/2 - 2*k**2 + 1. Let z(o) be the second derivative of b(o). Factor z(a).
-3*(a - 1)**2*(a + 1)
Let o = 10 - 10. Let i = -13 + 16. Determine f, given that o + 0*f**i - 1/2*f**2 + 1/2*f**4 + 0*f = 0.
-1, 0, 1
Let c(f) be the second derivative of -f**6/540 + f**5/45 - f**4/9 - f**3/6 + f. Let p(h) be the second derivative of c(h). Let p(i) = 0. What is i?
2
Let n = -1 + 3. Factor -5*i**4 + 6*i**3 + 12*i + 2*i**4 - 24*i**n + 8*i**3 + i**3.
-3*i*(i - 2)**2*(i - 1)
Let s(w) be the second derivative of -w**7/336 - w**6/40 - 13*w**5/160 - w**4/8 - w**3/12 + 8*w. Factor s(x).
-x*(x + 1)**2*(x + 2)**2/8
Factor -343/5 + 147/5*k - 21/5*k**2 + 1/5*k**3.
(k - 7)**3/5
Let y = -6/347 + 4194/1735. Factor 12/5*k - y - 3/5*k**2.
-3*(k - 2)**2/5
Suppose 0 = 4*i - 5 - 103. Find d such that -40 + 40 - 18*d**2 - i*d - 3*d**3 = 0.
-3, 0
Let m = 89/42 + -11/6. Let d = 21 - 19. Let 0*j + 0 + m*j**d = 0. What is j?
0
Let a be 2/(16/(-3)) + (-57)/(-24). Determine j so that 0 + 3/5*j**a - 1/5*j = 0.
0, 1/3
Let o(z) be the third derivative of 0*z**3 + 1/90*z**5 - 1/18*z**4 + 0*z - 6*z**2 + 0. What is j in o(j) = 0?
0, 2
Factor 0 - 2/13*i**2 + 2/13*i**3 - 4/13*i.
2*i*(i - 2)*(i + 1)/13
Let t(h) be the first derivative of -h**7/840 + h**6/160 - h**5/80 + h**4/96 - 3*h**2/2 + 2. Let c(l) be the second derivative of t(l). Factor c(o).
-o*(o - 1)**3/4
Let d(v) be the third derivative of -4*v**7/105 - v**6/12 + v**5/2 + 5*v**4/3 + 4*v**3/3 + v**2 - 9*v. Find s such that d(s) = 0.
-2, -1, -1/4, 2
Let 0 + 0*t**2 + 0*t - 1/3*t**3 = 0. What is t?
0
Find g such that 2/3*g**2 + 20/3 - 14/3*g = 0.
2, 5
Let o(d) be the second derivative of d**8/168 + 2*d**7/105 + d**6/60 + d**2 + 5*d. Let p(k) be the first derivative of o(k). Let p(w) = 0. What is w?
-1, 0
Let f(w) be the second derivative of -w**6/90 + w**5/60 + w**4/12 - w**3/18 - w**2/3 - 20*w. Factor f(o).
-(o - 2)*(o - 1)*(o + 1)**2/3
Let r = 853/6 - 142. Factor 1/6*y**2 - r + 1/6*y**3 - 1/6*y.
(y - 1)*(y + 1)**2/6
Let s(f) = f**2 + 7*f + 8. Let d be s(-4). Let u be -16*(d + 23/6). Find j such that 8/3*j + 2/3 + 2/3*j**4 + u*j**3 + 4*j**2 = 0.
-1
Let z(g) be the first derivative of -1/4*g**2 + g - 1/3*g**3 + 1/8*g**4 - 4. Factor z(a).
(a - 2)*(a - 1)*(a + 1)/2
Let u be -3 - ((-2 - 0) + -3). Factor u + 8*p**2 - 6*p**2 + 7*p - 3*p.
2*(p + 1)**2
Let y(s) be the third derivative of s**6/160 - s**5/40 - 3*s**4/32 + 9*s**2. Find v, given that y(v) = 0.
-1, 0, 3
Factor 0 - 2/3*l**2 - 2*l.
-2*l*(l + 3)/3
Let x(w) be the first derivative of w**9/756 - w**7/210 + 4*w**3/3 + 1. Let o(m) be the third derivative of x(m). Factor o(k).
4*k**3*(k - 1)*(k + 1)
Let p = 73/39 + -7/13. Determine x so that 2*x + p*x**3 - 1/3 - 3*x**2 = 0.
1/4, 1
Let n be ((-6)/(-12))/(1/22). Factor n*o - 9*o + o**2 + 2 - 5*o.
(o - 2)*(o - 1)
Suppose 4*b + 12 = -4*l, -2*l - 3*b = -0*l + 11. Suppose 8 - 2 = 2*g. Let g*f + f**3 + f**l - 3*f**2 - 2*f = 0. Calculate f.
0, 1
Let f(k) be the third derivative of k**9/544320 - k**8/90720 + k**7/45360 - 2*k**5/15 - 4*k**2. Let x(b) be the third derivative of f(b). Factor x(n).
n*(n - 1)**2/9
Let d(h) be the third derivative of 0*h - 1/3*h**3 + 0 - h**2 - 1/48*h**4 - 1/1440*h**6 - 1/160*h**5. Let u(j) be the first derivative of d(j). Factor u(f).
-(f + 1)*(f + 2)/4
Let w(c) = 9*c**3 - 24*c**2 - 51*c - 12. Let l(j) = -10*j**3 + 24*j**2 + 52*j + 13. Let y(p) = -6*l(p) - 5*w(p). Factor y(r).
3*(r - 3)*(r + 1)*(5*r + 2)
Suppose -2 = 2*c + 4. Let q(v) = v**4 - 8*v**3 + 6*v**2 + v. Let j(y) = -y**3 + y**2. Let b(d) = c*q(d) + 21*j(d). What is a in b(a) = 0?
-1, 0, 1
Let k = 13 + -10. Factor g**2 - 3*g**2 - k*g**3 + 2*g**4 + 3*g**3.
2*g**2*(g - 1)*(g + 1)
Suppose -4*z**3 + 83*z - 83*z - 4*z**2 = 0. Calculate z.
-1, 0
Let b(x) = x**2 + 6*x - 6. Let s(z) = z**2 + z. Let g(r) = -b(r) + 4*s(r). Let f(c) = -c**2 - c - 1. Let y(w) = 2*f(w) + g(w). Find q, given that y(q) = 0.
2
Let u(h) = -h**4 + h**3 - h**2 + h. Let r(q) = 4*q**4 - 8*q**3 - 6*q**2 - 2*q. Let p(j) = r(j) + 2*u(j). Factor p(i).
2*i**2*(i - 4)*(i + 1)
Let r(f) = 3*f**3 - 9*f**2 - f + 7. Let t(n) = -3*n**3 + 9*n**2 - 6. Let y(x) = 3*r(x) + 2*t(x). What is a in y(a) = 0?
-1, 1, 3
Suppose -3*n = -3*x - 30, 4*n + 2*x - 24 = -2*x. Let l = -6 + n. Factor -1/2*d + 1/4 + 1/4*d**l.
(d - 1)**2/4
Let d(s) be the first derivative of s**6/42 + 3*s**5/35 + s**4/14 - 2*s**3/21 - 3*s**2/14 - s/7 - 4. Suppose d(b) = 0. What is b?
-1, 1
Let r(n) be the first derivative of 2*n**3/15 + n**2/5 - 23. Factor r(h).
2*h*(h + 1)/5
Let v = -5 - -7. Factor 6 + 12*r - 2*r**2 + 3*r**2 + 2 + 3*r**v.
4*(r + 1)*(r + 2)
Suppose -5*a + 20 = 4*j, -a + 0*a + 4 = -4*j. Let z(w) be the second derivative of 0*w**3 - 1/10*w**5 + 0*w**4 + 0 - w + 1/15*w**6 + j*w**2. Factor z(g).
2*g**3*(g - 1)
Let p(a) be the first derivative of 3*a**4/4 - a**3 - 3*a**2/2 + 3*a + 2. Find o, given that p(o) = 0.
-1, 1
Let q(f) be the third derivative of -f**8/112 + f**6/20 - f**4/8 - f**2. Factor q(x).
-3*x*(x - 1)**2*(x + 1)**2
Let q be (-6)/(-10) + (-28)/(-20). Factor q*i**5 - 5*i + 5*i - 2*i**4 - i - i**5 + 2*i**2.
i*(i - 1)**3*(i + 1)
Let k(m) be the first derivative of 10 + 2*m + 0*m**2 - 2/3*m**3. Factor k(t).
