15 + z**2/5 + 19. Determine n so that k(n) = 0.
0, 1
Suppose -5*x + 5*w + 55 = 0, -2*x + w + 2*w + 18 = 0. Factor 6*v + 12 - x + 15*v**2 - 6*v**2.
3*(v + 1)*(3*v - 1)
Factor -4*t + 2*t**2 - 3*t**2 - 5*t**2 - 2*t**3.
-2*t*(t + 1)*(t + 2)
Let 24/11*c + 18/11 + 6/11*c**2 = 0. Calculate c.
-3, -1
Let r(t) = -t**3 - t**2 + 1. Let b(h) = 14*h**3 - 12*h**2 + 18*h - 12. Let x(o) = b(o) + 8*r(o). Solve x(y) = 0.
1/3, 1, 2
What is o in -4*o - 5 - 2 + 2*o**2 + 2*o + 3 = 0?
-1, 2
Let n be (-1 + -5)*(-12)/18. Let z be n + 4 + (-120)/21. Factor 32/7*i**3 + 2/7*i + 0 + z*i**2.
2*i*(4*i + 1)**2/7
Let i(o) be the first derivative of 0*o**2 + 0*o**3 + 0*o - 4 - 1/15*o**5 + 1/12*o**4. Solve i(m) = 0.
0, 1
Let s = -240 - -242. Find r, given that 1/4*r**s + 1 - r = 0.
2
Let b(k) be the first derivative of -k**5/15 + k**4/4 - k**3/9 - k**2/2 + 2*k/3 - 2. Suppose b(p) = 0. What is p?
-1, 1, 2
Let v(t) = 3*t**4 + 7*t**3 - 10*t + 2. Let n(q) = 3*q**4 + 6*q**3 - 9*q + 3. Let d(u) = 2*n(u) - 3*v(u). What is g in d(g) = 0?
-2, 0, 1
Let p = -13 + 17. Let f(w) = 2*w - 7. Let b be f(5). Factor -p - b*j**2 - 3*j + 7*j + 2*j**2.
-(j - 2)**2
Let h(q) = 12*q + 27. Let k be h(-2). Factor -1/2*o**3 - k*o**2 - 6*o - 4.
-(o + 2)**3/2
Factor -2/7*n**4 + 0 + 4/7*n**2 + 2/7*n**3 + 0*n.
-2*n**2*(n - 2)*(n + 1)/7
Let a(r) be the first derivative of r**7/84 + r**6/30 - r**4/12 - r**3/12 - r - 1. Let b(j) be the first derivative of a(j). Find u, given that b(u) = 0.
-1, 0, 1
Let m(z) be the second derivative of z**7/315 + z**6/225 - z**5/50 - z**4/18 - 2*z**3/45 - 20*z. Factor m(p).
2*p*(p - 2)*(p + 1)**3/15
Let k(p) be the third derivative of -1/2688*p**8 + 7*p**2 + 0*p**4 + 0*p**3 - 1/840*p**7 + 0*p + 0*p**5 - 1/960*p**6 + 0. Solve k(m) = 0 for m.
-1, 0
Factor -b - 3/4 - 1/4*b**2.
-(b + 1)*(b + 3)/4
Let g(d) be the first derivative of 5*d**4/4 + 55*d**3/3 + 95*d**2/2 + 45*d + 9. Suppose g(l) = 0. What is l?
-9, -1
Let r = 0 + 2. Factor -1 - 3*v + v**4 + v**3 + v**2 + r*v**3 + 0*v**4 - 1.
(v - 1)*(v + 1)**2*(v + 2)
Solve 1/2*q**2 + 0 - 3*q = 0.
0, 6
Let n = 102 + -100. Let k(d) be the third derivative of 0*d + n*d**2 + 0 - 1/270*d**5 + 0*d**3 - 1/54*d**4. Suppose k(w) = 0. What is w?
-2, 0
Let l(n) be the second derivative of 0*n**3 + 1/70*n**5 + 1/70*n**6 + 0 - 4*n + 0*n**4 + 0*n**2 - 5/294*n**7. Factor l(g).
-g**3*(g - 1)*(5*g + 2)/7
Factor 8/7 + 2/7*w**2 + 8/7*w.
2*(w + 2)**2/7
Let q(u) be the first derivative of 9*u**3 + 6*u**4 + 6*u - 36/5*u**5 - 27/2*u**2 + 2. Let q(a) = 0. What is a?
-1, 1/2, 2/3
Let o(k) be the second derivative of k**5/50 - k**4/5 + 4*k**3/5 - 8*k**2/5 + k. Factor o(q).
2*(q - 2)**3/5
Let f(m) be the first derivative of m**4 - 8*m**3 - 30*m**2 - 32*m + 26. Factor f(n).
4*(n - 8)*(n + 1)**2
Let j(i) be the second derivative of -3*i + 0 - i**2 + 0*i**3 + 1/6*i**4. Determine s so that j(s) = 0.
-1, 1
Let x(r) be the third derivative of -r**7/35 - r**6/12 + r**5/6 + 5*r**4/12 - 2*r**3/3 - 3*r**2. Find t, given that x(t) = 0.
-2, -1, 1/3, 1
Factor 0 - 4/7*v**3 + 16/7*v**2 - 16/7*v.
-4*v*(v - 2)**2/7
Let l = 26 + -17. Let k(y) = -2*y**4 + 8*y**3 - 2*y**2 - 4*y. Let z(a) = 5*a**4 - 17*a**3 + 4*a**2 + 8*a. Let r(h) = l*k(h) + 4*z(h). Let r(u) = 0. What is u?
-2, -1, 0, 1
Let l(c) be the first derivative of c**6/120 - 3*c**5/40 + c**4/4 - 2*c**3/3 - 6. Let j(n) be the third derivative of l(n). Factor j(u).
3*(u - 2)*(u - 1)
Let i = -158/5 - -32. Find c, given that 4/5*c**3 - i*c**4 + 0*c**2 - 4/5*c + 2/5 = 0.
-1, 1
Let t(n) be the first derivative of -2*n**5/105 - n**4/7 - 26*n**3/63 - 4*n**2/7 - 8*n/21 - 14. Factor t(d).
-2*(d + 1)**2*(d + 2)**2/21
Let y(a) be the first derivative of -a**5/5 - a**4/4 + a**2/2 + a + 2. Suppose -j = 2*j + 6. Let g(p) = p**3 - p. Let u(d) = j*y(d) + 2*g(d). Factor u(v).
2*(v - 1)*(v + 1)**3
Let j = -68 + 68. Let t(n) be the third derivative of 0*n - 1/12*n**5 + 1/12*n**4 + 1/210*n**7 - 1/336*n**8 + 0*n**3 + 2*n**2 + 1/40*n**6 + j. Factor t(k).
-k*(k - 1)**3*(k + 2)
Let a(z) = 2*z**3 - 6*z + z + 8*z**3 + 7*z**2 - 7 + 0*z**3. Let o(n) = 5*n**3 + 3*n**2 - 3*n - 3. Let i(m) = -2*a(m) + 5*o(m). Factor i(w).
(w - 1)*(w + 1)*(5*w + 1)
Let a(w) be the first derivative of w**6/45 + 4*w**5/15 + 4*w**4/3 + 32*w**3/9 + 16*w**2/3 + 2*w + 1. Let o(n) be the first derivative of a(n). Factor o(y).
2*(y + 2)**4/3
Let n = -71 + 75. Let v(f) be the second derivative of 0*f**5 + 1/4*f**3 + 0*f**2 + 0 + 1/10*f**6 - 1/4*f**n - 1/28*f**7 + 4*f. Factor v(m).
-3*m*(m - 1)**3*(m + 1)/2
Let a(h) be the second derivative of -h**5/5 - 10*h**4/3 + 46*h**3/3 - 24*h**2 - 10*h - 3. Factor a(g).
-4*(g - 1)**2*(g + 12)
Let l(h) be the third derivative of h**6/1260 - h**5/105 + h**4/28 + 2*h**3/3 - h**2. Let n(q) be the first derivative of l(q). What is p in n(p) = 0?
1, 3
Suppose -3*r + 2*w - 4*w = -6, 4*w = 12. Let b = 11 + -54/5. Factor b*z**4 + 1/5*z - 1/5*z**2 + r - 1/5*z**3.
z*(z - 1)**2*(z + 1)/5
Suppose -t = -3*d + 4, d + 2*t + 6 = 5*d. Suppose -1 = -5*h + 2*i + d, 14 = h + 3*i. Factor -3*b**3 + b**3 + h*b + 0*b.
-2*b*(b - 1)*(b + 1)
Let w(q) be the second derivative of -1/10*q**4 + 0 - 2/5*q**5 + 0*q**2 + 3*q + 2/15*q**3 + 7/25*q**6. Solve w(d) = 0 for d.
-1/3, 0, 2/7, 1
Suppose 12*a = 10 - 10. Let d(y) be the third derivative of -y**2 - 1/21*y**4 + 4/21*y**3 + a + 1/210*y**5 + 0*y. Determine m so that d(m) = 0.
2
Let x(u) be the first derivative of -2*u**5/55 + u**4/22 + 4*u**3/33 - 4. Factor x(z).
-2*z**2*(z - 2)*(z + 1)/11
Factor -8/13*f + 6/13 + 2/13*f**2.
2*(f - 3)*(f - 1)/13
Suppose -2*q + 8*q = 12. Find t, given that 0*t + 1/4*t**3 + 0*t**q + 0 - 1/4*t**4 = 0.
0, 1
Let t(s) be the first derivative of -s**6/36 + s**5/30 + s**4/24 - s**3/18 + 2. Factor t(x).
-x**2*(x - 1)**2*(x + 1)/6
Let c(f) be the second derivative of -32*f**7/21 + 16*f**6/3 - 8*f**5 + 20*f**4/3 - 10*f**3/3 + f**2 + 2*f. Suppose c(g) = 0. What is g?
1/2
Let m(a) be the second derivative of -a**4/78 + a**3/13 - 2*a**2/13 - 30*a. Factor m(v).
-2*(v - 2)*(v - 1)/13
Determine a so that -2/11*a**3 + 16/11*a + 46/11*a**2 - 38/11*a**4 - 14/11*a**5 - 8/11 = 0.
-2, -1, 2/7, 1
Let x(o) = o**2 - 3*o - 2. Let u be x(4). Factor 2/7 - 8/7*c**u + 6/7*c.
-2*(c - 1)*(4*c + 1)/7
Let x(i) = i**2 - 4*i - 3. Let n be x(5). Factor -3*l**2 + 7 + n*l**2 + l - 5 + 0*l.
-(l - 2)*(l + 1)
Let b(m) be the third derivative of m**7/420 + m**6/240 - m**5/120 - m**4/48 - 9*m**2. Factor b(s).
s*(s - 1)*(s + 1)**2/2
Factor 1/9*r**3 - 2/9*r**2 - 1/9*r + 2/9.
(r - 2)*(r - 1)*(r + 1)/9
Let j = -5107/146 - 38/73. Let v = j - -36. Solve 3/4*s**4 - 1/4 + 1/2*s**3 - v*s**2 + 1/4*s**5 - 3/4*s = 0 for s.
-1, 1
Let j = -297/2 + 149. Find f such that 0*f**2 - 1 - j*f**3 + 3/2*f = 0.
-2, 1
Suppose b = -b + 2*w + 126, -w = -3*b + 183. Let o be 20/b*(1 - 0). Let -1/3*t**3 - o + 1/3*t**2 + 1/3*t = 0. Calculate t.
-1, 1
Factor 0*c - 1/2*c**3 + 0 - 1/2*c**2.
-c**2*(c + 1)/2
Suppose 0 = 2*b + 3*o - 9, -5*o + 15 = -2*b + 3*b. Let r(m) be the first derivative of b*m + 2/3*m**3 - 1 + 0*m**2. Factor r(t).
2*t**2
Let l(y) be the third derivative of 2*y**7/105 - 2*y**6/15 + 2*y**5/5 - 2*y**4/3 + 2*y**3/3 + y**2. Solve l(d) = 0 for d.
1
Suppose 21/2*v**3 - 3/2*v**4 - 21/4*v**5 + 3*v**2 - 3/2 - 21/4*v = 0. Calculate v.
-1, -2/7, 1
Let n(m) = 5*m**2 - 6*m + 1. Let q(b) = 9*b**2 - 11*b + 1. Let a(r) = -7*n(r) + 4*q(r). Let h be a(3). Determine f so that h*f + 2/11*f**2 - 2/11 = 0.
-1, 1
Let n = 65 - 60. Find d, given that 8/7*d**4 + 0 + 8/7*d**2 + 2/7*d**n + 12/7*d**3 + 2/7*d = 0.
-1, 0
Let o(b) = 95*b**2 - 80*b + 21. Let n(k) = -284*k**2 + 240*k - 64. Let w(i) = 5*n(i) + 16*o(i). Factor w(a).
4*(5*a - 2)**2
Let o(j) be the second derivative of 0 + 2*j + 2/9*j**4 + 0*j**2 + 1/5*j**5 + 1/63*j**7 + 1/9*j**3 + 4/45*j**6. Factor o(h).
2*h*(h + 1)**4/3
Let 3/2*g**2 + 2 - 1/4*g**3 - 3*g = 0. Calculate g.
2
Let r(c) be the first derivative of -c**5/5 - c**4/2 + c**3/3 + c**2 + 3. Factor r(y).
-y*(y - 1)*(y + 1)*(y + 2)
Let u(q) be the second derivative of q**7/5040 + q**6/1440 - q**4/6 + 3*q. Let o(a) be the third derivative of u(a). Factor o(l).
l*(l + 1)/2
Let k(t) be the second derivative of -2*t**7/21 - 26*t**6/15 - 7*t**5 + 49*t**4/3 - 23*t + 2. Find o such that k(o) = 0.
-7, 0, 1
Let t(u) = 17*u - 148. Let k be t(9). Suppose 5/2*c + 1/2 + 5*c**3 + 1