 x**2 - x + 1. Let d(r) = -2*r**3 - 3*r**2 - 3*r + 1. Let i(a) = d(a) - o(a). Let i(p) = 0. Calculate p.
-1, 0
Let d(y) be the second derivative of y**4/18 - y**3/9 - y. Solve d(w) = 0 for w.
0, 1
Let d(y) be the first derivative of y**6/24 + y**5/10 - y**3/6 - y**2/8 + 20. Solve d(g) = 0 for g.
-1, 0, 1
Find i, given that -157 - 229 - 3584*i - 5681*i**4 - 126 - 10976*i**3 - 9408*i**2 + 879*i**4 = 0.
-4/7
Factor 0 - 7*g**2 - 1/3*g**4 - 10/3*g - 4*g**3.
-g*(g + 1)**2*(g + 10)/3
Let m = 63 + -61. Let g(a) be the third derivative of 1/4*a**3 - 1/40*a**5 - 1/32*a**4 + m*a**2 + 0 + 1/160*a**6 + 0*a. Determine k so that g(k) = 0.
-1, 1, 2
Solve 2/7*u**3 - 2/7*u + 0*u**2 + 0 = 0.
-1, 0, 1
Suppose 4*u + 5*s - 31 = 0, -s - 4*s = -5*u + 5. Let w(d) be the second derivative of -1/12*d**u + 0 - 1/2*d**2 + 1/3*d**3 + d. Factor w(h).
-(h - 1)**2
Let b be -4 - 20/(-2 - 3). Let k(n) be the third derivative of 0*n + 3/80*n**5 + b*n**3 - 3/280*n**7 + 2*n**2 - 1/16*n**4 + 0 + 1/80*n**6. Solve k(r) = 0.
-1, 0, 2/3, 1
Let f(p) be the second derivative of p**7/294 + p**6/42 + p**5/70 - p**4/6 - p**3/14 + 9*p**2/14 + 5*p. Find c, given that f(c) = 0.
-3, -1, 1
Let v(o) be the first derivative of o**3 + 3*o**2 + 3*o + 6. Suppose v(t) = 0. What is t?
-1
Let l(k) be the first derivative of -k**9/4536 + k**8/504 - 2*k**7/315 + k**6/135 - 2*k**3/3 + 2. Let w(y) be the third derivative of l(y). Factor w(f).
-2*f**2*(f - 2)**2*(f - 1)/3
Find a, given that 4*a**4 - 2*a**4 - 5*a**2 + 5*a**3 - a**4 - a**3 = 0.
-5, 0, 1
Let l(y) be the third derivative of -y**6/780 + 2*y**5/195 - 5*y**4/156 + 2*y**3/39 + 6*y**2. Factor l(w).
-2*(w - 2)*(w - 1)**2/13
Let h(t) be the second derivative of t**6/1440 - t**5/240 + t**4/96 - t**3 - 6*t. Let w(n) be the second derivative of h(n). Let w(u) = 0. Calculate u.
1
Let d be (-84)/(-24) - (-1)/(-2). Let n(y) be the second derivative of 1/40*y**5 + 0*y**2 + 0 + y + 1/12*y**d - 1/12*y**4. Solve n(u) = 0.
0, 1
Let n(h) be the second derivative of -h**6/1260 - h**5/105 - h**4/21 + h**3/3 - 3*h. Let t(l) be the second derivative of n(l). Solve t(j) = 0.
-2
Solve -2/3*f**5 + 4/3*f**3 - 2/3 + 4/3*f**2 - 2/3*f**4 - 2/3*f = 0.
-1, 1
Let b(x) be the first derivative of 0*x + 16/55*x**5 + 7/22*x**4 - 3 + 1/11*x**6 + 4/33*x**3 + 0*x**2. Solve b(h) = 0.
-1, -2/3, 0
Let v = -87 - -88. Let m(b) = -2*b - 5. Let y be m(-4). Find h, given that 4*h**2 + h**y - 2*h**2 - h**2 + v - 2 - h = 0.
-1, 1
Let i = -3/4 - 11/12. Let u = i + 13/6. Determine v so that -u*v + v**2 - 1/2*v**3 + 0 = 0.
0, 1
Suppose 2*r + 52 = 58. Let m(i) be the third derivative of 0*i - 3*i**2 + 1/120*i**6 + 1/30*i**5 + 0 + 0*i**r + 1/24*i**4. Let m(u) = 0. What is u?
-1, 0
Factor 3/7*k + 0 - 6/7*k**3 - 3/7*k**2.
-3*k*(k + 1)*(2*k - 1)/7
Let s(a) = 2*a**3 + 5*a**2 + 3*a - 5. Let r(b) = -9*b**3 - 21*b**2 - 12*b + 21. Let f(x) = -5*r(x) - 21*s(x). Factor f(u).
3*u*(u - 1)*(u + 1)
Let s = 182/75 + 6/25. Let l = 202 - 199. What is g in -s*g**l + 0*g - 2/3*g**4 - 8/3*g**2 + 0 = 0?
-2, 0
Let b(d) be the third derivative of -d**6/720 + d**5/90 - 5*d**4/144 + d**3/18 - 12*d**2. Factor b(r).
-(r - 2)*(r - 1)**2/6
Let k be (-2)/10 + 112/35. Let v(x) be the second derivative of -2*x - 2/9*x**k + 2/3*x**2 + 0 + 1/36*x**4. Let v(o) = 0. What is o?
2
Suppose 2/3*n**4 - 1/3*n - n**5 + 4/3*n**3 + 0 - 2/3*n**2 = 0. Calculate n.
-1, -1/3, 0, 1
Let t be (-2)/11 - (-12)/66. Let -3/4*f**4 - 3/4*f**3 - 1/4*f**2 + t + 0*f - 1/4*f**5 = 0. Calculate f.
-1, 0
Let y(w) = -w + 7. Let j be y(5). Let z(m) be the first derivative of 1/15*m**3 - 2/5*m**2 - j + 4/5*m. Factor z(p).
(p - 2)**2/5
Factor 1/2 - 7/4*m - 1/2*m**2 + 7/4*m**3.
(m - 1)*(m + 1)*(7*m - 2)/4
Find z such that 4/3*z**2 - 2/3*z**5 + 4/3*z**3 - 2/3*z**4 - 2/3 - 2/3*z = 0.
-1, 1
Let s = -84 - -265/3. Let l = s + -4. Factor -1/3*h**2 + l + 0*h.
-(h - 1)*(h + 1)/3
Let u be 2/(-7)*(2 + -3). Factor -2/7*k**4 - u*k**3 + 0 + 2/7*k + 2/7*k**2.
-2*k*(k - 1)*(k + 1)**2/7
Let l(m) = 49*m**4 - 23*m**3 - 168*m**2 - 71*m + 39. Let r(o) = -25*o**4 + 11*o**3 + 84*o**2 + 35*o - 19. Let f(t) = -3*l(t) - 7*r(t). Factor f(d).
4*(d - 2)*(d + 1)**2*(7*d - 2)
Let g = -2 - -5. Let c(r) be the third derivative of 0 + 0*r**g + 1/72*r**4 + 4*r**2 - 1/180*r**5 + 0*r. Factor c(n).
-n*(n - 1)/3
Factor 64 + 4*y**5 - 8*y**4 - 64 + 4*y**3.
4*y**3*(y - 1)**2
Suppose 0 = 4*y - 16, 0*y = 4*j - 4*y - 192. Let g be j/80 + 3/(-12). Factor 4/5*k**2 - 2/5*k**3 - g*k + 0.
-2*k*(k - 1)**2/5
Let t(u) be the first derivative of 2*u**5/115 - 8*u**3/69 - 9. Determine g so that t(g) = 0.
-2, 0, 2
Factor 36/5*x**2 + 4/5*x**3 + 108/5*x + 108/5.
4*(x + 3)**3/5
Let u(x) be the third derivative of -x**8/840 + x**7/180 + x**6/180 - 5*x**4/24 + x**2. Let n(k) be the second derivative of u(k). Solve n(q) = 0 for q.
-1/4, 0, 2
Let y(i) be the third derivative of i**6/360 + i**5/120 - i**4/12 + i**3/6 + i**2. Let q(b) be the first derivative of y(b). Determine n so that q(n) = 0.
-2, 1
Let o(x) be the first derivative of x**5/20 + x**4/8 + x**2 + 1. Let i(w) be the second derivative of o(w). What is k in i(k) = 0?
-1, 0
Let n(m) = m**3 + 5*m**2 + 3*m. Let d be n(-4). Let y(f) be the third derivative of -2*f**2 + 1/60*f**5 + 1/12*f**d + 0 + 0*f + 1/6*f**3. Factor y(z).
(z + 1)**2
Let u(g) be the third derivative of g**5/240 + g**4/16 + 5*g**3/24 + 24*g**2. Solve u(q) = 0.
-5, -1
Factor 0 + 4*k + 1/3*k**2.
k*(k + 12)/3
Let g(p) = -p**3 + p**2. Let y(f) = -4*f**3 + 7*f**2 - 7*f + 4. Let l(m) = 10*g(m) - 2*y(m). Factor l(v).
-2*(v - 1)**2*(v + 4)
Suppose -4*h + 4*r + 68 = 0, -5*h = -0*h - 3*r - 95. Suppose -22 + h + u**4 - u**3 = 0. Calculate u.
0, 1
Let v = -5 + 7. Factor 1 - 5 - v + 10*t + 2*t**4 + 2 - 2*t**3 - 6*t**2.
2*(t - 1)**3*(t + 2)
Suppose -2*j - 48 = -5*j. Factor 12 + j*k + 3*k + k**2 + 3*k**2 - 3*k.
4*(k + 1)*(k + 3)
Let t be 13/4 - (-6)/(-24). Factor -8*m**4 - m**5 - 3*m**5 + 4*m**3 + t*m**3 - 11*m**3.
-4*m**3*(m + 1)**2
Let d(w) = -4*w**2 + 4*w + 1. Let t be 4/(-10) + (-46)/10. Let u(y) = -3*y**2 + 3*y + 1. Let a(l) = t*d(l) + 7*u(l). Determine n, given that a(n) = 0.
-1, 2
Let z(f) = -f + 9. Let w be z(5). Suppose a = -0*a + w. What is y in -11*y**3 + 5*y**3 - 4*y**2 + a*y**3 = 0?
-2, 0
Suppose 0 = -13*w + 8*w + 5. Let p be w - (-1 + (-14)/(-9)). Suppose 2/9*n**4 + 0 - 2/9*n**2 + p*n**3 - 4/9*n = 0. What is n?
-2, -1, 0, 1
Let x be ((-154)/735)/((-1)/25). Let y = x - 32/7. Factor -y*k**3 + 0 + 0*k**2 + 0*k.
-2*k**3/3
Let o(g) = 6*g**2 + 4*g + 6. Let b(n) = 2*n**2 + n + 2. Let m(k) = 8*b(k) - 3*o(k). Determine i, given that m(i) = 0.
-1
Factor 17 + 4*d**2 - 6*d**2 - 15.
-2*(d - 1)*(d + 1)
Let o(w) be the second derivative of w**7/21 + w**6/15 - w**5/5 - w**4/3 + w**3/3 + w**2 + 4*w. Factor o(v).
2*(v - 1)**2*(v + 1)**3
Let j be (-18)/4*4/6. Let h = 1 - j. Factor 0 + 0*g - 2/3*g**3 + 0*g**2 - 2/3*g**h.
-2*g**3*(g + 1)/3
Let a(z) be the second derivative of z**5/20 - z**4/6 - 5*z**3/6 + 3*z**2 - 27*z + 1. Solve a(u) = 0 for u.
-2, 1, 3
Let t(f) = f**2 - 4*f + 4. Let l be t(6). Let r = l + -11. Factor 1/2*z**2 + 1/2*z**3 + 0 + 0*z - 1/2*z**r - 1/2*z**4.
-z**2*(z - 1)*(z + 1)**2/2
Let n(r) be the third derivative of -r**8/840 - r**7/420 + r**6/180 + r**5/60 + r**3/3 - r**2. Let k(g) be the first derivative of n(g). Factor k(p).
-2*p*(p - 1)*(p + 1)**2
Let b(z) be the first derivative of z**6/360 - z**4/24 + z**3/3 + 3. Let x(j) be the third derivative of b(j). Let x(g) = 0. What is g?
-1, 1
Determine k so that -2/9*k**2 + 0 + 4/9*k**3 - 4/9*k + 2/9*k**4 = 0.
-2, -1, 0, 1
Factor 6*w**2 + 9*w**4 + 15*w**3 - 86 + 48 + 38.
3*w**2*(w + 1)*(3*w + 2)
Let b(t) be the third derivative of 5*t**2 + 1/240*t**6 + 0 + 1/360*t**5 + 0*t**3 + 0*t**4 - 1/315*t**7 + 0*t. Factor b(i).
-i**2*(i - 1)*(4*i + 1)/6
Let f(n) be the third derivative of -n**6/8 + 9*n**5/20 - 3*n**4/8 - n**3/2 + 2*n**2 + 22. Determine u so that f(u) = 0.
-1/5, 1
Let k(j) be the first derivative of 1/180*j**5 + 1/540*j**6 - 1/18*j**4 + 0*j + 0*j**2 - 1 + j**3. Let r(u) be the third derivative of k(u). Factor r(l).
2*(l - 1)*(l + 2)/3
Let h(j) be the first derivative of -8*j**6/3 - 28*j**5/3 - 32*j**4/3 - 8*j**3/3 + 8*j**2/3 + 4*j/3 - 13. Solve h(x) = 0.
-1, -1/4, 1/3
Factor -18/7*b**3 - 12/7*b**4 - 12/7*b**2 - 3/7*b + 0 - 3/7*b**5.
-3*b*(b + 1)**4/7
