ve of -b**5/30 + b**4/6 - b**3/3 + b**2. Factor k(h).
-2*(h - 1)**2
Let r(v) be the second derivative of -v**7/210 - v**6/50 - 3*v**5/100 - v**4/60 - 17*v. Factor r(k).
-k**2*(k + 1)**3/5
Suppose 0 = 2*w + 4*n + 16, -4*w + 2*n - 32 = -n. Let p = w + 11. Factor -3*y**2 - 4*y**4 - 9*y**3 - 4*y**4 - p*y**5 - y**4.
-3*y**2*(y + 1)**3
Suppose 18 = 5*d - 12. Suppose u = -2*c + 7*c - d, 0 = -2*c + u. Factor 6*h + 2 + 1 - 6 + 0*h**2 - 3*h**c.
-3*(h - 1)**2
Let r be 3 - (3 + (-2)/2). Let p be (-5 + 10)*(r - 0). Determine s, given that 6/7*s**3 + 0 + 2/7*s**p + 0*s + 2/7*s**2 + 6/7*s**4 = 0.
-1, 0
Let t be -3*1 + (-33)/(-11). Let n(d) be the second derivative of t - 1/9*d**3 + 0*d**2 + 2*d - 1/18*d**4. Factor n(c).
-2*c*(c + 1)/3
Let f(x) be the second derivative of -x**3/6 + 3*x**2 + x. Let o be f(4). Factor -2*y**2 + y**3 + y + 1 - 2*y + y**o.
(y - 1)**2*(y + 1)
Suppose -5*w - 38 = -4*t + t, -4 = w. Let o(b) = b**2 - 2*b - 3. Let p be o(-2). Factor 5*m - p*m + t*m + 0*m - 3*m**2.
-3*m*(m - 2)
Factor 0*d - 1/5*d**5 + 1/5*d**3 + 1/5*d**2 + 0 - 1/5*d**4.
-d**2*(d - 1)*(d + 1)**2/5
Let m(t) be the second derivative of t**7/63 + 7*t**6/45 - t**5/15 - 23*t**4/9 + 65*t**3/9 - 25*t**2/3 - 20*t. Factor m(h).
2*(h - 1)**3*(h + 5)**2/3
Let r be 0/(7 + -4 - 4). Let z(l) be the third derivative of r*l + 2/3*l**3 + 0 - 1/60*l**6 + 1/12*l**4 + 3*l**2 - 1/15*l**5. Suppose z(h) = 0. What is h?
-2, -1, 1
Factor -50*w**3 - 32*w**2 - 38*w**2 - 25*w**3 + 72*w**4 + 40 - 27*w**4 + 60*w.
5*(w - 2)*(w - 1)*(3*w + 2)**2
Let k(l) be the third derivative of l**5/150 + l**4/30 + 3*l**2. Suppose k(a) = 0. What is a?
-2, 0
Let r(l) = -3*l**2 + 23*l - 16. Let u(k) = 30*k**2 - 231*k + 159. Let a(c) = 21*r(c) + 2*u(c). Factor a(m).
-3*(m - 6)*(m - 1)
Let y(n) be the first derivative of n**7/18 - 19*n**6/90 + n**5/4 - n**4/36 - n**3/9 + 3*n - 1. Let x(k) be the first derivative of y(k). Factor x(d).
d*(d - 1)**3*(7*d + 2)/3
Let u = 4 - 4. Suppose -14 = -3*s + l, s - 5*s + 3*l + 22 = 0. Let 0*a**3 + 2*a**s + 4/3*a**5 + u + 0*a - 2/3*a**2 = 0. What is a?
-1, 0, 1/2
Solve -9/5*x**4 + 12/5*x + 3/5 + 6/5*x**2 - 12/5*x**3 = 0 for x.
-1, -1/3, 1
Let m(f) be the third derivative of f**5/20 + f**4/4 + f**3/2 - f**2 - 4*f. Solve m(w) = 0.
-1
Suppose 15 = 3*i, -3*d + 3*i = -4*d - 104. Let t = 361/3 + d. Let 0*l + 1/3*l**2 - 5/3*l**3 + 0 + t*l**4 = 0. Calculate l.
0, 1/4, 1
Let m(s) be the first derivative of -4*s**5/25 - 4*s**4/5 - 8*s**3/5 - 8*s**2/5 - 4*s/5 + 9. Suppose m(q) = 0. What is q?
-1
Let b(x) = x + 5. Let t be b(-5). Suppose 2*y - 7*y + 15 = t. Suppose 0*c + 16*c + 8 - y*c**2 + 9*c**2 = 0. What is c?
-2, -2/3
Factor 2/7*f**2 + 0 - 2/7*f.
2*f*(f - 1)/7
Solve -5/2*z**2 + 1/2 + 1/2*z + 3/2*z**3 = 0 for z.
-1/3, 1
Let n = -37 + 52. Let u = 28 - n. Suppose -4*f + f - 9*f**3 - u*f - 4 - 21*f**2 = 0. Calculate f.
-1, -2/3
Let m(u) be the second derivative of 1/3*u**2 + 0 - 1/15*u**6 + u + 1/9*u**4 + 2/15*u**5 - 4/9*u**3. Find r such that m(r) = 0.
-1, 1/3, 1
Suppose 2*y - 12 = 4*g - 6*g, 0 = -3*g + 5*y + 10. Suppose 2*l**3 + 0*l**g + 3*l**4 - l**5 + 3*l - 4*l**3 - 1 - 2*l**2 = 0. What is l?
-1, 1
Let a(g) be the first derivative of 2*g**5/55 + g**4/22 + 13. Factor a(r).
2*r**3*(r + 1)/11
Suppose -5*a = 3*w - 18, -5*w - 9 = -4*a - 2*w. Let d(p) be the first derivative of p + 1/6*p**a + 3/4*p**2 - 2. Suppose d(f) = 0. Calculate f.
-2, -1
Let y be 4/18 + 129/27. Suppose 3*m + 1 = 2*c, -21 + y = -2*m - 2*c. Factor -w + 2*w + 3*w**2 + 3*w**3 - w**m.
w*(w + 1)*(2*w + 1)
Suppose 5*s = -t - 2*t - 16, -5*s - 18 = 4*t. Let k be s - (-1 + 0 + -1). Find v, given that k*v**3 + 1/2*v + 3/4*v**2 + 0 - 1/4*v**4 = 0.
-1, 0, 2
Let p = 3/2 - -11. Let g = -59/6 + p. Find d such that 0 + 2*d**3 - g*d - 16/3*d**2 + 6*d**4 = 0.
-2/3, 0, 1
Let a(s) = s**3 - 10*s**2 + s - 7. Let b be a(10). Factor -12*n**b - 3*n**4 - 2*n**4 + 0*n**4 - 12*n**2 + n**4 - 4*n.
-4*n*(n + 1)**3
Let a be 1/(0 - 4/(-20)). Let i(z) be the first derivative of -4/3*z**2 + 4/3*z**3 + 2/15*z**a + 2 + 2/3*z - 2/3*z**4. Factor i(x).
2*(x - 1)**4/3
Factor 11*s + 2 - s**3 + 2*s - 10*s.
-(s - 2)*(s + 1)**2
Let v(w) be the first derivative of -14*w**5/5 - w**4 + 14*w**3 + 20*w**2 + 8*w + 22. Solve v(d) = 0 for d.
-1, -2/7, 2
Suppose -20 = -4*j - 3*t, 0 + 20 = 4*j - t. Suppose -u = -2*u + j. Factor -u*d**4 + 10*d**5 - 4*d + 17*d**4 - d**5 - 12*d**2 - 5*d**3.
d*(d - 1)*(d + 1)*(3*d + 2)**2
Let z(o) = 2*o**5 + 3*o**4 + o**2 + 3. Let h(i) = i**5 + i**4 - i**3 + i**2 + 1. Let p be (3/6)/((-2)/(-12)). Let r(u) = p*h(u) - z(u). Factor r(a).
a**2*(a - 1)**2*(a + 2)
Let s be ((-1)/(8/(-8)))/(-2 - -7). Factor s*c**5 + 1/5*c - 2/5*c**3 + 0*c**2 + 0*c**4 + 0.
c*(c - 1)**2*(c + 1)**2/5
Factor -29*n + 13*n + 1 - 6*n**2 + 7*n - 3*n**5 + 10*n + 2*n**3 + 5*n**4.
-(n - 1)**3*(n + 1)*(3*n + 1)
Let b(g) be the third derivative of -g**10/120960 + g**9/60480 - g**4/6 - 3*g**2. Let s(v) be the second derivative of b(v). Factor s(z).
-z**4*(z - 1)/4
Let w(v) be the third derivative of -5*v**2 + 0*v + 0 + 1/168*v**8 + 0*v**4 - 1/30*v**5 + 0*v**3 - 1/60*v**6 + 1/105*v**7. Determine f so that w(f) = 0.
-1, 0, 1
Let -365*n**3 - 36*n + 347*n**3 + 12 + 4*n**4 - n**4 + 39*n**2 = 0. Calculate n.
1, 2
Let i(v) = 5*v**2 - 1. Suppose -5*k + 60 = d, -5*d + 47 = 2*k - 0*k. Let y(z) = -14*z**2 + 3. Let w(j) = k*i(j) + 4*y(j). Factor w(h).
-(h - 1)*(h + 1)
Let v(a) be the first derivative of 0*a - 9*a**3 + 1 + 18*a**4 - 48/5*a**5 + 3/2*a**2. Factor v(u).
-3*u*(u - 1)*(4*u - 1)**2
Let v be 78/20 + (-4)/(20/(-3)). Factor 0*d + 6 - v*d**3 - 21/2*d**2.
-3*(d + 1)*(d + 2)*(3*d - 2)/2
Let d(v) = -3*v**2 + 89*v + 30. Let i be d(30). Factor i - 3/5*l**3 + 3/5*l**4 - 3/5*l**2 + 3/5*l.
3*l*(l - 1)**2*(l + 1)/5
Let b(l) be the second derivative of l**5/120 - l**4/8 + 3*l**3/4 - l**2 + 6*l. Let p(w) be the first derivative of b(w). Factor p(n).
(n - 3)**2/2
Factor -12*a**4 + 18*a**3 - 27/4*a**2 + 0*a + 0.
-3*a**2*(4*a - 3)**2/4
Let g(b) = b**3 + 4*b**2 - 8*b - 3. Let k be g(-5). Find s, given that -5*s**2 + 5*s**3 - 3*s**4 - 3*s**2 - k*s + 16*s + 2*s**4 = 0.
0, 1, 2
Let l = 805/4 - 201. What is o in -1/4*o - 1/2*o**2 + 0 - l*o**3 = 0?
-1, 0
Let r(p) be the second derivative of -3*p**5/20 + p**3/2 - 21*p. Factor r(m).
-3*m*(m - 1)*(m + 1)
Let f(h) be the second derivative of 2*h**6/5 + 2*h**5 + 4*h**4 + 4*h**3 + 2*h**2 + 2*h. What is y in f(y) = 0?
-1, -1/3
Let p = 8 + -18. Let r = 5 + p. Let f(w) = -3*w**3 - 4*w**2 - 2*w - 6. Let q(d) = d**2 + d + 1. Let s(b) = r*q(b) - f(b). Factor s(i).
(i - 1)*(i + 1)*(3*i - 1)
Let y(z) be the second derivative of z**4/6 - 2*z**3/3 + z**2 - 7*z. Factor y(g).
2*(g - 1)**2
Let f(r) be the second derivative of r**6/10 + 3*r**5/10 - 16*r. Determine m so that f(m) = 0.
-2, 0
Let h(s) be the first derivative of 4/15*s**3 + 4/5*s**4 + 0*s**2 + 1/5*s**5 + 0*s - 5/6*s**6 - 3. Suppose h(c) = 0. What is c?
-2/5, 0, 1
Let s(i) be the third derivative of i**6/120 - i**5/20 + i**4/8 - i**3/6 - 4*i**2. Factor s(d).
(d - 1)**3
Let t(k) be the third derivative of k**11/55440 + k**10/37800 - k**9/30240 - k**5/60 - 6*k**2. Let v(i) be the third derivative of t(i). Factor v(p).
2*p**3*(p + 1)*(3*p - 1)
Let m(a) be the second derivative of -1/168*a**7 + 0 - 1/40*a**6 - 3*a + 0*a**3 - 3/80*a**5 + 0*a**2 - 1/48*a**4. Factor m(r).
-r**2*(r + 1)**3/4
Let h be 271/546 - 5/10. Let p = 155/273 - h. Determine z so that 2/7 - p*z + 2/7*z**2 = 0.
1
Let q(i) be the second derivative of i**8/1176 - 2*i**7/735 - 3*i**2/2 - 4*i. Let s(z) be the first derivative of q(z). Find y such that s(y) = 0.
0, 2
Let x = -10/13 + 116/117. Find j such that -2/9 - 4/9*j - x*j**2 = 0.
-1
Suppose -6*i + 2*i + 18 = -5*q, 4*q - i = -21. Let b = q + 8. Find c such that 2/3*c - 2/3*c**3 + 0 + 0*c**b = 0.
-1, 0, 1
Let b = 11 + -11. What is h in 4*h**4 - 2*h**4 + b*h**2 - 2*h**2 = 0?
-1, 0, 1
Let h(a) be the first derivative of 9/5*a**5 - 15/2*a**4 + 6 + 46/3*a**3 - 33/2*a**2 - 1/6*a**6 + 9*a. Factor h(s).
-(s - 3)**2*(s - 1)**3
Let x(u) be the second derivative of -2*u**6/15 + 3*u**5/5 - u**4/3 - 2*u**3 + 4*u**2 - 17*u. Let x(f) = 0. What is f?
-1, 1, 2
Let k(c) be the third derivative of -c**5/240 - c**4/48 + 18*c**2. Let k(b) = 0. What is b?
-2, 0
Let o = -57 - -61. Find s, given that 0 - 2/7*s**o - 4/7*s + 6/7*s