h(d) be the second derivative of -9*d**5/70 - 25*d**4/42 + 2*d**3/7 - 8*d. Factor h(m).
-2*m*(m + 3)*(9*m - 2)/7
Let a(x) be the first derivative of -1/27*x**4 - 2*x + 0*x**2 + 7/135*x**6 + 0*x**3 + 2 - 1/18*x**5. Let r(u) be the first derivative of a(u). Factor r(s).
2*s**2*(s - 1)*(7*s + 2)/9
What is l in 1/2*l**2 + 0 - 1/2*l = 0?
0, 1
Let f(p) = p**3 + p**2 - 2*p + 3. Let g be f(-3). Let b = g - -9. Suppose 0*t**2 + 0 - 4/9*t**4 - 2/9*t**3 - 2/9*t**5 + b*t = 0. What is t?
-1, 0
Let i = 4 - -3. Let z(t) be the second derivative of -1/189*t**i + 1/30*t**5 + 2*t + 2/27*t**3 - 5/54*t**4 + 0 + 1/135*t**6 + 0*t**2. Factor z(r).
-2*r*(r - 1)**3*(r + 2)/9
Let a(w) be the third derivative of w**5/20 - 5*w**2. Factor a(i).
3*i**2
Let b(x) be the third derivative of -7*x**8/80 - 3*x**7/50 + 3*x**6/25 - x**5/25 - 6*x**2. Factor b(q).
-3*q**2*(q + 1)*(7*q - 2)**2/5
Let j be ((-7)/252)/((-9)/12). Let g(y) be the first derivative of 0*y**2 + 1 + 2/15*y**5 + 0*y + j*y**6 + 2/27*y**3 + 1/6*y**4. Suppose g(q) = 0. What is q?
-1, 0
Let a(r) = 9*r**4 - 28*r**3 + 60*r**2 - 41*r. Let u(d) = -26*d**4 + 84*d**3 - 180*d**2 + 122*d. Let t(c) = 14*a(c) + 5*u(c). Factor t(w).
-4*w*(w - 3)**2*(w - 1)
Let j(y) be the third derivative of 5*y**8/1008 - y**7/63 + y**5/18 - 5*y**4/72 - 19*y**2. Factor j(c).
5*c*(c - 1)**3*(c + 1)/3
Let x(h) be the first derivative of -h**8/448 - h**7/420 + h**6/160 + h**5/120 - 3*h**2/2 - 2. Let z(o) be the second derivative of x(o). What is i in z(i) = 0?
-1, -2/3, 0, 1
Let q = 26 + -30. Let l be 65/(-15) + 1 - q. Factor -2/3*k + 0 - l*k**2.
-2*k*(k + 1)/3
Let f(h) = -h**2 + h + 3. Let v be f(0). Let j(l) = 5*l**2 + 4*l. Let z(w) = -4*w**2 - 3*w. Let s(o) = v*j(o) + 4*z(o). Determine p so that s(p) = 0.
0
Let r(z) = -z**5 + 12*z**4 - 10*z**3 - 12*z**2 + 11*z. Let y(v) = v**4 - v**3 - v**2 + v. Let m(f) = -4*r(f) + 36*y(f). Factor m(j).
4*j*(j - 2)*(j - 1)**2*(j + 1)
Let m(a) be the first derivative of -3/5*a**5 + 0*a + a**2 - 1/4*a**4 + a**3 - 1/6*a**6 + 3. Find c such that m(c) = 0.
-2, -1, 0, 1
Let z(o) = -o**2 - 11*o - 6. Let n be z(-10). Suppose 8 + 0 = n*j. Factor 0*k + k**3 + 3*k + 2*k**j - 3*k**2 + 1 - 4*k.
(k - 1)**2*(k + 1)
Let f(u) be the first derivative of -5*u**3/4 - 21*u**2/8 - 3*u/2 + 2. Find n, given that f(n) = 0.
-1, -2/5
Let w = 73659/138886 + -1/18939. Let i = w + -1/33. Factor -3/2*r + i*r**2 + 3/2*r**3 - 1/2.
(r - 1)*(r + 1)*(3*r + 1)/2
Suppose -14*c + 146 - 104 = 0. Determine m so that -5*m + c + 7/3*m**2 - 1/3*m**3 = 0.
1, 3
Suppose 20 + 4 = 4*u + 2*s, -12 = -4*u + s. Let o(w) = w. Let t be o(u). Factor y**4 - y**2 + 7*y**2 - 3*y**4 - t*y**2.
-2*y**2*(y - 1)*(y + 1)
Let l be (2 - 5) + (-174)/(-4). Let i(c) = -c**3 + 8*c**2 - 8*c - 6. Let z be i(6). Let l*j**3 + 9*j**2 + 4 - 81/2*j**4 - z*j = 0. Calculate j.
-2/3, 1/3, 2/3
Let w(f) be the first derivative of 2*f**3/27 - 2*f**2/3 + 17. Factor w(z).
2*z*(z - 6)/9
Let s be (13/3 - 1) + 22/(-66). Let l(p) be the third derivative of 0*p**s - 1/20*p**5 + 0*p + 0 - p**2 + 0*p**4. Find n, given that l(n) = 0.
0
Let a(m) be the first derivative of m**6/21 - 8*m**5/35 + 5*m**4/14 - 4*m**3/21 + 12. Determine t so that a(t) = 0.
0, 1, 2
Factor -3*y + 9/2 - 3/2*y**2.
-3*(y - 1)*(y + 3)/2
Let j = 63 - 42. Solve 3*m**2 - 5 + j + 11 - 18*m = 0 for m.
3
Let p(j) = j**2 + 5*j - 33. Let y be p(-9). Solve 0*z - 1/2*z**4 - 1/6*z**5 - 1/6*z**2 - 1/2*z**y + 0 = 0.
-1, 0
Suppose -4*g + 1 + 3 = 0. Let s(m) = m**5 - 5*m**3 - m**2 + 2*m + 1. Let a(i) = i**3 - i**2 + i + 1. Let r(c) = g*s(c) + a(c). Factor r(y).
(y - 2)*(y - 1)*(y + 1)**3
Let h(s) = 3*s**2 + 3*s - 17. Let x(v) = 17*v. Let l be x(1). Let i(a) = 0*a + 0 - a**2 - 6 + a + 2*a**2. Let f(q) = l*i(q) - 6*h(q). Factor f(y).
-y*(y + 1)
Suppose 0 = -d - 2 + 4. Factor 8*x**2 - x**2 + 2*x**d + 3*x.
3*x*(3*x + 1)
Let u = 87/10 + -41/5. Find f, given that -3/2*f - 1/2*f**2 + 3/2*f**3 + u = 0.
-1, 1/3, 1
Let d(f) be the first derivative of -6 + 7/8*f**4 - 3/2*f**3 + 1/2*f**2 + 0*f. Determine b, given that d(b) = 0.
0, 2/7, 1
Factor 1/4*r**5 + 0*r**2 + 0*r + 1/4*r**3 - 1/2*r**4 + 0.
r**3*(r - 1)**2/4
Factor 0*d**2 + 0 + 1/7*d**3 - 1/7*d.
d*(d - 1)*(d + 1)/7
Let k(i) be the first derivative of -8/21*i**3 + i**2 - 4/7*i - 2/7*i**4 - 3. Solve k(v) = 0 for v.
-2, 1/2
Let r = -6 - -9. Suppose 2*l - r*l - 3*a + 17 = 0, -2*l = -4*a + 16. Let 2*j - l*j - j**3 + 2*j**2 + j - j**2 - 1 = 0. Calculate j.
-1, 1
Let v(b) = 3*b - 5. Let n(q) = -q**2 - 1. Let i(a) = n(a) - v(a). Factor i(x).
-(x - 1)*(x + 4)
Let h(d) be the second derivative of -d**5/60 + d**3/18 + 2*d. Find m such that h(m) = 0.
-1, 0, 1
Let t = -4 + 4. Let q(x) be the third derivative of 4/3*x**3 + 1/3*x**4 + t*x - 3*x**2 + 0 + 1/30*x**5. Factor q(y).
2*(y + 2)**2
Let k = 142/65 - 18/13. Factor -k*b**2 - 8/5 - 12/5*b.
-4*(b + 1)*(b + 2)/5
Let r be 1 - -1 - (-2 + 4). Let y(u) be the second derivative of -u + r*u**2 + 0 - 1/3*u**3 + 1/10*u**5 + 0*u**4. Factor y(x).
2*x*(x - 1)*(x + 1)
Let k(t) be the third derivative of t**7/126 + t**6/9 + t**5/2 - 15*t**3/2 - 27*t**2. Let k(x) = 0. What is x?
-3, 1
Let a be 20/(-3) - (3 - (5 + 5)). Suppose 0*l - 1/3*l**3 + 1/3*l**2 - a*l**4 + 1/3*l**5 + 0 = 0. What is l?
-1, 0, 1
Factor 4/7*z + 2/7*z**2 + 2/7.
2*(z + 1)**2/7
Suppose 5*u - 35 = -5*f, 5*u + 1 = 4*f - 0. Find o such that o**3 - o**3 + 2*o**4 + f*o**5 + 2*o - 4*o**3 - 2*o**2 - 2*o**3 = 0.
-1, 0, 1/2, 1
Factor -7/9 - i**2 + 1/9*i**3 + 5/3*i.
(i - 7)*(i - 1)**2/9
Factor -4/5 + 4/5*h**2 + 2/5*h - 2/5*h**3.
-2*(h - 2)*(h - 1)*(h + 1)/5
Suppose -168 = 3*h - 6*h. Suppose -h*a + 4*a**5 + 56*a + 4*a**4 = 0. Calculate a.
-1, 0
Suppose 3*y = 2*a - 27, 2*a - 13 = -y + 18. Let n be (49/a + -3)*5. Suppose 2/3*v**4 + 16/3*v**3 - 8/3*v - 8/3*v**5 - n*v**2 + 2/3 = 0. What is v?
-1, 1/4, 1
Determine a so that 0*a + 0*a**2 + 0 - 1/6*a**3 = 0.
0
Let v(b) be the third derivative of b**8/1008 - b**6/120 + b**5/90 - 23*b**2. Solve v(l) = 0.
-2, 0, 1
Let w be ((-2)/4)/((-69)/(-34)). Let p = 2/23 - w. What is v in p*v**5 + 1/3*v**4 - 1/3*v**2 + 0 + 0*v - 1/3*v**3 = 0?
-1, 0, 1
Let d = 51 + -49. Solve d*z**2 + 1/3*z**4 - 4/3*z**3 - 4/3*z + 1/3 = 0 for z.
1
Factor 4*g**2 - 6*g**3 - 16*g - 8*g**2 + 4*g**4 + 14*g**3 + 8*g.
4*g*(g - 1)*(g + 1)*(g + 2)
Solve t**2 + 2/3*t**4 + 1/6*t + 0 + 3/2*t**3 = 0 for t.
-1, -1/4, 0
Let d(g) = 2*g**2 + 5*g - 4. Let x be d(1). Let -4/3*t**x + 0 + 2/3*t**4 - 2/3*t**2 + 4/3*t = 0. Calculate t.
-1, 0, 1, 2
Factor 1/4*p**3 - 3/4*p**2 + 0 + 1/2*p.
p*(p - 2)*(p - 1)/4
Suppose 15 = 3*z + 3*v, -4*v + 0*v = -4*z + 4. Suppose 2*h - j + 5*j + 6 = 0, 0 = z*h - 3*j - 27. Factor -2/5*c**h - 6/5*c**3 + 0 + 0*c + 2/5*c**2 + 6/5*c**4.
-2*c**2*(c - 1)**3/5
Let g(z) be the second derivative of -1/4*z**3 + 3/2*z**2 + 4*z + 0 - 1/8*z**4. Suppose g(a) = 0. What is a?
-2, 1
Let q(k) = k + 2. Let c be q(-2). Let -2*g**5 + 2*g - g**4 + 4*g**2 - 4*g + c*g**5 + 4*g**3 - 2 - g**4 = 0. Calculate g.
-1, 1
Suppose s = 3*s. Factor 0 + s*u + 0*u**2 - 1/4*u**3 + u**4.
u**3*(4*u - 1)/4
Suppose 0 = t - 3*t + 14. Suppose t*m = 3*m. Factor 3 - 2*h**2 - 3*h + 0 + m - 4.
-(h + 1)*(2*h + 1)
Let k(f) be the third derivative of f**8/1344 - f**7/840 - f**6/480 + f**5/240 + 22*f**2. Factor k(a).
a**2*(a - 1)**2*(a + 1)/4
Let j be (-4)/(-5) + (-2)/(-10). Let 4 + j - 5 + 4*b**2 = 0. What is b?
0
Suppose -4*l + 3 = -5. Solve 13*i + 16 + 4*i**l - 3*i**2 - 5*i = 0 for i.
-4
Let d(x) = 3*x**2 + 5*x + 1. Let g be d(-2). Factor -4/7*n**g + 0 - 2/7*n**4 + 2/7*n**2 + 4/7*n.
-2*n*(n - 1)*(n + 1)*(n + 2)/7
Let k(l) be the second derivative of 1/6*l**3 + 0*l**2 + 1/20*l**5 - 1/6*l**4 + 3*l + 0. Determine i, given that k(i) = 0.
0, 1
Determine u, given that 0 + 5/2*u**2 - u = 0.
0, 2/5
Let k = 0 - 24. Let n be 2/9 - k/135. Determine u, given that 0 - n*u**3 + 0*u + 2/5*u**2 = 0.
0, 1
Find m, given that -1/2*m**5 - m**3 - m**2 + 3/2*m - 1/2 + 3/2*m**4 = 0.
-1, 1
Let x(l) be the second derivative of l**4/12 + 2*l**3/3 + 2*l**2 + l. Find p, given that x(p) = 0.
-2
Let y(a) be the third derivative of a**7/1260 + a**6/180 + a**5/72 + a**4/72 - 7*a**2. Let y(i) = 0. Calculate i.
-2, -1, 0
Let u be ((-1)/(-3))/(35/15). Factor -1/7*r - 1/7*r**4 - u + 2/7*r**2 + 2/7*r**3 - 1/7*r**5.
-(r - 1)**2*(r + 1)**3/7
Let w = 457/38 + -48/19. Let b = -9 + w. Sol