/4
Let y be 1 - (-1 + 0) - 312/162. Let p(u) be the second derivative of -1/54*u**4 - y*u**3 + 0 - 2*u + 1/90*u**5 + 0*u**2. Suppose p(q) = 0. What is q?
-1, 0, 2
Factor 2/9*s**3 + 0*s + 2/9*s**4 - 2/9*s**5 + 0 - 2/9*s**2.
-2*s**2*(s - 1)**2*(s + 1)/9
Let g be -4*-1*(-3)/(-68). Let x = 7/153 + g. Factor -8/9 - 8/9*y - x*y**2.
-2*(y + 2)**2/9
Let n(s) be the first derivative of -15*s**6/2 + 168*s**5/5 - 195*s**4/4 + 28*s**3 - 6*s**2 - 3. Let n(b) = 0. What is b?
0, 1/3, 2/5, 1, 2
Suppose -24 = -5*j - 14. Suppose -j*g = -0*g. Factor g - 4*v**3 - 2/3*v**2 + 0*v - 16/3*v**4.
-2*v**2*(2*v + 1)*(4*v + 1)/3
Factor 0 - 2/3*j**2 + 2/3*j.
-2*j*(j - 1)/3
Let k(l) be the second derivative of 0*l**3 - 3*l - 1/6*l**4 + 1/42*l**7 + 0 - 1/20*l**5 + 1/15*l**6 + 0*l**2. Factor k(z).
z**2*(z - 1)*(z + 1)*(z + 2)
Suppose 0 = -8*t + 46 - 6. Let v(r) be the third derivative of 4*r**2 + 0 + 0*r + 0*r**3 - 1/30*r**t + 0*r**4. Suppose v(k) = 0. What is k?
0
Let f(k) be the first derivative of 1 - 4/3*k - 1/6*k**4 - 5/3*k**2 - 8/9*k**3. Solve f(n) = 0 for n.
-2, -1
Let o(p) be the third derivative of p**9/60480 - p**7/1680 - p**6/360 + p**5/10 - 2*p**2. Let k(y) be the third derivative of o(y). Factor k(a).
(a - 2)*(a + 1)**2
Let w(o) be the second derivative of -1/40*o**5 + 1/60*o**6 - 2*o + 1/84*o**7 + 0 - 1/24*o**4 + 0*o**2 + 0*o**3. Factor w(a).
a**2*(a - 1)*(a + 1)**2/2
Let y be (-1 - 1)/(-2*(-20)/(-16)). Factor 2/5*n**2 + y*n + 0.
2*n*(n + 2)/5
Let v(n) = n**2 + 4*n. Let s be v(-5). Suppose 5 + 5 = s*c. Find l, given that 2*l**2 + 6*l**2 - 6*l**c - 2*l = 0.
0, 1
Let n(m) be the third derivative of 9*m**2 + 0 + 1/100*m**6 + 0*m**4 + 0*m**3 + 0*m - 1/75*m**5 - 1/840*m**8 + 0*m**7. Factor n(f).
-2*f**2*(f - 1)**2*(f + 2)/5
Let n(b) = 15*b**3 + b**2 + 2*b - 2. Let g be n(1). Let c = g + -14. Factor -1/4*d**c + 1/4 + 0*d.
-(d - 1)*(d + 1)/4
Factor 28/5*s**2 - 2/5*s**4 + 2/5*s**5 - 22/5*s - 12/5*s**3 + 6/5.
2*(s - 1)**4*(s + 3)/5
Suppose -3*u + 16 = u. Let c(m) be the first derivative of -2/21*m**3 + 2/35*m**5 + 3 + 1/14*m**u - 1/21*m**6 + 0*m**2 + 0*m. Solve c(h) = 0.
-1, 0, 1
Let 1/3*j + 0 - 1/3*j**3 + 1/3*j**4 - 1/3*j**2 = 0. What is j?
-1, 0, 1
Let z be (1/3)/((-2)/(-12)). Factor -2*l + 1 + 2*l**3 - 1 + 7 - 1 - 6*l**z.
2*(l - 3)*(l - 1)*(l + 1)
Let y(b) be the first derivative of -b**4/4 + b**3 + 9. Suppose y(u) = 0. Calculate u.
0, 3
Suppose 3*d - 5 = -2*j, 2 = 3*d + 4*j + 1. Let k(f) be the first derivative of -7/3*f**d - 4*f - 8*f**2 - 1. Factor k(t).
-(t + 2)*(7*t + 2)
Factor 0*o**3 + 6*o**3 + 0*o**5 + 8*o**4 - 10*o**3 - 4*o**5.
-4*o**3*(o - 1)**2
Let w(p) = -p - 9. Suppose 8 = -a - 3. Let d be w(a). Solve -6 + y - y - 3*y**3 - 9*y**d + 18 = 0 for y.
-2, 1
Let j be 37/15 + (-19)/(-95). Determine k, given that -8/3 + j*k - 2/3*k**2 = 0.
2
Factor 2/5*j + 0 - 2/5*j**4 + 2/5*j**2 - 2/5*j**3.
-2*j*(j - 1)*(j + 1)**2/5
Let f = 6 + -5. Let l = f + 2. Determine h so that -3*h**3 + 6*h**2 + l - 6 + 3 = 0.
0, 2
Let w(d) be the third derivative of 0*d**4 + 0*d - 2*d**2 + 0 + 1/120*d**6 - 1/60*d**5 + 0*d**3. Solve w(i) = 0 for i.
0, 1
Factor 1/2*h**3 + 1/4*h**4 + 0 + 0*h + 1/4*h**2.
h**2*(h + 1)**2/4
Let d(p) = -p**2 + 6*p - 5. Let i be d(2). Let q(s) be the first derivative of -1/5*s**5 + 0*s**i + 0*s + 1/4*s**4 + 2 + 0*s**2. Find c such that q(c) = 0.
0, 1
Let g be (-1 + 3)/((-4)/(-6)). Find c, given that -9*c**4 + 3*c**g + 9*c**2 + 0*c**4 - 5*c + 2*c = 0.
-1, 0, 1/3, 1
Let c(d) be the first derivative of -5*d**3/3 + 15*d**2 + 1. Determine g so that c(g) = 0.
0, 6
Let d(y) be the second derivative of y**6/40 + y**5/16 - y**4/48 - 5*y**3/24 - y**2/4 - 6*y + 5. Factor d(b).
(b - 1)*(b + 1)**2*(3*b + 2)/4
Let m be (-38)/(-30) - (-12)/(-18). Factor 0*h + 0 + 3/5*h**3 - m*h**5 - 3/5*h**4 + 3/5*h**2.
-3*h**2*(h - 1)*(h + 1)**2/5
Let o = 1364 - 1362. Factor g**4 + 0 + 1/2*g**5 + 1/2*g**3 + 0*g**o + 0*g.
g**3*(g + 1)**2/2
Let k(q) be the second derivative of q**6/45 + q**5/15 - 2*q**3/9 - q**2/3 + 15*q + 1. Let k(h) = 0. Calculate h.
-1, 1
Let x(a) = -a**5 + 5*a**4 - 6*a**2. Let t(o) = -3*o**5 + 11*o**4 - 13*o**2. Suppose -2 = l + 2*w, 2*l - 3*l - 4*w = -6. Let i(k) = l*x(k) + 4*t(k). Factor i(r).
-2*r**2*(r - 1)*(r + 2)**2
Determine t so that -2*t - 2/3*t**2 + 0 = 0.
-3, 0
Let r = 77/3 + -25. Let k(h) = h**2 + 7*h + 9. Let n be k(-6). Let 0 + 0*p**2 + 1/3*p**n + 1/3*p**5 + 0*p + r*p**4 = 0. Calculate p.
-1, 0
Let t(r) be the second derivative of r**6/6 - r**5/2 + 5*r**3/3 - 5*r**2/2 + 11*r. Suppose t(s) = 0. Calculate s.
-1, 1
Let l(c) be the second derivative of -c**7/147 + 4*c**6/35 - 2*c**5/7 - c**4/21 + c**3 - 10*c**2/7 - 3*c - 3. Determine o so that l(o) = 0.
-1, 1, 10
Let h be 2/5 - (-962)/(-30). Let g = h + 32. Find a such that 4/3*a**2 - g - a = 0.
-1/4, 1
Let a be 1/(-8) - 66/(-16). Suppose -3*g - g - 3*n + 1 = 0, -4*n - a = 4*g. Factor 0*q - 1/3*q**2 - 1/3*q**g - 2/3*q**3 + 0.
-q**2*(q + 1)**2/3
Let d(x) = 2*x**3 - 28*x**2 + 34*x - 8. Let f(p) = -p**3 + 28*p**2 - 34*p + 7. Let h(m) = -5*d(m) - 4*f(m). Find v such that h(v) = 0.
2/3, 1, 3
Let x(z) be the third derivative of -z**9/7560 - z**8/1050 - z**7/525 + z**3/2 + 6*z**2. Let c(g) be the first derivative of x(g). Factor c(v).
-2*v**3*(v + 2)**2/5
Solve 2*k**2 + 3*k**2 + 23*k - 13*k = 0.
-2, 0
Let x(o) be the first derivative of -16*o**3/15 + 6*o**2/5 - 2*o/5 + 4. Factor x(p).
-2*(2*p - 1)*(4*p - 1)/5
Let k(q) = 2 + 6*q**2 + 4*q**3 + q**3 - 4*q**3 - 2*q**3. Let t be k(6). Factor -1/2*y - 1/2*y**t + 1.
-(y - 1)*(y + 2)/2
Let o(n) be the second derivative of -n**4/4 - 2*n**3 - 6*n**2 + 8*n. Factor o(k).
-3*(k + 2)**2
Let x(t) = 5 + 8*t**2 + t**3 - 5 - 9*t + 9. Let d be x(-9). Factor 0 - 3*w**4 + 7*w + 2*w**4 - 2 - d*w**2 + 5*w**3.
-(w - 2)*(w - 1)**3
Factor -2*t**4 - 4*t**3 - 2*t**4 - 8 + 12*t**2 + 0*t**4 + 5*t - t.
-4*(t - 1)**2*(t + 1)*(t + 2)
Let r = -15 - -17. Let b be (11/(-66))/(r/(-3)). Suppose 5/2*z**2 - 5/2*z**3 + b - 5/4*z - 1/4*z**5 + 5/4*z**4 = 0. Calculate z.
1
Let b(a) = 3*a - 9 + 2*a - 5*a + a. Let z be b(9). Factor -2/5*g + z - 2/5*g**3 - 4/5*g**2.
-2*g*(g + 1)**2/5
Let t(w) = w**2 - 9*w + 10. Let i be t(8). Factor -2/3*a - 1/6 - 1/2*a**i + 2/3*a**3 + 2/3*a**4.
(a - 1)*(a + 1)*(2*a + 1)**2/6
Let b(z) be the first derivative of -5*z**5/2 + 5*z**4/6 + 16*z**3/3 + 4*z**2 + 3*z - 8. Let w(t) be the first derivative of b(t). Factor w(l).
-2*(l - 1)*(5*l + 2)**2
Suppose -2*u - 4 = p - 5*p, -4 = -u. Let s be (-5)/2*(-18)/5. Find t, given that -s*t**2 - 4*t + 3*t**3 + 6*t + 4*t**p = 0.
0, 2/7, 1
Let b = 7 + -5. Suppose b*g - 6 = -g. Factor 6/5*x**2 - 4/5 + g*x.
2*(x + 2)*(3*x - 1)/5
Factor 0*a - 4/5*a**3 - 4/5*a**2 + 0.
-4*a**2*(a + 1)/5
Suppose 39*r = 44*r. Let v(g) be the first derivative of 2/15*g**3 + 0*g + 3 + r*g**2. Solve v(q) = 0.
0
Factor 0*o + 0 + 2/7*o**2.
2*o**2/7
Let q be 14/24 + 1/(-4). Let n(c) = c**2 + 31*c + 84. Let r be n(-28). What is u in -q*u**2 + 0 + r*u - 1/3*u**3 = 0?
-1, 0
Let v = -142 - -146. Let r(s) be the second derivative of -3*s + 1/5*s**2 + 0 - 11/100*s**5 - 3/10*s**3 + 1/50*s**6 + 1/4*s**v. Let r(z) = 0. What is z?
2/3, 1
What is i in -2/5*i + 0 + 1/5*i**2 = 0?
0, 2
Let i(q) be the second derivative of -13/4*q**4 + 0 + 4*q + 6*q**2 - 3/4*q**5 - 2*q**3. Determine t so that i(t) = 0.
-2, -1, 2/5
Let w(f) = -f**2 - 20*f - 19. Let y be w(-19). Let p = 2/203 - -8/29. Suppose 0 + p*h**4 - 2/7*h**2 + y*h + 0*h**3 = 0. Calculate h.
-1, 0, 1
Let i be 2 - 5 - ((-4)/(-8) + -4). Let s(g) be the first derivative of -3/4*g**4 - g**3 - i*g**2 - 1/5*g**5 + 0*g - 1. Factor s(h).
-h*(h + 1)**3
Let r(n) be the second derivative of 2*n**7/63 + n**6/18 + n**5/60 - 9*n. What is i in r(i) = 0?
-1, -1/4, 0
Let y = 22 + -19. Let a(x) be the second derivative of 0*x**y - 2*x + 0 + 0*x**4 + 1/63*x**7 + 0*x**2 + 2/45*x**6 + 1/30*x**5. Factor a(o).
2*o**3*(o + 1)**2/3
Determine z so that 4 + 6*z**2 + 3*z - 6*z**3 - z**4 + 3*z**5 - 2*z**4 - 7 = 0.
-1, 1
Let z(g) = g**3 - g**2 - g + 2. Let y be z(2). Suppose c + 3*x = -c + 2, -4*c = -y*x - 24. Factor c*b**4 - b**5 - b - 2*b**2 - 2*b**4 + 2*b.
-b*(b - 1)**3*(b + 1)
Let a(n) be the first derivative of n**3 + 9*n**2 - 30. Suppose a(o) = 0. Calculate o.
-6, 0
Suppose 4*v + v = 0. Determine o, given that v*o**3 + 5*o**3 + 2*o**2 - 3*o**2 - 4*o**3 = 0.
0, 1
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