0.
-2, 3/7, 1
Let f be (-688)/(-258) - (-1 + 2/3). Determine k so that 4/3*k**f - 7/3*k**5 - 4*k**4 - 2/3 + 14/3*k**2 + k = 0.
-1, 2/7, 1
Let b(w) = -8*w**2 + 3*w + 5. Let l(d) = -3*d**2 + d + 2. Let h(m) = 4*b(m) - 11*l(m). Suppose h(k) = 0. What is k?
-2, 1
Let x(t) = 21*t**2 - 63*t - 12. Let y(l) = 42*l**2 - 125*l - 25. Let h(n) = -11*x(n) + 6*y(n). Factor h(m).
3*(m - 3)*(7*m + 2)
Suppose 270 = 4*d + 5*u, -d + 6*u - u = -80. Let x be (-3)/(-6) + (-15)/d. Let 0*m**3 - 2/7*m + x*m**5 + 0 + 4/7*m**2 - 4/7*m**4 = 0. What is m?
-1, 0, 1
Let u(s) be the third derivative of 0*s + 0*s**6 + 0 + 1/840*s**7 + 0*s**4 + 0*s**3 + 6*s**2 - 1/240*s**5. Factor u(i).
i**2*(i - 1)*(i + 1)/4
Let q(i) be the third derivative of -5/16*i**4 + 5*i**2 + 1/224*i**8 - 1/35*i**7 + 0*i + 0 + 1/2*i**3 + 1/20*i**5 + 1/20*i**6. Factor q(u).
3*(u - 2)*(u - 1)**3*(u + 1)/2
Let o be -9 - -4 - (-88)/16. Factor 0 + 1/2*y - o*y**2.
-y*(y - 1)/2
Let d(a) be the first derivative of -4*a**5/5 + a**4 + 4*a**3/3 - 2*a**2 - 6. Factor d(b).
-4*b*(b - 1)**2*(b + 1)
Let x(o) = 6*o**2 - 16*o + 10. Let r(i) = 2*i**2 - 5*i + 3. Let z(p) = 16*r(p) - 5*x(p). Factor z(s).
2*(s - 1)*(s + 1)
Suppose 12 = k - 4*y, -k - 5*y - 15 = -4*k. Factor -g - g - 2*g**3 + k*g + 4*g**2.
-2*g*(g - 1)**2
Let t(y) = y**2 - y - 39. Let v be t(-6). Determine h so that -1/2*h + 1/4*h**2 + 0 + 1/4*h**v = 0.
-2, 0, 1
Let c(g) = g**2 - 7*g - 6. Let u be c(8). Solve -5*t**3 - 4*t**u + 2*t**3 - 2*t + t**3 = 0 for t.
-1, 0
Let i(b) be the first derivative of -b**6/42 - 2*b**5/35 - b**4/28 - 8. Factor i(y).
-y**3*(y + 1)**2/7
Factor -13*a - a**4 - 6*a**2 + 8 + 5*a + 8*a**3 - a**4.
-2*(a - 2)**2*(a - 1)*(a + 1)
Let m(g) = -13*g**3 - 4*g**2 - 2*g + 4. Let j be m(-3). Suppose 0 = -5*s + 25 + j. Factor -30*w**4 - 42*w**5 + s*w**4 - 8*w**5 - 8*w**3.
-2*w**3*(5*w - 2)**2
Suppose 5*n + 14 = -2*u - u, -2*n - 4 = 2*u. Factor 1/4*w**4 - 1/4*w**5 + 0 + 1/4*w**3 + 0*w - 1/4*w**u.
-w**2*(w - 1)**2*(w + 1)/4
Let h(t) be the first derivative of -2/5*t**2 - 2/15*t**3 + 2 - 2/5*t. Suppose h(j) = 0. What is j?
-1
Factor 5*v**2 - 110 + 355 + 64*v + 6*v.
5*(v + 7)**2
Let j(f) be the first derivative of 2*f**3/3 + 9. Let j(y) = 0. Calculate y.
0
Let z = 15 + -10. Let n(d) be the second derivative of 4/5*d**3 - 7/5*d**4 + 0*d**2 - 27/70*d**7 + 27/50*d**z + 0 + 2*d + 27/50*d**6. Factor n(t).
-3*t*(t + 1)*(3*t - 2)**3/5
Factor -149*x + 149*x + 3 - 4*x**2 + x**2.
-3*(x - 1)*(x + 1)
Let r be 3 - (-2 - (1 - 15)). Let u = 11 + r. Factor -2/7*q**u + 0 + 2/7*q**3 + 0*q.
2*q**2*(q - 1)/7
Suppose 0 = 5*j - 5 + 5. Factor 1/4*o**3 + 0*o**2 + 0 + j*o - 1/4*o**4.
-o**3*(o - 1)/4
Let h be 42/7*(-1)/(-2). Suppose -2*p = h*m - 13, 3*p + 3*m = 2*p + 11. Factor 4/9 - 40/9*c**p + 2/3*c.
-2*(4*c + 1)*(5*c - 2)/9
Let h = -4 + 4. Let j(d) be the third derivative of 1/44*d**4 - 1/33*d**3 - 1/110*d**5 + 0 + 3*d**2 + 1/660*d**6 + h*d. What is i in j(i) = 0?
1
Let p = -28 - -62. Let i = -32 + p. Solve -1/4*q + 3/4*q**3 + 0 - 1/2*q**i = 0.
-1/3, 0, 1
Let y(h) be the third derivative of 3*h**8/2800 + h**7/1400 - h**6/300 + 4*h**3/3 - 5*h**2. Let s(m) be the first derivative of y(m). Factor s(n).
3*n**2*(n + 1)*(3*n - 2)/5
Let r(p) be the second derivative of p**2 + 0 + 1/30*p**5 + p + 0*p**4 - 1/3*p**3. Let v(w) be the first derivative of r(w). Factor v(o).
2*(o - 1)*(o + 1)
Suppose 0 = -4*p - 12, 2*r = -r - 2*p + 15. Suppose 5*v - 3 = 3*w, -r*w + 3*w = 3*v + 4. Factor 0*x + v + 1/3*x**3 - 1/3*x**2.
x**2*(x - 1)/3
Let i = -1062 + 1067. Factor 5*p**2 + 5/2*p**i + 2*p**3 + 1 - 6*p**4 - 9/2*p.
(p - 1)**3*(p + 1)*(5*p - 2)/2
Let z(h) be the second derivative of -h**7/420 - h**6/540 + h**3/3 - 3*h. Let g(w) be the second derivative of z(w). Factor g(a).
-2*a**2*(3*a + 1)/3
Let j be (-1 + 3 + -2)/2. Factor -3/5*o**2 + 3/5*o + j.
-3*o*(o - 1)/5
Let k(z) be the second derivative of z**5/80 + z**4/16 + z**3/12 + 3*z. Factor k(s).
s*(s + 1)*(s + 2)/4
Let o(x) be the second derivative of x**4/102 - x**3/17 + 2*x**2/17 + 8*x. Factor o(l).
2*(l - 2)*(l - 1)/17
Let m(b) be the first derivative of -2*b - 1/2*b**4 - 2*b**3 + 3 - 3*b**2. Let m(t) = 0. What is t?
-1
Let o(d) be the second derivative of 0 - 8/3*d**3 + 3*d + 2*d**2 + 2/15*d**6 - 4/5*d**5 + 2*d**4. Factor o(b).
4*(b - 1)**4
Let d(j) be the third derivative of -j**4/12 - j**3/6 + 4*j**2. Let i be d(-2). Factor -2/3*p**5 - 2*p**i + 0 - 2*p**4 + 0*p - 2/3*p**2.
-2*p**2*(p + 1)**3/3
Let 53 - 53 - 4*k**2 - k**2 = 0. What is k?
0
Factor 0 - 4/3*h**4 - 4*h**3 - 4/3*h - 4*h**2.
-4*h*(h + 1)**3/3
Let p(o) be the first derivative of o**4/2 - 4*o**3 + 9*o**2 - 8*o - 19. Suppose p(g) = 0. Calculate g.
1, 4
Let i(s) be the third derivative of s**7/70 - s**6/40 + 6*s**2. Factor i(h).
3*h**3*(h - 1)
Let z(i) be the first derivative of i**5 + 5*i**4/4 + 10. Factor z(v).
5*v**3*(v + 1)
Let 94*c**2 - 52*c**2 + 13*c - 3*c**3 - 48*c**2 - 4*c = 0. What is c?
-3, 0, 1
Let c(z) = -z**2 + z + 1. Let w(l) = l**2 - 4*l + 8. Let a(o) = o**2 - 8*o + 15. Let p(k) = 3*a(k) - 5*w(k). Let u(s) = c(s) + p(s). Factor u(q).
-3*(q - 1)*(q + 2)
Let h be -4 + 948/30 + -2. Find b, given that h*b**3 + 24/5*b + 96/5*b**2 + 2/5 = 0.
-1/4
Let w(h) = -h**2 - 6*h + 3. Let a be w(-6). Let -2*y + 3*y - y**3 + a*y - 2 - y = 0. What is y?
-2, 1
Let w(o) = -o. Let g be w(-5). Factor 4*t**g - 5*t**5 + 2*t**3 + 0*t**3 - t**5.
-2*t**3*(t - 1)*(t + 1)
Let r(h) = -h**3 - h**2 - h + 1. Let j(f) = -1 - 8*f**3 - 3*f + 10*f**3 + 4*f. Let n(c) = -3*j(c) - 3*r(c). Factor n(b).
-3*b**2*(b - 1)
Let f(l) be the first derivative of -14*l**6/9 - 2*l**5/5 + 3*l**4/2 - 4*l**3/9 - 20. What is t in f(t) = 0?
-1, 0, 2/7, 1/2
Let t(n) = -3*n + 60. Let x be t(19). Solve -1/2*o**4 - o**5 + 1/2*o**2 - 1/2*o + 0 + 3/2*o**x = 0.
-1, 0, 1/2, 1
Suppose -2*v = -3*g + 9, -v + 4*g - 2*g = 6. Let i(j) be the second derivative of v - 1/3*j**3 - 2*j + 1/6*j**4 + 0*j**2. Factor i(b).
2*b*(b - 1)
Let p(h) be the second derivative of -h**4/24 - h**3/6 - h**2/4 + 6*h. Factor p(x).
-(x + 1)**2/2
Let b(r) be the second derivative of 1/2*r**4 - 1/5*r**5 + 1/2*r**2 - 2/3*r**3 + 1/30*r**6 + 0 + 3*r. Factor b(u).
(u - 1)**4
Let r(k) be the third derivative of -1/28*k**4 - 1/245*k**7 + 0*k + 0 + 1/21*k**3 + 1/105*k**5 + 2*k**2 + 1/1176*k**8 + 1/210*k**6. Let r(s) = 0. What is s?
-1, 1
Let i(a) be the first derivative of -a**7/5460 - a**6/2340 - 5*a**3/3 - 4. Let s(w) be the third derivative of i(w). Let s(u) = 0. Calculate u.
-1, 0
Factor -56*y + 4*y**2 + 56*y.
4*y**2
Determine t so that t + 10*t**3 - 2538*t**4 + 5*t**2 + 2543*t**4 - t = 0.
-1, 0
Let d(x) be the first derivative of x**4/16 + x**3/4 - x**2/8 - 3*x/4 + 71. Factor d(f).
(f - 1)*(f + 1)*(f + 3)/4
Let t be -1 + 1 + 4 + (-96)/27. Let u(m) be the first derivative of 1/18*m**4 + 2 - 1/9*m**2 - t*m + 4/27*m**3. Factor u(g).
2*(g - 1)*(g + 1)*(g + 2)/9
Let o be 9/63 - 27/(-7). Let q(v) be the second derivative of 0 + 1/60*v**o - 1/10*v**2 - 2*v + 1/30*v**3 - 1/100*v**5. Factor q(m).
-(m - 1)**2*(m + 1)/5
Suppose -4*i + 3*i + 2 = 0. Suppose l = 4*b + i, -b = 4*l - 2*b - 8. Factor l*z + 1 - 5/4*z**2.
-(z - 2)*(5*z + 2)/4
Factor -a**3 + a**4 + 0*a**4 + 6*a**3 - 3*a**3.
a**3*(a + 2)
Let o(z) be the third derivative of -z**8/504 - z**7/315 + z**6/30 + 7*z**5/45 + 11*z**4/36 + z**3/3 + 4*z**2. Factor o(r).
-2*(r - 3)*(r + 1)**4/3
Factor -4/7 + 2/7*p**2 - 2/7*p.
2*(p - 2)*(p + 1)/7
Suppose 5*r + 4*j - 3*j = 65, 0 = -3*j + 15. Factor -27*v**4 - 8*v + 9*v**4 + r*v**2 + 14*v**4.
-4*v*(v - 1)**2*(v + 2)
Let g(i) = -i**5 + 4*i**4 - 6*i**3 - 4*i**2 + 7*i. Let p(r) = -r**5 + 4*r**4 - 7*r**3 - 5*r**2 + 8*r + 1. Let h(s) = 3*g(s) - 2*p(s). Let h(x) = 0. What is x?
-1, 1, 2
Let -553 + 6*s**2 - 3*s**4 + 553 - 3*s**3 = 0. What is s?
-2, 0, 1
Factor 2*t**2 + 32*t + 0*t**2 + 11*t**2 - t**2 + 16.
4*(t + 2)*(3*t + 2)
Let t be (3 - 0)/1 + (2 - -1). Let y(h) be the first derivative of 7*h**2 - 4*h + 3 - 2/5*h**5 + 5/2*h**4 - t*h**3. Factor y(x).
-2*(x - 2)*(x - 1)**3
Let h be (13 - -2)/3 + 1. Let w(d) be the first derivative of -2*d + 1 - 1/3*d**h + 4/3*d**3 - d**2 + d**4 - 2/5*d**5. Factor w(z).
-2*(z - 1)**2*(z + 1)**3
Let t be 12/(-4) + 65 + -1. Let m = t - 547/9. Factor 0*x**2 + m*x**4 + 0*x + 0 + 0*x**3.
2*x**4/9
Let z(r) be the second derivative of -r**4/3 + 8*r**3/3 - 8*r**