et n be (-3 - (-5)/h) + 3. Factor 0*l - n*l**2 + 0 - 1/6*l**3.
-l**2*(l + 1)/6
Let h be 3/9 - 11/(-3). Factor -4*g - 1 + h*g + 2*g - g**2 + 0*g.
-(g - 1)**2
Let s(g) = 18*g**4 + 12*g**3 + 6*g**2 + 30*g - 21. Let o(i) = i**4 + i**3 + i**2 + i - 1. Let f(h) = 15*o(h) - s(h). Find m such that f(m) = 0.
-2, 1
Let k = -177 + 357/2. Determine f, given that -1/2 - k*f - 3/2*f**2 - 1/2*f**3 = 0.
-1
Suppose 2*c + 175 = 5*c - 4*v, -227 = -4*c - v. Let y be (-2)/(-7) + c/21. Factor -4*d**5 - 13*d**3 + 2 + 4*d - 4*d**2 - y*d**3 - 7*d**4 - 7*d**4.
-2*(d + 1)**4*(2*d - 1)
Let d(t) = -2*t**4 - 2*t**3 + 4*t**2 + 2*t - 2. Let m(q) = -q**3 - q**2 + q + 1. Let x(g) = -2*d(g) - 4*m(g). Determine b, given that x(b) = 0.
-2, -1, 0, 1
Let r(w) be the third derivative of w**6/480 + w**5/240 - 9*w**2. Factor r(c).
c**2*(c + 1)/4
Let f be ((-648)/(-9))/(-9) + 8. Factor f - 2/9*v**4 + 0*v**2 - 2/9*v**3 + 0*v.
-2*v**3*(v + 1)/9
Let -8/7 - 2/7*x**2 - 8/7*x = 0. Calculate x.
-2
Determine g so that -641*g**2 + g**4 - g + 2*g - g**3 + 640*g**2 = 0.
-1, 0, 1
Suppose 0 = -5*a + 12 + 3. Factor -5*u**3 + 6*u**4 - 10*u**3 + u**2 + 8*u**a.
u**2*(u - 1)*(6*u - 1)
Suppose -3*t - 16 + 4 = 0. Let y be (-12)/42 + t/(-14). Factor y + 2/7*o + 2/7*o**2.
2*o*(o + 1)/7
Let w(i) = -i**2 - 4*i + 7. Let x be w(-5). Let a(s) be the first derivative of 2*s + 1/6*s**3 - s**2 + x. Factor a(g).
(g - 2)**2/2
Let w(n) be the second derivative of n**5/15 - 4*n**4/9 + 2*n**3/3 + n. Factor w(c).
4*c*(c - 3)*(c - 1)/3
Let s be (-110)/56 + (16 - 14). Let q(a) be the third derivative of 0*a - 1/21*a**3 + 2*a**2 - 1/420*a**6 - s*a**4 + 0 - 1/70*a**5. Let q(v) = 0. What is v?
-1
Let g be 2/4 + 39/26. Let z(h) be the second derivative of -1/40*h**5 + 1/8*h**4 - g*h + 0 - 1/4*h**3 + 1/4*h**2. Find u such that z(u) = 0.
1
Let m(l) = l**2 + 5*l + 2. Let n be m(-5). Solve 18 + 0*j**3 - 2*j**3 - 18 + n*j**4 = 0 for j.
0, 1
Suppose -4*y + 0*y = -8. Let -3*l**3 - 3*l**2 + 5*l**3 + 2*l**3 + 2*l**y = 0. What is l?
0, 1/4
Let x(f) be the third derivative of 0*f - 1/4*f**4 + 0 - 1/2*f**3 + 1/20*f**6 + 1/70*f**7 + 6*f**2 + 0*f**5. Determine g, given that x(g) = 0.
-1, 1
Let t be 0 - (0 - 213/666). Let a = t + 1/74. Let 0 - 1/3*k**2 + 0*k + 1/3*k**4 - 1/3*k**3 + a*k**5 = 0. Calculate k.
-1, 0, 1
Let t(y) be the first derivative of -9/4*y + 3/4*y**2 + 7 - 1/12*y**3. Suppose t(a) = 0. What is a?
3
Let -z - 6/5 - 1/5*z**2 = 0. What is z?
-3, -2
Suppose x + 3*n = 4*x + 6, x - 2*n + 6 = 0. Factor 2*h - 5*h + 0 + x + h**2.
(h - 2)*(h - 1)
Let q(o) be the first derivative of 3*o**4/4 + 4*o**3 + 6*o**2 + 33. What is d in q(d) = 0?
-2, 0
Let r(v) be the second derivative of -1/9*v**2 + 0 + 2/27*v**3 - 6*v - 1/54*v**4. Find g, given that r(g) = 0.
1
Let r(g) = -9*g**3 - 15*g**2 - 3*g + 5. Let t(y) = -9*y**3 - 15*y**2 - 3*y + 6. Suppose 15 = -q - 4*q. Let j(z) = q*r(z) + 2*t(z). Let j(i) = 0. What is i?
-1, 1/3
Let c(g) be the first derivative of g**9/1512 - g**7/140 + g**6/90 + 2*g**3 + 5. Let l(q) be the third derivative of c(q). Factor l(b).
2*b**2*(b - 1)**2*(b + 2)
Let y be -3 - ((-6)/8 - 924/240). Factor -2/5*o**2 + y*o - 8/5.
-2*(o - 2)**2/5
Let o(f) = f**3 - 26*f**2 + 50*f - 48. Let z be o(24). Factor 0 + z*g + 1/6*g**4 + 1/3*g**2 + 1/2*g**3.
g**2*(g + 1)*(g + 2)/6
Let w = 578/9 + -64. Suppose 2/9*q**2 + w + 4/9*q = 0. What is q?
-1
Let v = -342 - -2396/7. Factor 0 + 2/7*h**2 - 2/7*h**4 - v*h**5 + 0*h + 2/7*h**3.
-2*h**2*(h - 1)*(h + 1)**2/7
Factor -1 - 2*t**3 - 3*t**3 + 5*t + 1.
-5*t*(t - 1)*(t + 1)
Let -2/5*j**5 - 2/5*j + 4/5*j**3 - 1/5 - 1/5*j**4 + 2/5*j**2 = 0. What is j?
-1, -1/2, 1
Factor -2/5*g**5 + 4/5*g**3 - 2/5*g + 0 + 0*g**2 + 0*g**4.
-2*g*(g - 1)**2*(g + 1)**2/5
Let r be ((-94)/4)/(5/(-6)). Let v = r + -28. Factor 2/5*k + 0*k**2 - 2/5*k**3 - v*k**4 + 1/5.
-(k - 1)*(k + 1)**3/5
Suppose 5*y + 0*o - 18 = 4*o, 3*y - 2*o = 10. Suppose 0 = -y*h - h. Factor -1/4*u**5 - 1/4*u**4 + h*u + 1/4*u**3 + 1/4*u**2 + 0.
-u**2*(u - 1)*(u + 1)**2/4
Let x(h) be the first derivative of 3*h**5/40 - 11*h**4/48 + h**3/6 + 7*h**2/2 - 9. Let a(s) be the second derivative of x(s). What is v in a(v) = 0?
2/9, 1
Let a(v) be the second derivative of -v**5/20 - v**4/3 - v**3/6 - v**2 + 5*v. Let i be a(-4). Factor 0*z**3 - 2/3*z**i + 0 + 2/3*z**4 + 0*z.
2*z**2*(z - 1)*(z + 1)/3
Let v(w) be the third derivative of -w**6/24 - w**4/24 + w**2. Let d(u) = 4*u**3. Let h(m) = 3*d(m) + 2*v(m). Factor h(r).
2*r*(r - 1)*(r + 1)
Let n(w) be the third derivative of w**6/320 + w**5/80 - w**4/64 - w**3/8 + 23*w**2. Determine b so that n(b) = 0.
-2, -1, 1
Let p(j) be the first derivative of 4/21*j**3 + 1/14*j**4 + 4 + 1/7*j**2 + 0*j. Factor p(n).
2*n*(n + 1)**2/7
Suppose 116 = l - 5*l - 4*n, -4*l + 2*n - 140 = 0. Let u = 67/2 + l. Let 0*i + u*i**2 - 1/2 = 0. What is i?
-1, 1
Let w(h) = -2*h - 3. Let y be w(-3). Suppose 13*c**3 - 13*c**y + 1 + c**4 - 2*c**2 = 0. What is c?
-1, 1
Let o = 0 - -3. Suppose 3*v - 3*w - 3 = 0, -3 = -2*v + w + o. Find s, given that -5*s**3 + 3*s**4 - 3*s**2 - s**v - 2*s**5 + s - 2*s**5 + 9*s**5 = 0.
-1, 0, 1/4, 1
Determine a so that 2*a**3 + 2 - 4*a**3 - 18*a + 6 + 0 + 12*a**2 = 0.
1, 4
Let a be 12/12*((-7)/6)/(-7). Let u(l) be the first derivative of -a*l**3 - 3/4*l**2 - l + 3. Determine d so that u(d) = 0.
-2, -1
Factor 16/7*m + 0*m**2 - 4/7*m**4 - 12/7*m**3 + 0.
-4*m*(m - 1)*(m + 2)**2/7
Let n be (4 + 14)/(9/6). Suppose 0 = n*j - 8*j. Factor 0 + 0*c - 1/2*c**2 + 1/2*c**4 + j*c**3.
c**2*(c - 1)*(c + 1)/2
Let p(d) be the first derivative of 3*d**5/5 + 15*d**4/4 + 8*d**3 + 6*d**2 - 4. Factor p(w).
3*w*(w + 1)*(w + 2)**2
Let y(x) be the first derivative of -1/3*x**3 - 1/5*x**5 + 0*x**2 + 1/2*x**4 + 1 + 0*x. Factor y(s).
-s**2*(s - 1)**2
Let j(z) be the first derivative of -z**3/2 + 3*z/2 + 25. Factor j(h).
-3*(h - 1)*(h + 1)/2
Let m(j) be the third derivative of 0*j**3 + 0*j**4 - 2*j**2 + 1/90*j**6 + 0 + 0*j + 1/315*j**7 + 1/90*j**5. Factor m(p).
2*p**2*(p + 1)**2/3
Let g(b) be the third derivative of 1/12*b**3 + 3*b**2 + 1/105*b**7 + 0 + 1/96*b**4 - 1/24*b**5 - 5/1344*b**8 + 1/120*b**6 + 0*b. Find h such that g(h) = 0.
-1, -2/5, 1
Let a(c) be the third derivative of -c**9/12096 + c**7/1680 - c**5/480 - c**3/2 + c**2. Let j(i) be the first derivative of a(i). Factor j(z).
-z*(z - 1)**2*(z + 1)**2/4
What is f in -11*f**3 + 254*f**4 - 259*f**4 - 4*f**3 = 0?
-3, 0
Let h = 1917 - 345059/180. Let n(d) be the third derivative of 0*d + 0 - h*d**5 - 2/9*d**3 - 2*d**2 - 1/18*d**4. Factor n(k).
-(k + 2)**2/3
Factor 1/3*t**2 + 2/3 + t.
(t + 1)*(t + 2)/3
Let n(a) be the second derivative of -a**6/600 + a**5/150 - a**4/120 + a**2 - 2*a. Let y(t) be the first derivative of n(t). Find o such that y(o) = 0.
0, 1
Let d(g) be the second derivative of -g**7/1050 + g**5/150 - g**3/30 + 3*g**2 + 7*g. Let j(q) be the first derivative of d(q). Factor j(p).
-(p - 1)**2*(p + 1)**2/5
Let w(l) = 2*l**2 - 14*l - 6. Let a(z) = -3*z**2 + 15*z + 6. Let b(i) = -5*a(i) - 6*w(i). Solve b(o) = 0 for o.
-2, -1
Let f = 6 + -4. Suppose 0 = 2*p - 3*h - f, -3*p - 5*h = p + 18. Let u(j) = j**2 - 3*j. Let n(b) = -b**2 + 4*b. Let z(m) = p*n(m) - 3*u(m). Solve z(i) = 0.
0, 1
Let w(o) be the first derivative of -2*o**5/5 + 3*o**4/2 - 2*o**3 + o**2 + 27. Solve w(n) = 0.
0, 1
Let a be (-12)/30 + 12/5. Suppose a*t**2 + 2*t + 3*t + 0*t - 2 - 4*t**2 = 0. Calculate t.
1/2, 2
Let d(r) be the second derivative of -r**6/210 - r**5/70 - r**4/84 - 7*r. Factor d(j).
-j**2*(j + 1)**2/7
Find n such that -5/2*n**2 + 0*n + 0 = 0.
0
Let n(p) = -2 - 2*p**3 - 3*p + 4 + p + 3*p**2 + p**3. Let a be n(2). Factor -2*x**2 + x - 2*x + 0*x**a - x.
-2*x*(x + 1)
Let i(r) = -2*r**2 + 11*r - 2. Let f be i(5). Factor 0*b**2 + 0 + 2/3*b**5 + 2/3*b - 4/3*b**f + 0*b**4.
2*b*(b - 1)**2*(b + 1)**2/3
Let g(m) = -3*m**4 + 4*m**3 - 7*m**2 + 4*m + 2. Let n(h) = 4*h**4 - 4*h**3 + 8*h**2 - 5*h - 3. Let f(y) = -6*g(y) - 4*n(y). Factor f(d).
2*d*(d - 2)*(d - 1)**2
Let l(a) be the third derivative of -a**5/60 - a**4/6 + a**3/6 + a**2. Let q be l(-2). Find k, given that 4*k**2 - k**q + 2*k**3 - 4*k**2 - k = 0.
-1, 0, 1
Let c(p) be the first derivative of p**8/1008 + p**7/630 - p**6/360 - p**5/180 - 3*p**2/2 - 2. Let i(o) be the second derivative of c(o). Factor i(j).
j**2*(j - 1)*(j + 1)**2/3
Let g = -45 - -45. Let o =