4/36)/(4/24). Suppose -h + 8 = h. Find u, given that -8/3*u**h + 2/3*u**3 - o*u + 0 + 8/3*u**2 = 0.
-1, 0, 1/4, 1
Suppose 5*r + 4*h - 26 = 2*r, 2*h = -4*r + 28. Let y(a) = -3*a**2 + 2*a + 6. Let m(f) = -2*f**2 + 2*f + 5. Let g(k) = r*m(k) - 5*y(k). Factor g(j).
j*(3*j + 2)
Let i be (-16 - -13) + (-8)/(-2). Let w be (-4 - -3)*i/(-3). Determine m so that -1/3*m**3 + w*m + 0 - 1/3*m**4 + 1/3*m**2 = 0.
-1, 0, 1
Let h(q) be the second derivative of -1/4*q**4 - 1/2*q**3 + 0 - 4*q + 3*q**2. Factor h(i).
-3*(i - 1)*(i + 2)
Let k(s) = -s**3 - 6*s**2 + 6*s - 4. Let v be k(-7). Factor -x**2 + 0*x**2 + 2*x**2 + 4*x - v*x.
x*(x + 1)
Factor -20*d + 9*d**2 - 5*d**2 - 5*d**2 - 100.
-(d + 10)**2
Suppose 4*g + 6 = 2*y, 4*g = y - g - 9. Let b be (-1 + y)*(-2)/2. Factor -3*a + a + 6*a**2 - 3*a**b.
a*(3*a - 2)
Suppose -3*y - 2*m + 25 = 9, y + 4*m = 12. Factor -12*l**y - 7*l**5 + 2*l**5 - 25*l**3 + 10*l**3 - 6*l**2 + 2*l**5.
-3*l**2*(l + 1)**2*(l + 2)
Suppose -14 = -4*z - 3*z. Let r(s) be the second derivative of -1/6*s**4 + 0 - 2/5*s**5 + s + 4/3*s**3 + s**z. Factor r(u).
-2*(u - 1)*(u + 1)*(4*u + 1)
Let d(n) = n**2 + 4*n + 8. Let w(i) = -3*i**2 - 12*i - 23. Let y(b) = -11*d(b) - 4*w(b). Factor y(v).
(v + 2)**2
Suppose -10 = 2*d, -4*f - d + 0*d + 3 = 0. Let p be (2/(-4))/(-1*2). Factor -1/2 - p*u + 1/4*u**f.
(u - 2)*(u + 1)/4
Factor 8/9*j**2 + 0 + 32/9*j**3 + 14/9*j**4 + 0*j.
2*j**2*(j + 2)*(7*j + 2)/9
Let c = 54 - 49. Let g(w) be the second derivative of 3/10*w**6 + 3/10*w**c + 0 + 0*w**2 - 2*w + 0*w**3 - 1/4*w**4. Let g(j) = 0. Calculate j.
-1, 0, 1/3
Let h(c) = 6*c**4 - 48*c**3 - 51*c**2 + 3*c + 15. Let i(r) = -r - 2*r**2 - 1 + r**3 - r**4 + 0 + 2*r**2 + r**2. Let a(m) = h(m) + 15*i(m). Factor a(x).
-3*x*(x + 1)*(x + 2)*(3*x + 2)
Factor -1/4*x - 1 + x**2 + 1/4*x**3.
(x - 1)*(x + 1)*(x + 4)/4
Let r = 22 - 36. Let c = -10 - r. Factor -2*b**3 - 2/3*b**2 - 2*b**c - 2/3*b**5 + 0*b + 0.
-2*b**2*(b + 1)**3/3
Factor 11*x**3 + 4*x + 2*x**3 - 4*x**4 - x**3 + 2*x**3 - 14*x**2.
-2*x*(x - 2)*(x - 1)*(2*x - 1)
Suppose -4 = -3*j + 2. Let k = 5 + -3. Solve 2*f + 2*f**j + 0*f - 2 - 4*f + k*f**3 = 0.
-1, 1
Let t(j) be the third derivative of 0*j + 0 - 1/120*j**6 - 2*j**2 - 1/24*j**4 + 1/30*j**5 + 0*j**3. Factor t(a).
-a*(a - 1)**2
Let k(a) = -5*a**5 - 2*a**4 + 3*a**3 - 4. Let s(w) = -4*w**5 - 2*w**4 + 2*w**3 - 3. Let o(y) = 3*k(y) - 4*s(y). Factor o(l).
l**3*(l + 1)**2
Let u(n) = n**2 - 9*n + 2. Let g be u(9). Suppose p + 2*l = 7, -19 = 2*p - 7*p - g*l. Determine w so that p*w**2 + w**2 - 2*w**2 + 2*w + 0*w = 0.
-1, 0
Let o(q) be the first derivative of q**5/5 - q**4/2 + q**3/3 + 2. Let o(f) = 0. What is f?
0, 1
Let y(d) = 9*d**2 + 8*d - 1. Let v(i) be the first derivative of i**3 + 3*i**2/2 - 5. Let g(a) = -17*v(a) + 6*y(a). Factor g(k).
3*(k - 2)*(k + 1)
Factor 6*y**2 - 4*y + 2*y**2 - 6*y**2.
2*y*(y - 2)
Factor -10*y - 3 + 2 - 6*y**2 + 5.
-2*(y + 2)*(3*y - 1)
Suppose -3*b + 3 = 3*n, 3*n + 3*b = -2*b + 11. Let x be (30/25)/(n/(-10)). Solve 16*t + x*t + 1 - 5 - 25*t**2 = 0.
2/5
Let i(t) = -4*t**4 - 46*t**3 - 138*t**2 - 154*t - 58. Let r(u) = u**3 + u**2 - u - 1. Let y(c) = -i(c) - 6*r(c). Factor y(m).
4*(m + 1)**2*(m + 4)**2
Let j(b) = -13*b**2 + 15*b + 11. Let h(t) = 7*t**2 - 8*t - 6. Let f = -22 - -33. Let a(q) = f*h(q) + 6*j(q). Find k such that a(k) = 0.
0, 2
Let g(z) = 2*z + 17. Let a be g(-7). Let 3/2 - 3/4*o**a + 0*o**2 + 9/4*o = 0. What is o?
-1, 2
Let d be (15/(-25))/((-2)/(-10)). Let k be 3 + (d - 0 - -2). Factor 3*w**2 - 2 - w**k + 4*w**3 + 2 + 2*w**4.
2*w**2*(w + 1)**2
Suppose 2 = 5*q - 2*o, 0*o - 8 = -2*o. Let s = 4 + -2. Solve -2*u**2 - 2*u + 2*u**s + q*u**3 = 0 for u.
-1, 0, 1
Suppose 0*c + 0 - 5/6*c**3 + 5/6*c**2 = 0. Calculate c.
0, 1
Solve t**4 + 1/2*t**5 + 0*t**3 + 0*t**2 + 0*t + 0 = 0.
-2, 0
Let y(z) be the second derivative of z**4/60 + z**3/10 - 7*z. Determine h so that y(h) = 0.
-3, 0
Let f(w) be the third derivative of -121*w**7/1120 - 77*w**6/480 + w**5/4 - w**4/8 - w**3/2 - w**2. Let t(b) be the first derivative of f(b). Factor t(r).
-3*(r + 1)*(11*r - 2)**2/4
Let y(q) = q**3 - q + 1. Let h(k) = -4*k**3 - 3*k**2 + 7*k - 5. Let n(v) = -h(v) - 5*y(v). Find j such that n(j) = 0.
0, 1, 2
Let 0 - 1/4*b + 0*b**2 + 1/4*b**3 = 0. What is b?
-1, 0, 1
Solve 4*w - 4*w**2 + w**2 - 5*w = 0.
-1/3, 0
Let o(j) be the first derivative of -3*j**4/2 - j**3 + 3*j**2/2 + 9. Determine m so that o(m) = 0.
-1, 0, 1/2
Let y(x) = x**2 + x + 1. Let d(c) = c**2 + c + 2. Suppose h + 3*w = -3 + 4, -2*h = -2*w - 2. Suppose -2*i - h = -3. Let t(u) = i*d(u) - 2*y(u). Factor t(r).
-r*(r + 1)
Let l(t) = -4*t**3 - t**2 + 8*t. Let c(g) = -5*g**3 - 2*g**2 + 9*g. Let r(q) = 5*c(q) - 6*l(q). Suppose r(i) = 0. What is i?
-3, -1, 0
Let m(b) be the third derivative of -4*b**7/735 + b**6/70 - b**4/42 - 10*b**2. Factor m(n).
-4*n*(n - 1)**2*(2*n + 1)/7
Suppose -z - 6 = 4*z - 4*y, 0 = -4*y + 16. Solve -z*k**2 + k**2 - k**2 = 0 for k.
0
Suppose 4*b - 12 = -2*b. Suppose 0*t + 2/13*t**b + 0 = 0. What is t?
0
Let a(z) be the third derivative of -z**6/540 + z**5/54 - z**4/36 - z**3/3 + 13*z**2. Find f such that a(f) = 0.
-1, 3
Let o(n) be the third derivative of n**7/3360 + n**6/720 + n**5/480 - n**3/3 - 6*n**2. Let d(v) be the first derivative of o(v). Factor d(t).
t*(t + 1)**2/4
Let c(y) be the third derivative of -y**7/2520 - y**6/360 - y**5/120 - y**4/12 + 4*y**2. Let f(a) be the second derivative of c(a). Factor f(j).
-(j + 1)**2
Let z(d) be the third derivative of -d**6/600 + d**5/60 - d**4/30 - 20*d**2. Factor z(u).
-u*(u - 4)*(u - 1)/5
Let h = 60742 - 2673135/44. Let q = h + 45/4. Factor 0*i + 2/11 - q*i**2.
-2*(i - 1)*(i + 1)/11
Let i(x) be the third derivative of 2*x**7/105 - x**6/6 + 3*x**5/5 - 7*x**4/6 + 4*x**3/3 - 18*x**2. Factor i(d).
4*(d - 2)*(d - 1)**3
Let l be 3/(-8) - ((-2093)/(-392) - 6). Find r such that 4/7 - l*r - 4/7*r**2 + 2/7*r**3 = 0.
-1, 1, 2
Let c(m) be the second derivative of 2*m**6/15 + 2*m**5/5 - 4*m**3/3 - 2*m**2 - 10*m. Determine v so that c(v) = 0.
-1, 1
Let j(k) = k**2 - 1. Let x be j(-2). Let w(u) be the first derivative of -4/3*u**2 - 2/9*u**x + 2/3*u + 1 + 2/3*u**4. Find d, given that w(d) = 0.
-1, 1/4, 1
Let y(h) be the first derivative of -h**4/10 - 4*h**3/15 - h**2/5 - 4. Factor y(r).
-2*r*(r + 1)**2/5
Let i(y) be the second derivative of y**7/70 + y**6/50 - 3*y**5/50 - y**4/10 + y**3/10 + 3*y**2/10 - 3*y. Let i(p) = 0. What is p?
-1, 1
Solve 3*s**2 + 3 - 3 + 7*s + 2*s**2 + 2 = 0.
-1, -2/5
Let l(m) be the third derivative of -m**8/56 + m**7/70 + m**6/40 + 5*m**2. Determine s so that l(s) = 0.
-1/2, 0, 1
Let i(w) be the first derivative of 6*w**4 + 24*w**2 + 4/5*w**5 + 52/3*w**3 + 7 + 16*w. Factor i(g).
4*(g + 1)**2*(g + 2)**2
Let r = -34 - -36. Let j(f) be the first derivative of 1/12*f**3 - r + 0*f - 1/16*f**4 + 0*f**2. Factor j(y).
-y**2*(y - 1)/4
Let -5 - 9 - 10*b - 1 + 5*b**2 = 0. Calculate b.
-1, 3
Let c(r) = -r + 9. Let q be c(7). Factor 3 - 2 - 1 + 4*p**q + 4*p.
4*p*(p + 1)
Find q such that 6/5 + 8/5*q + 2/5*q**2 = 0.
-3, -1
Let a(l) = -l**3 - 4*l**2 - l. Let u = 6 - 10. Let j be a(u). Factor -8 + j - 108*m**2 - 12 - 72*m - 54*m**3.
-2*(3*m + 2)**3
Factor -148 + 2*l - 3*l**5 + 5*l**5 + 148 - 4*l**3.
2*l*(l - 1)**2*(l + 1)**2
Let t = 787/5 - 157. Let -1/5*h**2 - t*h - 1/5 = 0. What is h?
-1
Let a be -3*(-5 + -2 + 5). Let z be 22/a - (3 - 0). Factor 1/3*j**4 + 0*j + 1/3*j**2 + 0 + z*j**3.
j**2*(j + 1)**2/3
Let f(a) be the first derivative of -a**4/72 + a**3/36 - 2*a - 2. Let y(p) be the first derivative of f(p). Factor y(c).
-c*(c - 1)/6
Let u be 18/(-63) + 2/7. Solve -2*b + u*b**2 + 4/3 + 2/3*b**3 = 0 for b.
-2, 1
Let k(i) = 3*i**2 + 2*i - 2. Let o(l) = -2*l**2 + 1. Let n(u) = -k(u) - 2*o(u). Determine m so that n(m) = 0.
0, 2
Suppose -3*l - 9 = -2*n - 0*n, -l - 3 = -4*n. Let m(z) be the second derivative of n + 0*z**2 - 2*z - 1/21*z**3 - 1/42*z**4. Factor m(a).
-2*a*(a + 1)/7
Solve 7/5*t**3 - t**4 - 3/5*t**2 + 1/5*t**5 + 0*t + 0 = 0 for t.
0, 1, 3
Let a = -92/13 - -484/39. Determine j so that -a*j + 2/3 + 32/3*j**2 = 0.
1/4
Let t(z) be the second derivative of 1/12*z**2 + 1/12*z**4 - 1/9*z**3 + 1/180*z**6 - 1/30*z**5 + 0 + 3*z. Suppose t(d) = 0. What is d?
1
Let o(q) be the second derivative of q**4/102 + 14*q**3/17 + 441*q**2/17 - 43*q. What is i i