4 - 241. Let 0 - 1/2*c**i + 1/2*c - c**4 + c**2 = 0. What is c?
-1, -1/2, 0, 1
Suppose -2*z - 5*l - 12 = 0, -5*l - 18 = -z + 6. Let c(n) be the first derivative of -1 - 2*n**3 + 5/2*n**z + 8/5*n**5 - 2*n - 5*n**2. Factor c(r).
2*(r - 1)*(r + 1)**2*(4*r + 1)
Let k(i) be the first derivative of -7*i**5/20 - i**4/8 + 7*i**3/12 + i**2/4 + 5. Factor k(x).
-x*(x - 1)*(x + 1)*(7*x + 2)/4
Suppose -6 = 5*s - 1, 0 = -2*i + 5*s + 5. Factor 3/2*w**3 + 0 + 3/4*w**4 + i*w + 3/4*w**2.
3*w**2*(w + 1)**2/4
Factor 16*m - 49*m**3 + 147*m**3 + 112*m**2 + 98*m**3.
4*m*(7*m + 2)**2
Find o such that 24*o - 243/4*o**3 - 135/4*o**2 - 3 = 0.
-1, 2/9
Let i(t) be the third derivative of t**9/90720 - t**8/15120 - t**5/10 + t**2. Let j(c) be the third derivative of i(c). Determine u so that j(u) = 0.
0, 2
Let r = 9 + -5. Factor l + l**3 - 7*l**3 + r*l**2 + 9*l**3.
l*(l + 1)*(3*l + 1)
Let g(r) be the second derivative of 0 + 0*r**2 + 2/3*r**6 - 6/5*r**5 - 1/3*r**3 + r**4 - 1/7*r**7 + 3*r. Factor g(j).
-2*j*(j - 1)**3*(3*j - 1)
Let k(l) be the first derivative of -l**5/15 + l**3/3 + l**2/3 - 15. Factor k(i).
-i*(i - 2)*(i + 1)**2/3
Suppose 28 = -2*p - 30. Let r = 117/4 + p. Find w, given that -1/2 - w**2 + r*w**3 + 5/4*w = 0.
1, 2
Let r(j) be the third derivative of -j**7/210 + j**6/20 + 11*j**2. Suppose r(h) = 0. What is h?
0, 6
Let p(x) = x**2 + 5*x - 3. Let l be p(-6). Determine m, given that -4*m**3 + 6*m**l - 3*m**3 - 2*m**2 = 0.
-2, 0
Let t(a) be the first derivative of -2/3*a - 4/9*a**6 + 6/5*a**5 - 1/3*a**4 - 2 - 16/9*a**3 + 2*a**2. Find h such that t(h) = 0.
-1, 1/4, 1
Let a(f) be the second derivative of 5*f**7/42 - f**6/3 - f**5/4 + 5*f**4/6 + 7*f. Suppose a(b) = 0. What is b?
-1, 0, 1, 2
Suppose -8 - 62 = 5*t. Let g(p) = 1. Let x(s) = -s**2 + s + 9. Let k(h) = t*g(h) + 2*x(h). Factor k(z).
-2*(z - 2)*(z + 1)
Let u(l) be the first derivative of -l**4/4 + l**2/2 - l - 2. Let s(t) = -12*t**3 + 4*t**2 + 8*t - 10. Let y(a) = s(a) - 10*u(a). Solve y(k) = 0 for k.
0, 1
Factor 336*c**2 + 5*c**3 + 22*c + 0*c**3 + 18*c - 381*c**2.
5*c*(c - 8)*(c - 1)
Let b(n) be the first derivative of 3/16*n**4 + 9/8*n - 1/2*n**3 + 3/40*n**5 - 3 - 3/8*n**2. Factor b(z).
3*(z - 1)**2*(z + 1)*(z + 3)/8
Let k(n) be the second derivative of n**2 + 1/6*n**4 + 2/3*n**3 - 4*n + 0. Factor k(i).
2*(i + 1)**2
Let t = -28 - -32. Factor 2/3*u**5 - 2*u**2 + 0 + 4/9*u + 10/3*u**3 - 22/9*u**t.
2*u*(u - 1)**3*(3*u - 2)/9
Factor 15/4*c - 5/2 - 5/4*c**2.
-5*(c - 2)*(c - 1)/4
Let r(m) be the third derivative of -m**7/8820 + m**6/1260 - m**5/420 - m**4/4 - 3*m**2. Let n(x) be the second derivative of r(x). Factor n(i).
-2*(i - 1)**2/7
Let h be -2 + 2 - (-39 + -3). Let g be ((-4)/(-5))/(h/140). Let 2/3*k**4 + 8/3*k - 2*k**2 + g - 4/3*k**3 = 0. Calculate k.
-1, 2
Let f(c) = 10*c**4 - 24*c**3 - 14*c**2. Let y(l) = 2*l**4 - 5*l**3 - 3*l**2. Let o(z) = -6*f(z) + 28*y(z). Find d such that o(d) = 0.
0, 1
Let p = 3/28 - -47/84. Suppose -4*b - 17 = -17. Factor b*c + 2/3*c**4 - 2/3*c**2 + p*c**5 + 0 - 2/3*c**3.
2*c**2*(c - 1)*(c + 1)**2/3
Let l(p) be the first derivative of -2*p**5 - 15*p**4/4 + 10*p**3/3 + 15*p**2/2 + 23. Find t, given that l(t) = 0.
-3/2, -1, 0, 1
Let p(c) = -c**4 + c**3 - c**2. Let h(q) = 3*q**4 - 5*q**3 + 4*q**2. Let i(u) = 5*h(u) + 10*p(u). What is z in i(z) = 0?
0, 1, 2
Let i = -143/2 - -72. Let n(t) be the second derivative of i*t**4 + 8/3*t**3 - 4*t**2 - 7/10*t**5 + 2/15*t**6 + 0 + 2*t. Determine b so that n(b) = 0.
-1, 1/2, 2
Let a(k) = k**5 - k**4 + k**3 + k**2 + k - 1. Let u(s) = s**5 - s**4 + 3*s**3 + s**2 + 2*s - 2. Let z(v) = 2*a(v) - u(v). Find w such that z(w) = 0.
-1, 0, 1
Let l(t) be the second derivative of -t**4/12 + 2*t**3/3 - 2*t**2 - 12*t. Solve l(h) = 0 for h.
2
Let w(r) be the third derivative of -r**5/20 + r**3/2 - 4*r**2. Factor w(y).
-3*(y - 1)*(y + 1)
Let b(m) = -3*m - 1. Let h be b(-2). Let i be 10/(-15)*(-3)/h. Factor i - 4/5*w + 4/5*w**3 - 2/5*w**4 + 0*w**2.
-2*(w - 1)**3*(w + 1)/5
Let c(b) be the first derivative of -32*b**6/15 + 32*b**5/5 - b**4/5 - 152*b**3/15 + 34*b**2/5 - 8*b/5 - 4. Determine n, given that c(n) = 0.
-1, 1/4, 1, 2
Let w(k) = 6*k**4 + 2*k**3 + 4*k**2 + 4. Let h(t) = -4*t**3 - 8 - 4*t**2 - 1 + 2 - 11*t**4 - 3*t**2. Let z(j) = -4*h(j) - 7*w(j). Factor z(n).
2*n**3*(n + 1)
Suppose -5*v = v. Let q(i) be the third derivative of 0*i**4 - 1/70*i**7 + 0 + v*i**3 + 0*i - 1/20*i**5 + 2*i**2 - 1/20*i**6. Factor q(b).
-3*b**2*(b + 1)**2
Let t be 2/5 - 126/(-35). Factor 12*m**4 + 2*m**4 - 8*m**3 + 4*m**2 - 10*m**t.
4*m**2*(m - 1)**2
Let m(i) = i - 5. Let u be m(7). Factor 11 + r**3 - r + 3*r**u - 2*r**2 - 11 - r**4.
-r*(r - 1)**2*(r + 1)
Let -212 + 5 + 726*l**2 - 36 + 648*l**3 + 117*l**4 - 2*l**5 + 8*l**5 - 54*l = 0. Calculate l.
-9, -1, 1/2
Let s(y) = y + 16. Let q be s(-13). Determine t, given that -3*t**3 - 3*t**3 + t**q - 3*t**4 - t**3 = 0.
-2, 0
Determine b so that 15/4*b**2 + 0 - 3/4*b = 0.
0, 1/5
Let o(c) be the third derivative of -2*c**7/105 + c**6/30 + 4*c**5/15 - 2*c**4/3 - 3*c**2. Find g such that o(g) = 0.
-2, 0, 1, 2
Let k be (-4)/18 + 87/27. Let c(b) be the second derivative of 0*b**2 + 0 + 1/30*b**k + 0*b**4 - b - 1/100*b**5. Suppose c(v) = 0. What is v?
-1, 0, 1
Let t(b) be the second derivative of b**5/60 - b**4/36 - b**3/18 - 3*b**2/2 - 2*b. Let s(i) be the first derivative of t(i). Solve s(j) = 0 for j.
-1/3, 1
Let q(y) = -5*y + 43. Let i be q(8). Let c(p) be the second derivative of -1/2*p**i + 0 + 3/20*p**5 + p + 0*p**4 + 0*p**2. Factor c(f).
3*f*(f - 1)*(f + 1)
Suppose -2*h + 5*v = 3*v - 16, 0 = 5*h - 3*v - 32. Let z(t) be the first derivative of 4*t**2 + 8*t + 2 - 2*t**3 - 2/5*t**5 - 2*t**h. Factor z(w).
-2*(w - 1)*(w + 1)*(w + 2)**2
Suppose 5*w + 2*h - 18 = 0, 0 = 3*w - 2*w + 5*h - 22. Let m(s) be the second derivative of -1/30*s**5 + 0 + 0*s**w + 0*s**3 + s + 1/9*s**4. Factor m(n).
-2*n**2*(n - 2)/3
Let c(k) be the third derivative of 5*k**2 - 21/40*k**6 + 0 - 109/120*k**5 - 1/3*k**3 - 7/60*k**7 + 0*k - 3/4*k**4. Factor c(b).
-(b + 1)**2*(7*b + 2)**2/2
Solve 19*s + 2*s**3 - s**2 - s**4 - 19*s = 0 for s.
0, 1
Let z(t) be the third derivative of 0 + 1/6*t**4 + 1/10*t**5 + 0*t + t**2 - 1/3*t**3. Factor z(r).
2*(r + 1)*(3*r - 1)
Let w(m) be the first derivative of m**6/495 - m**5/660 - m**3 + 6. Let r(t) be the third derivative of w(t). Factor r(z).
2*z*(4*z - 1)/11
Determine r so that -6*r**2 - 30*r**3 + 33*r**4 - 48*r**4 + 9*r**3 = 0.
-1, -2/5, 0
Let h be (-1)/2*3/((-18)/24). What is j in -3/2*j + 3/2*j**3 + 1/2 - 5/2*j**h + 2*j**4 = 0?
-1, 1/4, 1
Let d(p) be the second derivative of 0*p**4 + 1/126*p**7 + 1/18*p**3 - 1/30*p**5 + 0*p**2 + 3*p + 0*p**6 + 0. Determine g so that d(g) = 0.
-1, 0, 1
Suppose -12 = -4*z - 0. Suppose s + 0 - 1/2*s**2 - 1/2*s**z = 0. What is s?
-2, 0, 1
Let p(z) be the second derivative of z**6/20 - z**4/4 + 3*z**2/4 - 10*z. Solve p(r) = 0.
-1, 1
Let v(i) be the second derivative of i**4/4 - i**3 - 9*i**2/2 - 7*i. Factor v(w).
3*(w - 3)*(w + 1)
Let x(f) = f**2 - 1. Let r = 17 - 20. Let u(c) = -3*c**2 - 4*c - 1. Let b(z) = r*u(z) - 6*x(z). Find h, given that b(h) = 0.
-3, -1
Let 5*m**3 - m**3 - 409 + 393 + 32*m - 20*m**2 = 0. What is m?
1, 2
Suppose 0*d = -5*d + 20. Let m be 7/(-14) - (-10)/d. Factor m*p + 13*p**2 + p - 3*p**3 - 10*p**2 - 3*p**4.
-3*p*(p - 1)*(p + 1)**2
Let l(u) be the first derivative of u**6/180 + u**5/60 + u**3/3 + 4. Let y(s) be the third derivative of l(s). Factor y(j).
2*j*(j + 1)
Let r be ((-1)/2)/(1/(-10)). Suppose -h - 20 = -4*s - 3, -r*h = -2*s + 31. Factor 0*c**4 - 8*c**3 + s*c**4 + 0*c - c**2 - 8*c**4 + 2*c.
-c*(c + 1)**2*(5*c - 2)
Factor -u**5 + 0*u + 0 - 2/3*u**2 - 8/3*u**4 - 7/3*u**3.
-u**2*(u + 1)**2*(3*u + 2)/3
Find a such that -9*a**2 - 3*a**3 + 3*a**4 + 2*a - 31 + a + 37 = 0.
-1, 1, 2
Let s(i) be the second derivative of i**7/42 - i**6/30 - i**5/4 + 5*i**4/12 + 2*i**3/3 - 2*i**2 - 2*i - 50. Let s(f) = 0. What is f?
-2, -1, 1, 2
Suppose 9*o - 5*o = 0. Let x(a) be the third derivative of -1/6*a**3 + 1/24*a**4 + 1/40*a**6 + 1/12*a**5 + o*a + 0 + a**2. Factor x(t).
(t + 1)**2*(3*t - 1)
Let c = -40 + 42. Let -14*a**3 + 0 - 8/3*a - 40/3*a**c = 0. Calculate a.
-2/3, -2/7, 0
Factor 9 - 2 - 3*v**2 + 12*v**3 - 7.
3*v**2*(4*v - 1)
What is o in 2/7*o**5 - 2 + 68/7*o**3 - 22/7*o**4 - 92/7*