**2 + 4. Let a be t(0). Suppose -8*k**3 - 5 + 14*k**5 - 6*k - 24*k**a - 2 + 3 + 28*k**2 = 0. Calculate k.
-1, -2/7, 1
Let j(l) = -l**3 - 21*l**2 + 2*l + 42. Let n be j(-21). Determine q so that 1/4*q**4 + 3/4*q**2 - 3/4*q**3 + n - 1/4*q = 0.
0, 1
Let g(o) = o**5 - o**4 - o**3 - o**2 - 1. Let t(n) = -23 - 9*n**3 + 11 + 0 - 9*n**2 - 15*n**4 + 9*n**5. Let l(q) = 12*g(q) - t(q). Let l(w) = 0. Calculate w.
-1, 0, 1
Suppose 0 = 28*b - 25*b. Let t(g) be the second derivative of 0*g**4 + 1/147*g**7 + b*g**3 + 0 - 1/70*g**5 + 0*g**2 + 3*g + 0*g**6. Find y, given that t(y) = 0.
-1, 0, 1
Let k = 349/3 + -118. Let c = k + 2. Let -c*u + 1/3*u**3 + 1/3*u**4 - 1/3*u**2 + 0 = 0. Calculate u.
-1, 0, 1
Let u = -5 + 9. Let -2*p**4 + 3*p + 0*p**3 - 3*p**3 + 3*p**2 - 3*p**u + 2*p**4 = 0. Calculate p.
-1, 0, 1
Let x be 48/(-4)*(-1)/3. Let g be (0 - x)/(-10 + 5). Factor -g*l**4 + 4/5*l**2 + 0 - 4/5*l + 1/5*l**5 + 3/5*l**3.
l*(l - 2)**2*(l - 1)*(l + 1)/5
Let c = -42 + 48. Let o(z) be the second derivative of 1/20*z**5 - 1/6*z**4 + 1/15*z**c + 0*z**2 + z + 0 - 1/6*z**3. Factor o(f).
f*(f - 1)*(f + 1)*(2*f + 1)
Suppose -133*d = -136*d + 6. Let f(g) be the third derivative of -1/6*g**4 - 1/30*g**5 + g**d - 1/3*g**3 + 0*g + 0. Determine c so that f(c) = 0.
-1
Let o(r) = -10*r**3 - 4*r**2 + 20*r - 14. Let a(v) = 2*v**3 + v**2 - 4*v + 3. Let s(t) = 14*a(t) + 3*o(t). Factor s(z).
-2*z*(z - 2)*(z + 1)
Let t(h) be the second derivative of 16*h**6/35 + 36*h**5/35 + 9*h**4/14 + 32*h. Factor t(d).
6*d**2*(4*d + 3)**2/7
Factor 20*b - 4*b - 5*b**2 - 8*b**2 + 9*b**2.
-4*b*(b - 4)
Let y be -3 + (5 - 1) - -1. Let -2/9*z + 0 - 2/9*z**y = 0. Calculate z.
-1, 0
Let t(c) be the first derivative of -c**4 - 28*c**3/3 - 22*c**2 - 20*c - 24. Factor t(j).
-4*(j + 1)**2*(j + 5)
Suppose 0 = 7*a - 7*a - 8*a. Let g(c) be the second derivative of -11/3*c**3 + a - 7/3*c**4 + 2/5*c**5 + 16/15*c**6 - 2*c**2 + 1/3*c**7 + 4*c. Factor g(u).
2*(u - 1)*(u + 1)**3*(7*u + 2)
Let a be 2 + 2 + (1 - 2). Factor -2*c**2 + c - 1 - 3*c + 2 + a.
-2*(c - 1)*(c + 2)
Let b be 5 + (-4)/8*6. Solve 5*u**2 - 8*u**2 + 4*u**b = 0 for u.
0
Let t(l) be the first derivative of -l**5/120 + l**3/12 - l**2/2 - 3. Let k(m) be the second derivative of t(m). Factor k(h).
-(h - 1)*(h + 1)/2
Factor -3 + 3 + 0 + 60*c + 44*c**3 - 8 - 96*c**2.
4*(c - 1)**2*(11*c - 2)
Factor -q**3 - 7*q**4 - 2 + 0*q**2 + 3*q**4 - 15*q**3 - 11*q - 21*q**2.
-(q + 1)*(q + 2)*(2*q + 1)**2
What is b in 4 + 8*b + 7 + b**2 + 5 = 0?
-4
Let a(w) = w**4 + w**3 - w**2 - w - 1. Let s(b) = 143*b**4 - 214*b**3 - 152*b**2 - 20*b + 4. Let y(z) = 4*a(z) + s(z). Factor y(c).
3*c*(c - 2)*(7*c + 2)**2
Let r(t) = -5*t**3 + 4*t**4 - 6*t - 3*t**4 + 2*t**2 - 4*t**2. Let f(c) = -c**3 - c. Let k = 47 + -41. Let b(d) = k*f(d) - r(d). Factor b(x).
-x**2*(x - 1)*(x + 2)
Suppose -19*g = -23*g + 12. Find q, given that 4/3*q**2 - 2/3*q**4 - q - 2/3 + q**g = 0.
-1, -1/2, 1, 2
Let w(a) = -2*a**4 + 2*a**3 - a**2 - 5. Let z(x) = -9*x**4 + 9*x**3 - 3*x**2 - 21. Let t(p) = -21*w(p) + 5*z(p). Suppose t(n) = 0. What is n?
-1, 0, 2
Let c = 888 + -5315/6. Solve -1/6*t**4 + t**3 - c*t**2 - 2/3 + 2*t = 0 for t.
1, 2
Let n(o) = o**3 + 7*o**2 - 4*o + 3. Let j be n(-6). Let r = j + -251/4. Factor 1/4 - 1/4*u**2 + 1/4*u - r*u**3.
-(u - 1)*(u + 1)**2/4
Let o be (-3)/(-2)*16/60. Find y, given that -4/5*y + 0 - o*y**2 = 0.
-2, 0
Suppose 17 = 5*q - 2*u, -4*q + 0*u = -2*u - 14. Let p = 17 - 17. Factor 0 + 0*z**q - 1/3*z**5 + 0*z + 1/3*z**4 + p*z**2.
-z**4*(z - 1)/3
Let d(x) be the second derivative of -x**5/90 + x**4/54 - 8*x + 3. Determine y so that d(y) = 0.
0, 1
Suppose 0 + 4/5*q**4 + 0*q + 4/5*q**2 + 8/5*q**3 = 0. What is q?
-1, 0
Let c be (0*(-5)/(-40))/(1 + -3). Factor -4/3*k**2 + 0 - 2/3*k**4 + 2*k**3 + c*k.
-2*k**2*(k - 2)*(k - 1)/3
Let w(p) be the first derivative of -p**4/22 - 2*p**3/33 + 2. Find g such that w(g) = 0.
-1, 0
Let z(p) = 12*p**2 + p**2 - p**4 - 4*p**2 - 8*p**2. Let l(r) = -2*r**2. Let o(h) = 2*l(h) + 4*z(h). Factor o(a).
-4*a**4
Let t(l) = -l - 9. Let i be t(-9). Suppose -10 = 5*w + 4*v, i = 3*w + w + 2*v + 2. Solve w*f**5 + 2*f - 4*f**3 + 0*f + 0*f = 0.
-1, 0, 1
Factor -2/3*s**5 + 2/3*s**4 + 0*s**2 + 0*s**3 + 0 + 0*s.
-2*s**4*(s - 1)/3
Suppose 10 = -2*c + 3*z + 28, 4*c = z + 16. Let d = -118/3 + 40. Factor -2/3*k**2 + 2/3*k**c + d*k**4 - 2/3*k + 0.
2*k*(k - 1)*(k + 1)**2/3
Suppose -4 = d - f - f, -5*d - 50 = -4*f. Let q = d - -29/2. Factor -1/2*w**3 - q*w**2 + 1/2*w + 1/2*w**4 + 0.
w*(w - 1)**2*(w + 1)/2
Let a be (-168)/(-36) + (-3 - 1). Let z be (12/(-15))/2*-5. Factor 4/3*f - a*f**z + 0.
-2*f*(f - 2)/3
Let n be (-24)/(-20)*10/(-3). Let j be 1 - (2 + n*1). Suppose -j*s - 2*s + 4*s - 4*s**2 = 0. Calculate s.
-1/4, 0
Find w such that -4/15*w**2 - 14/15*w - 8/15 + 2/15*w**3 = 0.
-1, 4
Let k be ((-1)/8)/(1*21/(-28)). What is a in -1/6*a**4 - 1/6*a**3 + 1/6*a**5 + 0*a + k*a**2 + 0 = 0?
-1, 0, 1
Let a = -51/2 - -26. Let t(m) be the first derivative of m**2 - 2 + 4/3*m**3 - 4*m - a*m**4. Factor t(k).
-2*(k - 2)*(k - 1)*(k + 1)
Let c = -27/5 - -29/5. Let -6/5*x + c*x**2 + 4/5 = 0. What is x?
1, 2
Suppose 18 = 5*q - 12. Suppose -q*r + 8 = -2*r. Suppose -r*z - 3*z**2 + 3*z**2 + 3*z**2 = 0. Calculate z.
0, 2/3
Let b be ((-2)/14*-2)/(1/7). Determine u so that 2/5*u**b + u**3 - 2/5 - u = 0.
-1, -2/5, 1
Let f(z) be the second derivative of z**9/6048 + z**8/2240 - z**6/1440 + z**3/2 + z. Let u(o) be the second derivative of f(o). Suppose u(s) = 0. What is s?
-1, 0, 1/2
Let b(n) = -2*n**2 + 3*n. Let v(i) = -i**2 + 2*i. Let s(z) = -z**3 - 8*z**2 - 2. Let c be s(-8). Let f(w) = c*b(w) + 3*v(w). Factor f(l).
l**2
Let a(c) be the first derivative of 3/2*c + 3/2*c**2 - 1 + 1/2*c**3. Determine u so that a(u) = 0.
-1
Let b(v) = -8*v - 6. Let f be b(3). Let o be 36/f*5/(-3). Find t, given that -6/5*t**3 + 0*t + 3/5*t**o + 3/5*t**4 + 0 = 0.
0, 1
Suppose -3*b**4 - 2*b**2 + 0*b**4 + 5*b**2 = 0. Calculate b.
-1, 0, 1
Let p(r) = -6*r**5 - 15*r**4 - 20*r**3 + 5*r**2 + 15*r + 4. Let h(f) = f**4 + f**2 + f. Let b(y) = -5*h(y) + p(y). Determine o so that b(o) = 0.
-1, 2/3
Let h(q) = 2 + q**3 - 3*q**3 - 1 + q. Let x be h(-1). Suppose 2*m - 2*m**x - m**3 + 0*m - 3*m = 0. Calculate m.
-1, 0
Let 36*m**2 + m - 450 - 4*m + 466 + 51*m = 0. Calculate m.
-2/3
Let v = 378 + -378. What is w in 0 - 1/4*w**4 + 0*w + 0*w**3 + v*w**2 = 0?
0
Factor -2/3*g - 4/3 + 6*g**2 + 26/3*g**3 + 10/3*g**4.
2*(g + 1)**3*(5*g - 2)/3
Let q(y) be the first derivative of -2/3*y - 5/18*y**4 - 11/9*y**2 + 8 - 26/27*y**3. Factor q(h).
-2*(h + 1)**2*(5*h + 3)/9
Solve 0 - 6/7*j**3 + 0*j - 4/7*j**2 = 0.
-2/3, 0
Let x(i) be the second derivative of 1/4*i**4 + 0*i**2 + 1/20*i**5 + 0 - 4*i - 1/10*i**6 - 1/6*i**3. Solve x(r) = 0.
-1, 0, 1/3, 1
Let r be ((-1)/21)/(30/42 - 1). Let j(w) be the first derivative of 2/9*w**3 + r*w**4 - 2 - 2/3*w - 1/3*w**2. Solve j(m) = 0.
-1, 1
Let x(w) = 1. Let h(c) = 3*c. Let s(n) = -h(n) - 3*x(n). Let t be s(-2). Suppose -4*r**t + 3*r**2 + 5*r**3 + r - 5*r**2 = 0. What is r?
0, 1
Let c(g) be the third derivative of -g**6/200 + g**4/40 - 3*g**2 - 5. Factor c(q).
-3*q*(q - 1)*(q + 1)/5
Let s be ((-72)/2)/((-15)/(-10)). Let h be s/(-9)*6/8. Determine y so that 6/5*y + 6/5*y**4 - 2/5*y**5 - 4/5*y**3 - 4/5*y**h - 2/5 = 0.
-1, 1
Let o(q) = -6*q**5 + 7*q**3 - 5*q**2 - q. Let d(w) = -3*w**5 + 3*w**3 - 3*w**2. Let p(c) = -5*d(c) + 3*o(c). Determine y, given that p(y) = 0.
-1, 0, 1
Let t be (-3)/(-9)*75/5. Let r(h) be the third derivative of -1/90*h**t + 0*h + 1/9*h**3 - 3*h**2 + 0*h**4 + 0. Factor r(a).
-2*(a - 1)*(a + 1)/3
Let 0 + 12/11*v - 2/11*v**3 + 2/11*v**2 = 0. Calculate v.
-2, 0, 3
Let z be 1 + -2 + 1 + 2. Let k be 6 - (1 + z/2). Suppose 0 + 0*t + 1/3*t**k + 1/3*t**3 - 1/3*t**5 - 1/3*t**2 = 0. What is t?
-1, 0, 1
Let z(k) be the second derivative of 13/45*k**6 - 5/63*k**7 - 1/18*k**4 + 3*k - 3/10*k**5 + 2/9*k**3 + 0 + 0*k**2. Let z(g) = 0. What is g?
-2/5, 0, 1
Let l(b) be the second derivative of -b**7/42 - b**6/10 - b**5/10 + b**4/6 + b**3/2 + b**2/2 - 6*b. Determine m, given that l(m) = 0.
-1, 1
Let u(f) = -f - 7. Let s be u(-12). Let w be (12/(-120))/((-2)/84). Factor 17/5*n**4 + 0 + 2/5*n + 11/5*n**2 + n**s + w*n**3.
n*(n + 1)**3*(5*n + 2)/5
Factor -3*i + 3*i**2 - 11*i**2 + 3*i**2 + 6*i**2.
i*(i - 3)
Let h(u) be the