at k(h) = 0.
-1, 0, 1
Let c = 6/83 - -124/581. Factor c*p + 2/7*p**2 - 2/7 - 2/7*p**3.
-2*(p - 1)**2*(p + 1)/7
Let k = -8 - -12. Suppose -k*h + h = 0. Let -8/3*q**2 + 8/9*q + 8/3*q**4 + h - 2*q**5 + 10/9*q**3 = 0. Calculate q.
-1, 0, 2/3, 1
Solve 32 - 47*r**2 - 20*r**2 + 7*r**2 - 24*r - r**4 + 64*r**3 - 11*r**4 = 0 for r.
-2/3, 1, 4
Let l(m) = -4*m**5 + m**4 + 13*m**3 + 17*m**2 + 9*m + 9. Let a(r) = r**5 - 3*r**3 - 4*r**2 - 2*r - 2. Let v(y) = 9*a(y) + 2*l(y). Determine i so that v(i) = 0.
-2, -1, 0, 1
Let f(x) be the first derivative of -x**6/540 - 2*x**3/3 + 1. Let n(c) be the third derivative of f(c). Factor n(t).
-2*t**2/3
Let n be (-12)/(-15)*5/2. Let t(s) = s**3 + 5*s**2 + 4*s + 4. Let l be t(-4). Factor g**5 - 4*g + 3*g**l - g**2 + 4*g**2 + 2*g**3 - 5*g**n + g - 1.
(g - 1)*(g + 1)**4
Let u(n) be the second derivative of -4*n + 0 - 1/30*n**4 + 1/5*n**2 + 0*n**3. Solve u(l) = 0.
-1, 1
Let h(n) be the second derivative of 2/3*n**3 - 7*n + 0*n**2 + 1/6*n**4 + 0. Suppose h(a) = 0. What is a?
-2, 0
Suppose 0*w - 2 = -w. Factor 8 + o**2 - o**2 - 40*o + 18*o**w.
2*(o - 2)*(9*o - 2)
Suppose -2*i = -0*i - 2*o - 8, 0 = 2*i - o - 6. Factor 0*u**i + 0*u**3 + 0 + 0*u + 2/7*u**5 - 2/7*u**4.
2*u**4*(u - 1)/7
Suppose 4*g - 16 = h, -g - 3*h = 3*g. Determine b so that -2*b**4 - g*b**3 + 3*b**2 + 3*b**5 - b**4 + 9 - 9 = 0.
-1, 0, 1
Let w(l) be the first derivative of 1/8*l**2 + 0*l + 1/6*l**3 + 1/16*l**4 + 1. Factor w(g).
g*(g + 1)**2/4
Factor -2/7*s**4 - 2/7*s**3 + 4/7 + 10/7*s + 6/7*s**2.
-2*(s - 2)*(s + 1)**3/7
Let d(q) = q**2 - 4. Let l be d(-3). Factor -8*p**3 - l + 5 + 8*p + 28*p**2 - 28*p**4.
-4*p*(p - 1)*(p + 1)*(7*p + 2)
Let u = -468 + 1877/4. What is m in 0 + 3/4*m**3 - 7/4*m**2 + 7/4*m**4 + 1/2*m - u*m**5 = 0?
-1, 0, 2/5, 1
Let a(v) be the second derivative of v**6/405 + v**5/180 - v**4/108 + v**3/6 + 3*v. Let m(i) be the second derivative of a(i). Suppose m(g) = 0. What is g?
-1, 1/4
Let d(x) be the first derivative of -x**4/10 + 4*x**3/5 - 11*x**2/5 + 12*x/5 - 5. Suppose d(r) = 0. What is r?
1, 2, 3
Let l(g) = 3*g**2 - 3*g - 6. Let a(n) = -3*n**2 + 4*n + 5. Let k(c) = 6*a(c) + 5*l(c). Factor k(i).
-3*i*(i - 3)
Let s(n) be the second derivative of 0 + 7*n + 1/3*n**3 + 0*n**2 + 1/12*n**4 - 1/30*n**6 - 1/10*n**5. Factor s(t).
-t*(t - 1)*(t + 1)*(t + 2)
Let n(b) = 4*b**4 + 11*b**3 + b**2 - 3*b. Let h(l) = 12*l**4 + 34*l**3 + 2*l**2 - 10*l. Let p(k) = 3*h(k) - 10*n(k). Factor p(z).
-4*z**2*(z + 1)**2
Let 0 - 9*h**3 - 10*h**2 - 7/2*h**4 - 4*h - 1/2*h**5 = 0. Calculate h.
-2, -1, 0
Let t(r) be the second derivative of -r**9/3780 + r**7/525 - r**5/150 - 5*r**3/6 + 2*r. Let a(w) be the second derivative of t(w). Let a(l) = 0. Calculate l.
-1, 0, 1
Let o(v) be the second derivative of 0*v**2 + 1/40*v**5 - 1/12*v**3 - 1/120*v**6 + 3*v + 0 + 1/48*v**4. Let o(x) = 0. What is x?
-1, 0, 1, 2
Factor -3/4*h**3 - 3/2*h - 9/4*h**2 + 0.
-3*h*(h + 1)*(h + 2)/4
Let o(l) be the first derivative of l**9/6048 + l**8/1680 + l**7/1680 - 8*l**3/3 + 8. Let t(n) be the third derivative of o(n). Factor t(v).
v**3*(v + 1)**2/2
Let g(y) be the first derivative of -y**6/240 - y**5/120 + y**4/48 + y**3/12 + 5*y**2 - 1. Let i(a) be the second derivative of g(a). Factor i(k).
-(k - 1)*(k + 1)**2/2
Determine g, given that -3/2*g**2 + 9 + 15/2*g = 0.
-1, 6
Let y(r) be the first derivative of r**6/27 - 4*r**5/45 - r**4/9 + 16*r**3/27 - 7*r**2/9 + 4*r/9 - 1. Factor y(c).
2*(c - 1)**4*(c + 2)/9
Factor 1/2*a**3 + 1/2*a + 0 + a**2.
a*(a + 1)**2/2
Let a(s) be the second derivative of s**4/36 + s**3/18 - s**2 + 5*s. Find q, given that a(q) = 0.
-3, 2
Let p = -6 + 4. Let t be 2 - (-2)/p - 1. Factor 0*d**3 + d**5 - d**4 - d**3 + d**2 + 0*d**4 + t*d**5.
d**2*(d - 1)**2*(d + 1)
Factor -2/5*w**3 + 0 - 2/5*w**4 + 2/5*w**2 + 2/5*w.
-2*w*(w - 1)*(w + 1)**2/5
Suppose 5 - 28 = -4*s + 3*b, 5*s - 24 = -b. Factor 1/3*l + 2*l**3 + 4/3*l**2 + 0 + 1/3*l**s + 4/3*l**4.
l*(l + 1)**4/3
Let -3/8 + 3/4*j**5 + 3/4*j**2 - 3/8*j**4 - 3/2*j**3 + 3/4*j = 0. Calculate j.
-1, 1/2, 1
Let k(f) be the second derivative of -5/42*f**4 - 1/3*f**3 - 2/7*f**2 + 0 + 3*f. Solve k(a) = 0 for a.
-1, -2/5
Solve 80/7*x + 242/7*x**2 + 8/7 + 30*x**3 = 0.
-2/3, -2/7, -1/5
Let x(r) be the third derivative of 25*r**6/72 - 20*r**5/9 - 95*r**4/18 - 40*r**3/9 + 26*r**2. Determine y so that x(y) = 0.
-2/5, 4
Let c be 7/14 - (-5)/2. Factor 86*y**2 - 84*y**3 - 36*y**4 + 2 - 62*y**c - 32*y**5 + 148*y**4 - 22*y.
-2*(y - 1)**3*(4*y - 1)**2
Suppose 0*g = -2*g + 24. Let l = g - 8. Factor -2*d**3 + 3*d**l + d**2 - d**3 - d**5 + 4*d**2 - 4*d**2.
-d**2*(d - 1)**3
Let u(o) be the first derivative of o**8/1680 - 2*o**7/525 + o**6/150 - 5*o**2/2 + 5. Let x(g) be the second derivative of u(g). Let x(s) = 0. Calculate s.
0, 2
Let v(u) be the second derivative of -u**4/2 + 5*u**3/2 - 9*u**2/2 - 7*u. Suppose v(f) = 0. Calculate f.
1, 3/2
Suppose -5*v - 4 + 13 = -h, 2*h = -3*v + 8. Let k(d) be the second derivative of 1/100*d**5 + 0*d**3 - 2*d + 0*d**v + 0 + 1/60*d**4. Factor k(c).
c**2*(c + 1)/5
Suppose 0*g - 12 = -4*g. Let w**3 + 2*w**2 - 2*w**2 + w**4 + 2*w**5 - 2*w**g = 0. What is w?
-1, 0, 1/2
Solve -3/4*r**3 + 3/4*r**4 + 0 + 3/4*r**5 + 0*r - 3/4*r**2 = 0 for r.
-1, 0, 1
Let b(x) = 6*x - 9. Let f be b(2). Factor 0*h**2 - 2/7*h**f + 6/7*h - 4/7.
-2*(h - 1)**2*(h + 2)/7
Suppose -2108*y + 2113*y - 25 = 0. Let 3*s**y + 0 + s**2 - 11/3*s**3 + 2/3*s - s**4 = 0. Calculate s.
-1, -1/3, 0, 2/3, 1
Let a = 0 + 22. Let w = a - 22. Determine d so that -6/5*d + 0*d**3 + w - 3/5*d**4 + 9/5*d**2 = 0.
-2, 0, 1
Let f(d) = 10*d**3 - 3*d**2 - 7*d. Let q(w) = -5*w**3 + w**2 + 4*w. Let j(b) = -6*f(b) - 11*q(b). Factor j(z).
-z*(z - 1)*(5*z - 2)
Let c(j) = -j**2 + 10*j - 4. Let u(x) = -x**2 + 5*x - 2. Suppose 3*i - 2*g - 2 = 0, -2*g + 9 = i - g. Let h(y) = i*c(y) - 10*u(y). Find p such that h(p) = 0.
2/3, 1
Let k(h) = 7*h**2 - h. Suppose 4*a - 16 = 0, g + 5*a = a + 15. Let u be k(g). Let u*d**4 + 7*d - 6*d**3 - d + 2 + 0*d**4 - 10*d**2 = 0. What is d?
-1, -1/4, 1
Factor -2 - 8*o - 2*o**2 - 7*o + 7*o - 4.
-2*(o + 1)*(o + 3)
Let o(m) = 2*m**2 + 2*m - 1. Let t be o(1). Suppose -10 = -q + 2. Find l such that -q*l**2 + 0*l**2 - 2*l**4 + 8*l - 2 + 0 + 8*l**t = 0.
1
Let c = -108 - -111. Let f(a) be the third derivative of 0*a**c + 0*a + 0 - 3*a**2 + 1/105*a**7 - 1/30*a**5 + 1/60*a**6 - 1/12*a**4. Factor f(w).
2*w*(w - 1)*(w + 1)**2
Let w(x) be the third derivative of x**6/360 + x**5/60 - x**3/6 - 2*x**2. Let v(j) be the first derivative of w(j). Factor v(g).
g*(g + 2)
Suppose 3*g = -4*o + 23, 3*g + 4*o - 3 = 4*g. Factor a**4 - 6*a**4 - 2*a**5 + 2*a**3 + g*a**4.
-2*a**3*(a - 1)*(a + 1)
Let x = -9 + 9. Let b(k) be the second derivative of -1/120*k**6 - 1/8*k**2 + x*k**3 + 0*k**5 - 4*k + 1/24*k**4 + 0. Factor b(q).
-(q - 1)**2*(q + 1)**2/4
Let 7/3*i - 1 + 1/3*i**3 - 5/3*i**2 = 0. Calculate i.
1, 3
Let q be (-5)/(50/(-8))*(-5)/(-6). Let a(i) be the first derivative of 0*i + q*i**3 + 4 + 2/15*i**5 - 1/2*i**4 - 1/3*i**2. Solve a(k) = 0.
0, 1
Let g = -350/27 - -2594/189. Let y = g + 2/3. Find b such that 2/7*b**3 + y*b - 4/7 - 8/7*b**2 = 0.
1, 2
Let s(i) be the third derivative of i**7/840 + i**6/40 + i**5/8 + 7*i**4/24 + 3*i**3/8 + 26*i**2. Factor s(g).
(g + 1)**3*(g + 9)/4
Let s(u) = u**3 + 5*u**2 - u - 6. Let x be s(-5). Let m be ((-4)/2*1)/x. Suppose p**2 - p**4 - p**3 - 2*p**m - p**3 = 0. Calculate p.
-1, 0
Let s(c) be the first derivative of 0*c**2 - 2 - 3/5*c**5 + 0*c**3 + 3/2*c**4 + 0*c. Factor s(a).
-3*a**3*(a - 2)
Let v(l) be the second derivative of 7*l**4/6 + 3*l**3 + 2*l**2 + 10*l. Solve v(x) = 0.
-1, -2/7
Let n be 4/14*(-21)/(-6). Let k be n + 10/(-14) + 0. Solve -2/7*p**4 - k*p**2 + 0 + 4/7*p**3 + 0*p = 0.
0, 1
Solve -2/7*w - 2/7*w**2 + 4/7 = 0.
-2, 1
Let c(h) = -5*h**3 - h**2 + 4*h - 2. Let j(o) = o**3 + o**2 - o. Let n(z) = c(z) + 4*j(z). Let a(t) be the first derivative of n(t). Factor a(s).
-3*s*(s - 2)
Let y(n) = -n**3 + n**2 - n - 1. Let q(r) = 10*r**3 - 10*r**2 + 3*r + 9. Let t(l) = -4*q(l) - 36*y(l). Determine p so that t(p) = 0.
-2, 0, 3
Let t(v) be the first derivative of v**6/12 + v**5/10 - 13. Factor t(k).
k**4*(k + 1)/2
Let n(t) be the third derivative of t**9/83160 + t**8/36960 - t**7/13860 - t**6/3960 - t**4/6 - 3*t**2. Let u(z) be the second derivative