 = -k**2 - k + 1. Let w(o) = -12*o**2 - 11*o + 11. Let x(q) = -22*m(q) + 2*w(q). Factor x(a).
-2*a**2
Suppose 4*t - 1 = 15. Let o = t - 1. Factor y**5 + 0*y**5 - o*y**4 + 2*y**4.
y**4*(y - 1)
Let r = -9 + 6. Let h be (2/24)/((-1)/r). What is a in -1/4*a**3 + 1/4*a**2 + h*a - 1/4 = 0?
-1, 1
Let n = -20 + 41/2. Let f be 2/4 + 0 + 1. What is a in f*a**3 - a**2 - 3/4*a**5 - 3/4*a + n*a**4 + 1/2 = 0?
-1, 2/3, 1
Determine b so that 22*b - b**2 - 8 - 9*b**2 - 6 + 2*b**2 = 0.
1, 7/4
Suppose 0 = -3*t - 2*q + 5 - 4, 0 = -t + q + 7. Factor o**4 - 2*o**t - 2*o**5 - o**2 + o**5 + 3*o**3.
-o**2*(o - 1)**2*(o + 1)
Factor 162/17 + 2/17*o**2 + 36/17*o.
2*(o + 9)**2/17
Let q(y) be the first derivative of -4*y**5/5 - 11*y**4/10 + 4*y**3/5 + y**2 - 4*y/5 - 2. Find n, given that q(n) = 0.
-1, 2/5, 1/2
Let w(t) be the first derivative of -t**6/360 + t**5/60 + 2*t**3/3 + 1. Let o(c) be the third derivative of w(c). Solve o(m) = 0.
0, 2
Factor -3/5*m**5 - 3/5*m**2 + 0*m + 0 - 9/5*m**3 - 9/5*m**4.
-3*m**2*(m + 1)**3/5
Let t(j) = j + 8. Let q be t(-5). Find k, given that -1 - k - k - k**q + 3*k + k**2 = 0.
-1, 1
Let q = 123 + -74. Let g be q/2 - (-1)/(-2). Let 3*o**2 - 25*o**4 + 4*o**4 + g*o**2 - 15*o - 6 + 15*o**3 = 0. What is o?
-1, -2/7, 1
Let f(p) be the third derivative of 1/90*p**5 - 1/180*p**6 + 0*p**3 + 0*p + 0 + 3*p**2 + 1/945*p**7 - 1/108*p**4. Factor f(k).
2*k*(k - 1)**3/9
Let n(z) be the first derivative of 0*z**3 - 1 + 1/24*z**4 - 2*z - 1/40*z**5 + 0*z**2. Let v(i) be the first derivative of n(i). Factor v(b).
-b**2*(b - 1)/2
Let z(s) be the third derivative of 0*s**4 + 1/3*s**3 + s**2 + 0*s - 1/30*s**5 + 0. Determine m so that z(m) = 0.
-1, 1
Let r(i) = 5*i**4 - 23*i**3 + 25*i**2 + i - 3. Let s(w) = 5*w**4 - 23*w**3 + 26*w**2 - 4. Let m(g) = 4*r(g) - 5*s(g). Factor m(h).
-(h - 2)**2*(h - 1)*(5*h + 2)
Solve 18*n**2 + 1350 + 2/5*n**3 + 270*n = 0 for n.
-15
Let x(u) be the second derivative of u**4 - 13*u**3/2 - 18*u**2 - 2*u - 6. Factor x(b).
3*(b - 4)*(4*b + 3)
Let o(z) be the second derivative of z**6/30 - z**5/20 - z**4/12 + z**3/6 + 5*z. Factor o(d).
d*(d - 1)**2*(d + 1)
Let s(z) be the third derivative of z**7/210 - z**6/30 + z**5/30 + z**4/6 - z**3/2 + 21*z**2. What is f in s(f) = 0?
-1, 1, 3
Factor 2*r**2 - 4*r**2 + 7*r - 4 + 0*r - r.
-2*(r - 2)*(r - 1)
Let c = 319 - 316. Suppose -81/2*n - 81/2 - 3/2*n**c - 27/2*n**2 = 0. Calculate n.
-3
Let c(j) be the third derivative of j**7/840 - j**6/240 - j**5/80 + j**4/24 + j**3/6 + 10*j**2. Solve c(x) = 0.
-1, 2
Suppose -8 = a + 2*v, -2*a + 0*v = -v - 9. Let l(o) be the first derivative of -2/3*o**3 - 2/3*o - 4 - 4/3*o**a. Find u, given that l(u) = 0.
-1, -1/3
Let w(d) be the second derivative of d**5/90 - d**4/18 + 4*d**2/9 + 7*d. Solve w(f) = 0 for f.
-1, 2
Let v(h) be the third derivative of -h**9/13608 + h**8/1890 - h**7/756 + h**6/810 - 2*h**3/3 - 3*h**2. Let u(m) be the first derivative of v(m). Factor u(l).
-2*l**2*(l - 2)*(l - 1)**2/9
Let v(s) be the first derivative of s**4/54 - s**3/27 - 2*s**2/9 - 3*s - 1. Let t(x) be the first derivative of v(x). Find o such that t(o) = 0.
-1, 2
Let i(m) = -6*m**2 + 19*m - 6. Let j(f) = f - 5. Let z be j(7). Let k(r) = 2*r**2 - 6*r + 2. Let h = 10 - 3. Let l(s) = h*k(s) + z*i(s). Factor l(u).
2*(u - 1)**2
Let a(u) be the third derivative of -2*u**2 + 0*u**4 + 0*u**3 - 1/90*u**5 + 0*u + 0. Factor a(s).
-2*s**2/3
Let p(w) = 2*w**3 + w**2 + 2*w - 3. Let l = -5 - -7. Let b(o) = o**3 + o - 2. Suppose 0 = -2*m - 4 - 2. Let x(k) = l*p(k) + m*b(k). Factor x(d).
d*(d + 1)**2
Let y = 4 + -2. Solve 26*b + b**3 - 12*b**3 + 3*b**5 + b**4 + 3*b**2 - 4 + 0*b**y - 18*b = 0 for b.
-2, -1, 2/3, 1
Let o(p) be the first derivative of -25*p**7/28 + 9*p**6/4 - 9*p**5/5 + p**4/2 - 3*p - 2. Let r(u) be the first derivative of o(u). Find z such that r(z) = 0.
0, 2/5, 1
Let v(m) be the first derivative of -1/12*m**3 + 3/4*m**2 - 9/4*m + 6. Find b, given that v(b) = 0.
3
Let j(f) = 7*f**4 - 19*f**3 + 41*f**2 - 40*f + 16. Let n(h) = 6*h**4 - 18*h**3 + 40*h**2 - 40*h + 16. Let z(t) = 4*j(t) - 5*n(t). Factor z(d).
-2*(d - 2)**3*(d - 1)
Let d = 8719/15 - 581. Solve 2/15*v + 0 - 2/15*v**5 + 4/15*v**4 - d*v**2 + 0*v**3 = 0 for v.
-1, 0, 1
Solve -1/5*t**2 - 2*t - 9/5 = 0 for t.
-9, -1
Let u(m) be the first derivative of m**5/10 + m**4/2 + 5*m**3/6 + m**2/2 - 7. Suppose u(y) = 0. What is y?
-2, -1, 0
Let s(u) be the second derivative of 2*u + 1/6*u**4 + 2*u**2 + u**3 + 0. Solve s(r) = 0.
-2, -1
Suppose -2*b - 2*b + 4 = 0. Let u = b - 0. Factor -1/4*k**2 + k - u.
-(k - 2)**2/4
Let y be (-10)/45 + 35/36. Factor -3/4*p**5 + y*p**4 + 0*p - 3/4*p**2 + 0 + 3/4*p**3.
-3*p**2*(p - 1)**2*(p + 1)/4
Let t(s) be the first derivative of -s**4/22 + 8*s**3/33 - 4*s**2/11 - 13. Find r, given that t(r) = 0.
0, 2
Let h(o) be the third derivative of -o**8/1680 - o**7/525 - o**6/600 + 17*o**2. Let h(i) = 0. Calculate i.
-1, 0
Suppose -5*d + 27 = -4*h, 8 + 1 = -2*d - 5*h. Suppose -d*j + 9 = -0. Factor -5/3*v**4 - 4*v**j - 2/3*v + 0 - 3*v**2.
-v*(v + 1)**2*(5*v + 2)/3
Let y(h) be the first derivative of -h**3 + 2 - 2*h - 2*h**2 - 1/40*h**5 - 1/4*h**4. Factor y(b).
-(b + 2)**4/8
Let n be 2 + -1 - ((-9)/(-4) + -2). Factor -n*g**2 + 0 - 1/4*g + g**3.
g*(g - 1)*(4*g + 1)/4
Let u(b) = -b**2 - 16*b + 14. Let g be u(-17). Let p be 4/g*(-3)/2. Suppose -1/4*f**p - 1/4 - 1/2*f = 0. What is f?
-1
Let q(r) = -9*r**3 + 4*r**2 + 19*r + 1. Let l(f) = -4*f**3 + 2*f**2 + 10*f + 1. Let o(d) = 5*l(d) - 3*q(d). Find a such that o(a) = 0.
-1, 2/7, 1
Suppose 5*v = v. Let x be 1 + (-6)/8 + v. Find h such that -3/4*h**2 - 1/4*h**3 - 3/4*h - x = 0.
-1
Let c(v) be the third derivative of 3*v**7/560 + 7*v**6/320 + v**5/32 + v**4/64 + 2*v**2. Factor c(y).
3*y*(y + 1)**2*(3*y + 1)/8
Let d(s) be the first derivative of s**6/15 + 4*s**5/15 - 4*s**4/27 - 32*s**3/27 + 16*s**2/9 + 4*s + 6. Let j(k) be the first derivative of d(k). Factor j(o).
2*(o + 2)**2*(3*o - 2)**2/9
Let s(i) = -i**2 - 6*i - 1. Let l(z) = z. Let x be (4 + -1)/6*0. Let a = 1 - x. Let w(r) = a*s(r) + 4*l(r). Factor w(k).
-(k + 1)**2
Let y(x) be the first derivative of 2 - 5 - 3*x - 3*x**3 + 0 + x**2 + 5*x**2. Find n such that y(n) = 0.
1/3, 1
Let i(k) = 6*k**4 + 5*k**3 - k**2 - 5. Let a(s) be the third derivative of -s**7/210 - s**6/120 + s**3/6 - s**2. Let c(f) = 5*a(f) + i(f). Factor c(u).
u**2*(u - 1)*(u + 1)
Suppose 0*a - 2*a = 0. Let s be -3 + 1 - (-32)/14. Factor a*q + s - 4/7*q**2 + 2/7*q**4 + 0*q**3.
2*(q - 1)**2*(q + 1)**2/7
Let l = 11/30 - -2/15. Let c = 1 + 1. Factor 1/2*t - l*t**c + 0.
-t*(t - 1)/2
Let y(h) be the third derivative of -h**6/270 + h**5/90 + 5*h**3/6 - 10*h**2. Let v(j) be the first derivative of y(j). Let v(z) = 0. What is z?
0, 1
Let h(k) be the first derivative of 0*k**2 - 1/2*k**4 + 2 - 2*k**3 + 8*k. Solve h(v) = 0 for v.
-2, 1
Let a(t) be the first derivative of -81*t**4/2 + 21*t**3 - 3*t**2 - 17. Determine i so that a(i) = 0.
0, 1/6, 2/9
Let r(d) be the third derivative of d**5/210 + 16*d**2. Factor r(i).
2*i**2/7
Factor 16 - 2*o**3 - 32*o + 249*o**2 - 2*o**3 - 229*o**2.
-4*(o - 2)**2*(o - 1)
Let r(o) be the third derivative of 0 + 4*o**2 - 1/150*o**6 + 1/15*o**3 + 0*o + 1/525*o**7 + 1/60*o**4 + 1/840*o**8 - 1/75*o**5. Factor r(q).
2*(q - 1)**2*(q + 1)**3/5
Let j(z) be the first derivative of 3*z**4/32 + 7*z**3/8 + 33*z**2/16 + 15*z/8 + 3. Suppose j(h) = 0. What is h?
-5, -1
Let j = 12/7 - 41/28. Solve 0*d - j*d**2 + 1/4 = 0.
-1, 1
Let i(a) = -a - 7. Let r be i(-10). Let 4 - 7*v**2 + r*v**2 - 4*v**4 + 4*v**2 - 8*v + 8*v**3 = 0. Calculate v.
-1, 1
Let w(n) be the second derivative of 2*n**7/21 + 4*n**6/15 - 2*n**4/3 - 2*n**3/3 + 5*n. Factor w(q).
4*q*(q - 1)*(q + 1)**3
Let k be (26/(-8))/((-4)/16). Suppose t - 4*d + 8 = -6*d, -4*t + d = -k. Find m, given that 2*m - 12/5*m**t + 14/5*m**4 - 2/5 - 4/5*m**3 - 6/5*m**5 = 0.
-1, 1/3, 1
Let r(j) be the third derivative of j**5/60 + j**4/12 - 2*j**2. Factor r(x).
x*(x + 2)
Let h be (-2)/7 - (-132)/21. Factor 3*f**3 + 2*f**4 + 3*f**3 + 2*f**3 - h*f**3.
2*f**3*(f + 1)
Let z(h) be the third derivative of 3/2*h**4 + 0*h - 13/20*h**5 - 2*h**3 - 1/70*h**7 + 3/20*h**6 + h**2 + 0. Factor z(m).
-3*(m - 2)**2*(m - 1)**2
Let h(u) = -3*u**4 + 66*u**3 - 87*u**2 + 60*u + 18. Let y(c) = c**4 - 19*c**3 + 25*c**2 - 17*c - 5