k) be the third derivative of -k**5/20 + 3*k**4/4 - 9*k**3/2 - 6*k**2. Factor p(r).
-3*(r - 3)**2
Factor -12*y - y**3 - 27*y**3 + 4*y**3 + 4*y**5 - 32*y**2.
4*y*(y - 3)*(y + 1)**3
Let r(v) = -v - 2. Let l be r(-11). Let o = l - 9. Determine p, given that -6/5*p**3 + 0 + o*p - 2/5*p**2 - 6/5*p**4 - 2/5*p**5 = 0.
-1, 0
Let f = 3 + -3. Let x be 6/(-9) - (f - 1). Suppose 1/3*j**3 - 1/3*j + x - 1/3*j**2 = 0. What is j?
-1, 1
Factor 0 - 6*k**2 + 0*k - 3/2*k**4 - 6*k**3.
-3*k**2*(k + 2)**2/2
Solve 0*b**3 - 1/7*b**4 + 2/7*b + 3/7*b**2 + 0 = 0 for b.
-1, 0, 2
Let o(t) be the third derivative of t**8/1176 - 2*t**7/735 + t**6/420 - 5*t**2. Factor o(j).
2*j**3*(j - 1)**2/7
Let j(v) be the third derivative of v**6/100 + 2*v**5/75 - v**4/12 - 2*v**3/15 + 8*v**2. Factor j(g).
2*(g - 1)*(g + 2)*(3*g + 1)/5
Let c(n) = 4*n**2 - 10*n + 10. Let a(k) = -5*k**2 + 11*k - 11. Let g(z) = 4*a(z) + 6*c(z). Factor g(j).
4*(j - 2)**2
Let y(r) be the first derivative of -2*r**5/5 - r**4 + 2*r**2 + 2*r + 1. Let y(p) = 0. What is p?
-1, 1
Let x(r) = -7*r**2 + 3*r + r**4 + 0*r**4 + 26*r**2 + 10 + 15*r. Let d(n) = n**3 - n**2 - n - 1. Let p(i) = 6*d(i) + x(i). Factor p(t).
(t + 1)**2*(t + 2)**2
Let m(i) be the first derivative of i**7/18 - i**6/45 - 7*i**5/60 + i**4/18 + 2*i + 4. Let d(j) be the first derivative of m(j). Suppose d(q) = 0. What is q?
-1, 0, 2/7, 1
Suppose 5*p + 11 + 4 = 0. Let t = 5 + p. Determine x, given that 1/3*x**t - 1/3 + 0*x = 0.
-1, 1
Let s be (-6)/9*6 - (0 - 4). Suppose 1/8*w**4 - 1/8*w**2 + s*w + 0 + 0*w**3 = 0. Calculate w.
-1, 0, 1
Let r(c) be the third derivative of 0 + 0*c - 7*c**2 + 1/180*c**5 - 1/18*c**4 + 2/9*c**3. Factor r(v).
(v - 2)**2/3
Let v = -74 + 74. Determine q, given that v - 4/9*q + 2/9*q**2 = 0.
0, 2
Let i(b) be the third derivative of -4*b**2 + 0*b + 0 + 2/75*b**5 + 0*b**4 + 0*b**3 + 1/525*b**7 + 1/75*b**6. Factor i(l).
2*l**2*(l + 2)**2/5
Let -4/5*s**3 - 4/5 + 4/5*s**2 + 4/5*s = 0. Calculate s.
-1, 1
Suppose 12 = 7*x - 5*x. Let m be (-2)/(-3 + 4/2). Let -t**m - t**2 + 8*t - x*t = 0. Calculate t.
0, 1
Let y = -103 - -106. Let l(g) be the third derivative of 4*g**2 + 0*g - 1/48*g**4 - 1/8*g**y + 1/240*g**5 + 0. Factor l(q).
(q - 3)*(q + 1)/4
Let y(b) be the second derivative of b**7/2940 + b**6/630 + b**5/420 - 4*b**3/3 - 9*b. Let q(u) be the second derivative of y(u). Find s such that q(s) = 0.
-1, 0
Let k(i) be the second derivative of i**6/165 + i**5/110 - i**4/33 - i. Suppose k(x) = 0. What is x?
-2, 0, 1
Let v(y) = y**2 - 6*y. Let q be v(6). Let a be (-4)/6*(-12)/5. Find c such that q*c + 6/5*c**3 - 2/5*c**2 + 0*c**4 + 0 - a*c**5 = 0.
-1, 0, 1/2
Let a(m) = m**2 + 6*m + 5. Let z be a(-5). Let j(y) be the first derivative of 1/5*y**2 + 2/15*y**3 - 1/10*y**4 + 1 - 2/25*y**5 + z*y. Factor j(w).
-2*w*(w - 1)*(w + 1)**2/5
Let j(f) be the second derivative of f - 1/15*f**3 + 0 + 1/50*f**5 + 0*f**2 + 1/75*f**6 - 1/30*f**4. Determine u, given that j(u) = 0.
-1, 0, 1
Suppose 6 = -2*t + 20. Determine h, given that -h**2 + 7*h + 2 - h**2 - t*h = 0.
-1, 1
Let p(h) be the first derivative of h**4/12 + h**3/8 - h**2/8 - 6*h + 1. Let r(m) be the first derivative of p(m). Factor r(d).
(d + 1)*(4*d - 1)/4
Let s(z) be the third derivative of -1/300*z**6 + 1/60*z**4 - 1/150*z**5 + 0 + 2*z**2 + 1/15*z**3 + 0*z. Solve s(p) = 0 for p.
-1, 1
Suppose -4*c = -3*h + 34, 5*c - 5*h = 4*c - 17. Let d(u) = u**2 + 1. Let v(t) = 4*t**2 + t + 4. Let x(m) = c*d(m) + 2*v(m). What is y in x(y) = 0?
-1
Let a be 0 + ((-191)/(-30) - (-58)/435). Determine g so that 4/3*g**3 + 1/3 + 17/6*g - 8/3*g**4 + a*g**2 = 0.
-1, -1/4, 2
Suppose -3*z + 3 = -3. Suppose s + 5 = 0, -z*x + 5*x - 26 = 4*s. Factor 3/2*w**x + 1 - 5/2*w.
(w - 1)*(3*w - 2)/2
Let s = 5 - 3. Suppose 3*w + w = -4*g, 0 = -s*g - 4. Factor -2*x + 4 - 2*x**2 + 0 - x**w + x**2.
-2*(x - 1)*(x + 2)
Let q be 0 + (5 - 0/(-1)). Factor -2/7*l + 8/7*l**2 - 12/7*l**3 + 8/7*l**4 + 0 - 2/7*l**q.
-2*l*(l - 1)**4/7
Let b(v) be the second derivative of -1/5*v**6 + 3/10*v**5 + v**4 - 1/2*v**3 - 1/14*v**7 + 0 - 3*v**2 + 5*v. Let b(j) = 0. Calculate j.
-2, -1, 1
Let z = 273 - 273. Determine m so that z + 0*m - 2/3*m**2 = 0.
0
Suppose -16 = -4*q, 5*h - 17 - 15 = -3*q. Determine s so that h*s**2 + 0*s**4 - 3*s**3 + 0*s**3 - 2*s**4 + s**3 = 0.
-2, 0, 1
Suppose -4*s - 5 = -3*q + s, 2*q + 5*s = 45. Let o be 28/q + (-10)/(-50). Factor -2*a**o - 4*a - 1/3*a**4 - 13/3*a**2 - 4/3.
-(a + 1)**2*(a + 2)**2/3
Let y be (6 + 0)*4/6. Factor q**y - 2 - q**2 + 0 + 2.
q**2*(q - 1)*(q + 1)
Let s(c) be the second derivative of -c**5/60 - c**4/4 - 4*c**3/3 - 10*c**2/3 - 10*c. Factor s(q).
-(q + 2)**2*(q + 5)/3
Suppose -4*a = 5*g + 35 + 2, 2*g + 3*a = -12. Let b = -17/2 - g. Find i such that 0 - 1/2*i**4 - i**3 - b*i**2 + 0*i = 0.
-1, 0
Let j(z) be the first derivative of z**6/10 + 3*z**5/10 + z**4/4 + 2*z + 6. Let i(x) be the first derivative of j(x). Find m such that i(m) = 0.
-1, 0
Let z(k) = -100*k**4 - 180*k**3 - 125*k**2 + 55*k - 55. Let o(j) = 11*j**4 + 20*j**3 + 14*j**2 - 6*j + 6. Let n(f) = -55*o(f) - 6*z(f). Factor n(g).
-5*g**2*(g + 2)**2
Let q(k) = -k**3 - 13*k**2 - 20*k - 8. Let p = -15 - -18. Let y(g) = 8*g**3 + 92*g**2 + 140*g + 56. Let i(z) = p*y(z) + 20*q(z). Factor i(o).
4*(o + 1)**2*(o + 2)
Let y(i) = -2*i**5 + 2*i**4 - i**3 - 3*i**2 + 4*i - 2. Let a(j) = j**5 + j**4 - j**3 + j**2 - j + 1. Let m(o) = -a(o) - y(o). Factor m(t).
(t - 1)**4*(t + 1)
Suppose 4 = 8*n - 6*n. Factor 2/3*s**3 + 2/3*s**n - 2/3*s + 0 - 2/3*s**4.
-2*s*(s - 1)**2*(s + 1)/3
Let s(k) be the third derivative of -5*k**8/756 + 11*k**7/945 + 13*k**6/270 - 7*k**5/270 - 4*k**4/27 - 4*k**3/27 - 6*k**2. Suppose s(v) = 0. Calculate v.
-1, -1/2, -2/5, 1, 2
Let d = 6/115 + 333/230. Find s such that -d*s + 0 - 3/2*s**2 = 0.
-1, 0
Factor 4*v**2 - 8 - v**4 - v**4 + 6.
-2*(v - 1)**2*(v + 1)**2
Let k be (-75)/600 - (-41)/(-16)*-2. Let 1/3*j**3 - 1/3*j**k + 0*j + 0*j**4 + 0*j**2 + 0 = 0. What is j?
-1, 0, 1
Let g(u) be the first derivative of -2*u - 2/3*u**3 + 3 + 2*u**2. Factor g(y).
-2*(y - 1)**2
Let w be 6*((-2)/5)/(4/(-5)). Factor -2/9*h**w + 0 - 4/9*h**2 - 2/9*h.
-2*h*(h + 1)**2/9
Let o(v) be the third derivative of -1/50*v**5 + 3/40*v**4 + 0*v + 0 + 2*v**2 - 1/10*v**3. Suppose o(w) = 0. What is w?
1/2, 1
Let g(r) be the second derivative of -r**7/210 - 2*r**6/75 - r**5/20 - r**4/30 + 13*r. Factor g(n).
-n**2*(n + 1)**2*(n + 2)/5
Let s(o) = o**3 - 4*o**2 + 5*o - 3. Let q be s(3). Solve z**3 - 4*z**q - 3*z + 19*z**2 - 13*z**2 = 0.
0, 1
Let o = -103/12 + 28/3. Let z(p) be the first derivative of -3/8*p**4 + o*p**2 + 1 + 1/2*p**3 - 3/2*p. Factor z(i).
-3*(i - 1)**2*(i + 1)/2
Let a(h) be the third derivative of -4*h**2 + 1/7*h**3 + 0*h - 1/420*h**6 + 0 - 1/12*h**4 + 1/42*h**5. Factor a(r).
-2*(r - 3)*(r - 1)**2/7
Let h = -10 - -14. Find f, given that 2 + h*f + 0 - 2*f - 2*f**3 - 2*f**2 = 0.
-1, 1
Let o(d) be the first derivative of -d**5/5 - d**4/10 + d**3/3 + d**2/5 - 4. Determine y, given that o(y) = 0.
-1, -2/5, 0, 1
Let u(v) be the third derivative of -v**6/1440 - v**5/480 + v**4/48 - v**3/2 - v**2. Let a(p) be the first derivative of u(p). Factor a(o).
-(o - 1)*(o + 2)/4
Factor 4/5*h**3 + 3/5*h + 7/5*h**2 + 0.
h*(h + 1)*(4*h + 3)/5
Suppose 1/4*n - 1/2 - 1/4*n**3 + 1/2*n**2 = 0. What is n?
-1, 1, 2
Let s be 32/80 - 8/70. Factor 2/7*h**3 + 4/7*h**2 + 0 + s*h.
2*h*(h + 1)**2/7
Let p be 28/3 + 1/(-3). Suppose p = 2*j - 3. Determine f so that -f**2 + 0 - 5 + j = 0.
-1, 1
Let y be ((-4)/(-15))/(12/10). Find i such that 0 + 0*i - 2/9*i**2 - 2/3*i**4 - 2/3*i**3 - y*i**5 = 0.
-1, 0
Let n be -2 - (-2)/(-2 + 3). Suppose -2*f + 5*f - 6 = 0. Suppose -5 + f*k**2 + n*k**3 + 3 + 2*k**3 - 2*k = 0. Calculate k.
-1, 1
Determine p so that -4/11 - 16/11*p - 7/11*p**2 = 0.
-2, -2/7
Let g(l) be the first derivative of -l**5/10 - l**4/2 - l**3 - l**2 - 2*l - 1. Let q(c) be the first derivative of g(c). What is x in q(x) = 0?
-1
Suppose 0 = -0*o + 5*o - 25. Determine u so that 0*u**3 + 2*u - o*u**3 + 3*u**3 + 0*u**3 = 0.
-1, 0, 1
Let x(g) be the first derivative of -g**5/5 + g**4/4 + g**3/3 - g**2/2 - 5. Factor x(v).
-v*(v - 1)**2*(v + 1)
Suppose 8*g - 16/3 - 22/3*g**3 + 4*g**4 + 4/3*g**2 - 2/3*g**5 = 0. What is g?
-1, 1, 2
Suppose -1/6*o**2 + 0 + 5/3*o = 0. Calculate o.
0, 10
Let g(k) be the se