
-2, -1, 0
Let s be 8/(-6)*(-5 - (-67)/14). Factor 2/7 + 4/7*z + s*z**2.
2*(z + 1)**2/7
Let x(r) be the second derivative of r**5/60 - r**4/24 + r**2/12 + 12*r. Solve x(d) = 0 for d.
-1/2, 1
Suppose 0 = -3*q + 3*y - 5*y - 21, 4*y - 48 = 4*q. Let m(b) = b + 11. Let u be m(q). What is t in -3*t**5 + t**2 + 0*t**4 + 2*t**u + 3*t**3 - 3*t**4 = 0?
-1, 0, 1
Let o(u) be the third derivative of -u**5/20 + u**4/2 - 3*u**3/2 + 8*u**2. Factor o(y).
-3*(y - 3)*(y - 1)
Factor 16*w**2 - 40/7 + 52/7*w + 20/7*w**3.
4*(w + 1)*(w + 5)*(5*w - 2)/7
Let a(g) be the first derivative of g**5/5 + 3*g**4/2 + 4*g**3 + 5*g**2 + 3*g - 43. Find q such that a(q) = 0.
-3, -1
Let d(g) be the third derivative of g**6/40 + g**5/20 - g**4/4 - 9*g**2. Factor d(t).
3*t*(t - 1)*(t + 2)
Let m = 3 - -2. Suppose 2*o - 3*a + 5*a - 8 = 0, 3*o - 2*a - 2 = 0. Solve d**5 - o*d**m - 6*d**5 - 2*d**4 = 0.
-2/7, 0
Let v(h) = -h**4 + 1. Let p(m) = 6*m**4 - 15*m**3 + 10*m**2 - 1. Let j(b) = -p(b) - v(b). Factor j(k).
-5*k**2*(k - 2)*(k - 1)
Let a(j) be the second derivative of -2*j**6/3 - 23*j**5/5 + 10*j**4/3 + 10*j. Factor a(b).
-4*b**2*(b + 5)*(5*b - 2)
Find p such that -4/5*p**2 - 14/5*p**3 - 4/5*p**5 - 14/5*p**4 + 0 + 0*p = 0.
-2, -1, -1/2, 0
Suppose 0 = -4*s + 7 + 5. Let c(p) be the second derivative of 0 + 0*p**s + 0*p**5 - 1/30*p**6 - 3*p + 1/12*p**4 + 0*p**2. Factor c(h).
-h**2*(h - 1)*(h + 1)
Let x(l) = -2*l + 12. Let p be x(6). Suppose -1/4*v**3 + 0 + p*v**2 + 1/4*v = 0. What is v?
-1, 0, 1
Find g such that 8/3 - 1/3*g**4 - g**3 + 4*g + 2/3*g**2 = 0.
-2, -1, 2
Let a(t) = t**3 + 5*t**2 - t + 7. Let d be a(-5). Factor 4*k**2 - 5*k**2 - 12 + k + d.
-k*(k - 1)
Suppose -2*r + 16 = 2*w, -w + 3*w + 8 = 4*r. Let b(z) be the second derivative of 3*z - 1/80*z**5 + 0*z**w + 1/24*z**3 + 0*z**2 + 0. Solve b(v) = 0 for v.
-1, 0, 1
Let g(s) be the second derivative of -s**5/38 - s**4/6 - 11*s**3/57 + 3*s**2/19 - 18*s. Determine p so that g(p) = 0.
-3, -1, 1/5
Let a(f) be the first derivative of 8*f**5/5 - 2*f**4 - 2*f**3 + 4*f**2 - 2*f - 6. Let a(j) = 0. What is j?
-1, 1/2, 1
Let l(j) be the third derivative of j**8/1344 - j**6/120 + j**5/120 + j**4/32 - j**3/12 - 8*j**2. Factor l(d).
(d - 1)**3*(d + 1)*(d + 2)/4
Let d(l) be the second derivative of -l**5 + 35*l**4/12 - 5*l**3/3 - 5*l**2/2 + 11*l. Factor d(f).
-5*(f - 1)**2*(4*f + 1)
Let l(d) be the second derivative of -4*d**6/135 - d**5/90 + 2*d**4/27 + d**3/27 - 4*d. Determine n, given that l(n) = 0.
-1, -1/4, 0, 1
Let m(x) be the third derivative of -5*x**8/1008 - 17*x**7/630 - 7*x**6/120 - 11*x**5/180 - x**4/36 - 6*x**2. Factor m(k).
-k*(k + 1)**3*(5*k + 2)/3
Find y, given that 2/7*y - 2/7*y**4 + 2/7*y**2 - 2/7*y**3 + 0 = 0.
-1, 0, 1
Let s(j) be the second derivative of 7*j**6/40 - 23*j**5/20 + 5*j**4/2 - 2*j**3 - 3*j**2 - 4*j. Let h(g) be the first derivative of s(g). Factor h(o).
3*(o - 2)*(o - 1)*(7*o - 2)
Factor 12*a**5 - 16*a**5 + 8*a**4 + 3*a + a - 8*a**2.
-4*a*(a - 1)**3*(a + 1)
Factor 5/2*w**2 + 1/2*w**3 - 9/2 + 3/2*w.
(w - 1)*(w + 3)**2/2
Let -144/11 - 24/11*m + 20/11*m**2 - 2/11*m**3 = 0. What is m?
-2, 6
Let q = -14 + 5. Let h be ((-6)/q)/((-1)/(-3)). Factor c + h*c**3 + 4*c**3 - 7*c**3.
-c*(c - 1)*(c + 1)
Let f(a) = 3*a**2 - 3*a - 4. Let k be f(-1). Suppose -2/9*r**3 + 0 - 4/9*r**k - 2/9*r = 0. What is r?
-1, 0
Let h(p) = -p**3 + 2*p**2 - 1. Let d be h(-1). Suppose -21 + 13 = -d*z. Let 6*r**2 + 2/3 - z*r = 0. Calculate r.
1/3
Factor 30*z**3 + 42*z**3 - 6*z**4 - 84*z**3 + 2*z**4.
-4*z**3*(z + 3)
Let c(b) be the third derivative of 0*b**3 - 3*b**2 + 1/12*b**4 - 1/30*b**6 + 0 - 1/30*b**5 + 0*b. Find p, given that c(p) = 0.
-1, 0, 1/2
Let s(g) be the first derivative of -g**6/300 + g**5/150 + 2*g**2 + 2. Let q(l) be the second derivative of s(l). Factor q(r).
-2*r**2*(r - 1)/5
Let t be 3/4 - (-3)/12. Let d be 3 + t - (-32)/(-12). Factor 2/3*c + 0 + 0*c**3 - 2/3*c**5 - d*c**2 + 4/3*c**4.
-2*c*(c - 1)**3*(c + 1)/3
Let a be -6*(12/9 - 1). Let y be 60/9*(-3)/a. Determine u so that -48/5*u**2 + 18*u**3 + 0 - y*u**4 + 8/5*u = 0.
0, 2/5, 1
Let z be ((-36)/108)/(0 - 1/3). Let l(t) be the first derivative of 8/5*t - 1/10*t**4 + z - 8/5*t**2 + 2/3*t**3. Solve l(v) = 0.
1, 2
Let g(b) = 15*b**2. Let d(o) = o**2 - 2. Let t(h) = 4*h**2 - 7. Let y(w) = -7*d(w) + 2*t(w). Let r(j) = g(j) - 18*y(j). Suppose r(k) = 0. Calculate k.
0
Let o = -943/12 - -238/3. What is k in -9/8 - 1/8*k**2 - o*k = 0?
-3
Let c(d) be the third derivative of d**6/420 - 2*d**5/105 - 11*d**4/84 - 2*d**3/7 - 2*d**2 + 19. Factor c(t).
2*(t - 6)*(t + 1)**2/7
Suppose 6*c - 4*c**2 + 4*c**4 - 2*c - 8*c + 8*c**3 - 4*c = 0. What is c?
-2, -1, 0, 1
Let j be ((-2)/4)/(-5 - (-36)/16). Let j*r + 0 + 2/11*r**2 = 0. What is r?
-1, 0
Let a(o) be the first derivative of o**3/4 + 5*o**2 - 7*o - 38. Factor a(p).
(p + 14)*(3*p - 2)/4
Suppose 2*n - 9 - 1 = 0. Suppose 0*s**n - 2*s**5 - 8*s**5 - s**3 + 11*s**5 = 0. What is s?
-1, 0, 1
Let x(w) = -2*w**3 + 1 - 3*w**3 - 4*w**3 + 5*w**3 + 2*w. Let d be x(-1). Factor -v - 6*v**3 + 1 + 4*v**3 + d*v - v**4.
-(v - 1)*(v + 1)**3
Let j be (-70)/(-8) + 4/16. Let m be j/3*2 - 1. Determine z so that -1/2*z**3 + 1/4*z + 0*z**2 + 0*z**4 + 0 + 1/4*z**m = 0.
-1, 0, 1
Factor 36*x**2 + 4*x**3 - 108*x + x**3 - 9*x**3 + 108.
-4*(x - 3)**3
Let b(j) be the second derivative of j**5/50 - j**3/15 + 2*j - 6. Factor b(x).
2*x*(x - 1)*(x + 1)/5
Suppose -3*t - 3*f + 18 = 0, 1 + 5 = 3*t - 3*f. Factor -2*s**2 - s**3 + t*s - 4*s + 4*s - 5*s.
-s*(s + 1)**2
Suppose d = -0*d - 4*w + 2, 2*w = 0. Let 12/5*a**d + a**4 + 2/5*a - 1/5 + 14/5*a**3 = 0. Calculate a.
-1, 1/5
Let k be 1 + (108/(-15) - -7). Determine x so that -k - 92/5*x**3 + 28/5*x + 64/5*x**5 + 32/5*x**4 - 28/5*x**2 = 0.
-1, 1/4, 1
Let 30*q**2 + q - 20*q**2 - 10*q - q**3 = 0. Calculate q.
0, 1, 9
Let j(t) = 15*t**2 - 80*t. Let a(i) = 8*i**2 - 40*i. Let m(o) = 5*a(o) - 3*j(o). Determine k, given that m(k) = 0.
0, 8
Factor 10*s**2 - 4*s**3 - 6*s**2 + 12*s**2 - 16*s.
-4*s*(s - 2)**2
Let v be 39/42 - (-21)/(-49). Factor -1/2*p**5 + 0*p**2 + p**3 + 0*p**4 + 0 - v*p.
-p*(p - 1)**2*(p + 1)**2/2
Let l(q) be the second derivative of 1/50*q**5 - 1/900*q**6 - 1/3*q**3 - 3/20*q**4 + 0*q**2 - q + 0. Let t(a) be the second derivative of l(a). Factor t(y).
-2*(y - 3)**2/5
Let z(t) = t**2. Let m(p) = p**3 + 5*p**2 - p + 1. Let n(s) = m(s) - 6*z(s). Solve n(d) = 0 for d.
-1, 1
Let q(s) be the third derivative of 0*s + 0*s**3 + 0 + 1/30*s**4 - 3*s**2 + 1/150*s**5. Factor q(p).
2*p*(p + 2)/5
Let s(q) be the first derivative of 0*q**2 + 1/6*q**3 + 0*q + 5. Let s(a) = 0. Calculate a.
0
Suppose 5*k - 20 = -5*k. Factor 0 + 9/4*d**k + 3/4*d.
3*d*(3*d + 1)/4
Let g(h) be the first derivative of -h**8/840 + h**6/180 - 2*h**3/3 - 3. Let t(i) be the third derivative of g(i). Determine y so that t(y) = 0.
-1, 0, 1
Let h(o) = 6*o**3 - 2*o**2 - 6*o. Suppose j - 2 = -0. Let d(y) = y**4 + y**3 - y**2 - y - 1. Let l(g) = j*d(g) - h(g). Factor l(i).
2*(i - 1)**3*(i + 1)
Suppose 0 = 2*w + 2*w - 60. Suppose w*i - 12*i = 6. Factor -1/3*q**3 + 1/3*q**5 - 1/3*q**4 + 0*q + 0 + 1/3*q**i.
q**2*(q - 1)**2*(q + 1)/3
Find f such that -2/7*f**4 - 6/7*f**2 + 6/7*f**3 + 2/7*f + 0 = 0.
0, 1
Let n(z) = -z**3 - 5*z**2 - 2*z - 7. Let g be n(-5). Suppose -r = 3*s - 18, 7 = 4*r - g*s + 2*s. Factor 0 + 0*q + 0*q**4 + 0*q**2 + 2/5*q**5 - 2/5*q**r.
2*q**3*(q - 1)*(q + 1)/5
Let o(b) be the third derivative of -b**5/90 - 5*b**4/36 + 2*b**3/3 - b**2. Factor o(a).
-2*(a - 1)*(a + 6)/3
Let n(a) be the second derivative of -1/36*a**4 - 1/18*a**3 + 0*a**2 + 0 - 3*a. Determine m so that n(m) = 0.
-1, 0
Determine c, given that 1/4*c**2 + 1/2*c + 0 = 0.
-2, 0
Let u(p) be the third derivative of -1/27*p**3 + 0 - 3*p**2 + 0*p + 1/270*p**5 + 1/108*p**4 - 1/540*p**6. Factor u(h).
-2*(h - 1)**2*(h + 1)/9
Let q(j) = j**3 - j**2 - j + 1. Let w(g) = 3*g**4 - 3*g**3 - 3*g**2 - 9*g - 12. Let k(x) = 6*q(x) + w(x). Solve k(n) = 0.
-1, 2
Let m(g) = 20*g**3 + 20*g**2 + 4*g - 4. Let a(y) = y**4 - 21*y**3 - 20*y**2 - 3*y + 5. Let r(h) = -4*a(h) - 5*m(h). Factor r(w).
-4*w*(w + 1)**2*(w + 2)
Let u = 73 + -68. Let l(p) be the third derivative of -1/840*p**7 + 0 + 0*p**u + 1/24*p**3 + 1/240*p**6 - 1/48*p**4 + 0*p + 2*p**2. Factor l(m).
-(m - 1)**3*(m + 1)/4
Let s = -6 - -2. Let j = s + 7. Factor -3 - 3*b**