= 20*h(n) - s(n). Factor z(p).
-4*(p - 3)**2*(p + 1)**2
Determine k so that 0*k**2 + 2/9*k**3 + 0 + 0*k**4 + 0*k - 2/9*k**5 = 0.
-1, 0, 1
Let d be 2 - (1800/(-665))/(-4). Let m = 2/19 + d. Determine x, given that -m*x**2 + 0 - 2*x**3 + 4/7*x = 0.
-1, 0, 2/7
Let o(q) be the second derivative of 1/20*q**5 + 1/2*q**2 - 1/12*q**4 + q + 0 - 1/6*q**3. What is a in o(a) = 0?
-1, 1
Let d be 8/10 + (-1924)/(-195). Suppose -d*k - 100/3*k**4 + 8/3 + 130/3*k**3 - 2*k**2 = 0. What is k?
-1/2, 2/5, 1
Let v be (2 + -1)/((-2)/(-8)). Suppose 3*j - w - 3*w - 6 = 0, 0 = -j + v*w - 6. Find u, given that 6*u**4 + 3*u**3 + 4*u**2 - 10*u**4 - j*u**5 + 3*u**3 = 0.
-1, -2/3, 0, 1
Let r = -10 + 10. Factor -2/9*z**4 + 0*z + r + 0*z**3 + 2/9*z**2.
-2*z**2*(z - 1)*(z + 1)/9
Suppose -4*g = 4*g - 40. Factor -3/2*a + 6*a**2 + 0 - 9*a**3 + 6*a**4 - 3/2*a**g.
-3*a*(a - 1)**4/2
Let h(r) = 6*r**3 - 6*r**2 + 3*r - 3. Let o(w) = -5*w**3 + 7*w**2 - 4*w + 2. Let j(q) = 2*h(q) + 3*o(q). Determine n, given that j(n) = 0.
0, 1, 2
Let m(l) be the third derivative of l**7/1365 + l**6/156 + 3*l**5/130 + 7*l**4/156 + 2*l**3/39 - l**2. Find k, given that m(k) = 0.
-2, -1
Let a = 7/3 + -5/6. Suppose -3/2*c**4 - 1/2*c**2 - a*c**3 + 0*c + 0 - 1/2*c**5 = 0. Calculate c.
-1, 0
Factor -4/3 + 2/3*v**3 + 0*v**2 - 2*v.
2*(v - 2)*(v + 1)**2/3
Suppose 2*m + x - 2 = 0, 0*m - 4*m = x - 6. Suppose 2/3*b + 4/3 - 2/3*b**m = 0. Calculate b.
-1, 2
Suppose -4*u - 26 = -3*h, -2*h - 3*h = 2*u. Determine g so that -g**3 - g**2 - 2*g + 3*g**2 + g**h = 0.
0, 1, 2
Let a(b) = b**5 - 22*b**4 - 32*b**3 - 20*b**2 + 4*b - 4. Let c(p) = -p**5 + 43*p**4 + 65*p**3 + 41*p**2 - 7*p + 7. Let f(w) = -7*a(w) - 4*c(w). Factor f(u).
-3*u**2*(u + 2)**3
Let m(x) = -6*x**4 - 6*x**3 + 12*x**2 - 5*x - 5. Let a(l) = 9*l**4 + 9*l**3 - 18*l**2 + 7*l + 7. Let n(g) = 5*a(g) + 7*m(g). Find q, given that n(q) = 0.
-2, 0, 1
Let d(g) be the first derivative of -3*g**5/5 + 3*g**4/2 - 3. Determine m so that d(m) = 0.
0, 2
Let k(w) be the second derivative of -w**6/45 - w**5/30 + 37*w. Factor k(m).
-2*m**3*(m + 1)/3
Let a be (-4)/(-18) + 4/9. Factor -1/3*f**3 + 1/3*f**2 + a*f + 0.
-f*(f - 2)*(f + 1)/3
Factor -4/5*p + 0 + 2/5*p**2.
2*p*(p - 2)/5
Let k be (-1)/(-18)*(5 + -1). Suppose -44*h = -38*h. Factor h - k*w**2 - 2/9*w.
-2*w*(w + 1)/9
Factor 1/8*q - 1/8*q**2 + 0 + 1/8*q**4 - 1/8*q**3.
q*(q - 1)**2*(q + 1)/8
Let i = 0 + 5. Suppose i*v + 4 = 3*c - 5, -v = -c + 3. Suppose 7/2*a + 7/2*a**5 - 7*a**c + 2*a**2 - 1 - a**4 = 0. What is a?
-1, 2/7, 1
Determine b, given that -3*b**2 - 507*b - 5 - 7 + 495*b = 0.
-2
Let n(t) be the second derivative of t**9/5040 - t**7/420 + t**5/40 - t**4/12 + 5*t. Let b(z) be the third derivative of n(z). Factor b(g).
3*(g - 1)**2*(g + 1)**2
Let k(m) be the first derivative of 2187*m**4/4 - 486*m**3 + 162*m**2 - 24*m - 10. What is y in k(y) = 0?
2/9
Let a(k) = 14*k**4 + 29*k**3 + 50*k**2 + 18*k. Let o(w) = -5*w**4 - 10*w**3 - 17*w**2 - 6*w. Let n(q) = -6*a(q) - 17*o(q). Factor n(d).
d*(d - 6)*(d + 1)**2
Let a = -1 + 6. Factor -a*v**2 + 2*v**2 - v**2 + 8*v + 12.
-4*(v - 3)*(v + 1)
Let t be ((-2)/(-3))/(1/18). Suppose 5*v - 4*c - t = 0, -4 - 5 = v + 3*c. Factor 0 + v*d + 2/9*d**3 + 0*d**2 + 4/9*d**4 + 2/9*d**5.
2*d**3*(d + 1)**2/9
Let t(k) be the first derivative of -5*k**4/4 + 8*k**3/3 - k**2/2 - 2*k - 19. What is d in t(d) = 0?
-2/5, 1
Let f(h) = 71*h**3 + 36*h**2 + 23*h. Let j(t) = -24*t**3 - 12*t**2 - 8*t. Let i(s) = 6*f(s) + 17*j(s). Determine k, given that i(k) = 0.
-1/3, 0
Let q(p) = 2*p**4 - 2*p**3 - 4. Let s(l) be the third derivative of l**7/210 - l**6/120 - l**3/2 + 5*l**2. Let m(w) = 3*q(w) - 4*s(w). Factor m(h).
2*h**3*(h - 1)
Let h(i) = -25*i**3 - 240*i**2 + 25*i + 205. Let s(v) = -2*v**3 - 20*v**2 + 2*v + 17. Let g(k) = 3*h(k) - 35*s(k). Factor g(t).
-5*(t - 1)*(t + 1)*(t + 4)
Let i(l) be the second derivative of -l**7/126 - 7*l**6/90 - 2*l**5/15 + 4*l**4/9 + 13*l. Solve i(r) = 0 for r.
-4, 0, 1
Let p be 26/(-20)*(-135)/(-18). Let o = p + 10. Suppose -1/2*f + 1/4 + o*f**2 = 0. What is f?
1
Suppose -5 - 13 = 3*v. Let i be -2*1 + v/(-1). Factor -3*f**i - 2*f**2 + f**4 + 2*f - 2*f**3 + 4*f**4.
2*f*(f - 1)**2*(f + 1)
Let b(s) be the second derivative of -1/4*s**4 + 1/2*s**3 - 3/20*s**5 + 0 + 4*s + 3/2*s**2. Factor b(x).
-3*(x - 1)*(x + 1)**2
Factor 20 - 5*i**2 + 3*i - 20*i + 2*i.
-5*(i - 1)*(i + 4)
Let b(k) = 3*k**2 + 3*k - 1. Let x(o) = 7*o**2 + 7*o - 2. Let y(f) = 9*b(f) - 4*x(f). Let r(n) = -5*n**2 - 2*n - 1. Let s(d) = r(d) - 4*y(d). Factor s(v).
-(v - 3)*(v + 1)
Let r be 3*((-52)/(-36) + -1). Let t(b) be the first derivative of -r*b**3 - 2*b**2 - 1/4*b**4 + 0*b + 1. Factor t(p).
-p*(p + 2)**2
Let c be (-198)/273 - (-2)/7. Let q = -2/13 - c. Suppose q*a**3 + 0 + 2/7*a + 4/7*a**2 = 0. What is a?
-1, 0
Let g(b) be the third derivative of -2/105*b**7 + 0*b**3 + 1/15*b**5 + 0 - 3*b**2 - 1/60*b**6 + 0*b + 1/12*b**4. Solve g(o) = 0 for o.
-1, -1/2, 0, 1
Suppose -3*l + 4 - 10 = 3*o, 4*o = 5*l + 37. Let t be 10/4 - o/6. What is y in -2/5*y**3 + 4/5 + 6/5*y + 0*y**t = 0?
-1, 2
Determine n, given that -3*n**4 + 99*n**3 - 103*n**3 - 11*n**4 = 0.
-2/7, 0
Let v be (-32)/12*(-2)/((-40)/(-6)). Solve -v*q + 2/5*q**3 + 0 + 2/5*q**2 = 0.
-2, 0, 1
Let t = 145/93 - 7/31. Find q, given that -2/3 + q + t*q**2 - 2/3*q**4 + q**5 - 2*q**3 = 0.
-1, 2/3, 1
Suppose -2*s = s - 6. Let n = s - 3/2. Let -1/2*j**3 + n*j**2 - 1/2*j**4 + 1/2*j + 0 = 0. Calculate j.
-1, 0, 1
Let p(r) = 2*r**4 + r**3 + r**2 - 4*r + 3. Let n(j) = -3*j**4 - j**3 - j**2 + 5*j - 4. Let u(x) = 3*n(x) + 4*p(x). Solve u(d) = 0 for d.
-1, 0, 1
Let t = -10 - -11. Suppose -3 + t = -q. Suppose 2/3 - 8/3*i**q + 2*i = 0. What is i?
-1/4, 1
Suppose 0 = -6*c + 4*c - 12. Let r be 5/(-225) + c/(-27). Determine b so that r*b**3 + 0 + 0*b**2 - 1/5*b = 0.
-1, 0, 1
Factor 3/4*f**2 - 3/4*f**4 + 0 + 0*f**3 + 0*f.
-3*f**2*(f - 1)*(f + 1)/4
Let x(u) be the third derivative of -u**5/60 + u**4/24 + u**3 + 30*u**2. Factor x(o).
-(o - 3)*(o + 2)
Let g(x) be the first derivative of x**6/120 - x**5/80 - x**4/48 + x**3/24 - 2*x + 4. Let n(k) be the first derivative of g(k). Find s, given that n(s) = 0.
-1, 0, 1
Find w such that 4*w**4 + 23*w**4 - 5*w**5 - 35*w**3 - 2*w**4 + 40*w - 3*w**2 - 2*w**2 - 20 = 0.
-1, 1, 2
Suppose 19 = -3*o - 29. Let q = o - -21. Find c such that 1/2*c - c**2 + c**4 - 1/2*c**q + 0 + 0*c**3 = 0.
-1, 0, 1
Suppose 5 = 5*n - 10. Let d be (-1 - -2) + 10/(-14). Solve 6/7*l**2 + 0 - d*l**n - 4/7*l = 0 for l.
0, 1, 2
Let f(i) be the second derivative of i**7/5040 - i**6/720 + i**5/360 - i**3/2 + 9*i. Let n(d) be the second derivative of f(d). Factor n(y).
y*(y - 2)*(y - 1)/6
Let d be (-3)/((-9)/(-2))*(-114)/152. Let 0 + d*s**5 + 0*s**4 - s**3 + 1/2*s + 0*s**2 = 0. What is s?
-1, 0, 1
Let x(o) be the first derivative of 2*o**5/55 - 2*o**3/33 - 2. Factor x(t).
2*t**2*(t - 1)*(t + 1)/11
Determine l so that -l**4 + 94*l**3 + 2*l + l**2 + 4*l**2 - 91*l**3 - l**5 = 0.
-1, 0, 2
Let d(h) be the first derivative of -h**6/3 + 3*h**5 - 41*h**4/4 + 17*h**3 - 29*h**2/2 + 6*h + 78. Let d(t) = 0. Calculate t.
1/2, 1, 2, 3
Let k(y) be the second derivative of -y**5/60 + y**4/18 - y**3/18 - 3*y. Factor k(x).
-x*(x - 1)**2/3
Let z(k) = 3*k**3 - k**2 - 2*k - 3. Let o(m) = -3*m**3 + 3*m + 4. Let u(h) = -3*o(h) - 4*z(h). Suppose u(f) = 0. Calculate f.
0, 1/3, 1
Let r(d) be the second derivative of 0 + 0*d**3 - 1/16*d**4 + 0*d**2 - 6*d. What is a in r(a) = 0?
0
Let s(q) be the first derivative of 2*q**6/3 - 8*q**5/5 - q**4 + 8*q**3/3 - 11. Determine l, given that s(l) = 0.
-1, 0, 1, 2
Let i(y) be the first derivative of -y**5/20 - 5*y**4/16 - y**3/2 + y**2/2 + 2*y + 20. What is r in i(r) = 0?
-2, 1
Suppose -m + 4*c - 6 = -4*m, 0 = -4*c. Find a such that 34 - 75*a - 27*a**3 + 90*a**m - 9*a - 10 = 0.
2/3, 2
Let p(l) = -5*l**2 + 20*l - 29. Let g(h) = -h**2 + h - 1. Let q(s) = 2*g(s) - p(s). Find o, given that q(o) = 0.
3
Solve -2/11*f**2 - 18/11*f + 0 = 0 for f.
-9, 0
Let d = -234 - -1178/5. Factor -8/5*u - 12/5*u**2 - 2/5*u**4 - 2/5 - d*u**3.
-2*(u + 1)**4/5
Let r(i) be the third derivative of i**7/210 + i**6/60 - 6*i**2. Determine d so that r(d) = 0.
-2, 0
Factor -2/11 + 2/11*r + 2/11*r**2 - 2/11*r**3.
-2*(r - 1)**2*(r + 1)/11
Let h(j) be the third derivative of -j**7/630 + j**6/30 - 3*j**5/1