 0 = m + 2*m - 3. Let t(o) = m*p(o) - 24*i(o). Factor t(a).
4*a**2*(a - 1)
Let h be (-9)/12 - (-35)/28. Determine k, given that k**2 + 1/2*k**3 + h*k + 0 = 0.
-1, 0
Solve -3*j**3 + 5*j**3 + 5*j**2 - 3*j**2 = 0 for j.
-1, 0
Let u(k) be the third derivative of k**8/7560 + k**7/1260 + k**6/1620 + k**4/8 + 5*k**2. Let g(l) be the second derivative of u(l). Factor g(s).
2*s*(s + 2)*(4*s + 1)/9
Let w(b) be the first derivative of 2*b**3/15 + b**2 + 8*b/5 + 29. Factor w(v).
2*(v + 1)*(v + 4)/5
Let i(z) be the first derivative of -z**4/4 - z**3/3 + z - 2. Let o(u) = -5*u**3 + 4*u**2 - 3*u + 2. Let y(m) = 2*i(m) - o(m). Factor y(p).
3*p*(p - 1)**2
Let m(a) be the third derivative of 1331*a**6/420 + 121*a**5/35 + 11*a**4/7 + 8*a**3/21 + 2*a**2. Factor m(f).
2*(11*f + 2)**3/7
Let a(b) be the third derivative of -b**7/1260 + b**5/60 - b**4/24 + 3*b**2. Let u(t) be the second derivative of a(t). Factor u(z).
-2*(z - 1)*(z + 1)
Suppose 2*b + 2 = 4*r + 6, 0 = -5*r. Find k such that -6*k**3 + 0*k**b - 2*k + 0*k**2 + 2 - 10*k**2 = 0.
-1, 1/3
Determine q, given that -119*q**2 + 0*q + 6*q + 121*q**2 = 0.
-3, 0
Factor -m - 5/2*m**2 + 0.
-m*(5*m + 2)/2
Let w = 204 - 321. Let a = w - -821/7. Determine c, given that -34/7*c**2 - 12/7*c**4 + 2*c - a + 34/7*c**3 = 0.
1/3, 1/2, 1
Let 1/2*i**2 + 0 - 1/4*i**3 - 1/4*i = 0. What is i?
0, 1
Let g(s) be the first derivative of 27/4*s**4 - 6*s - 5*s**3 - 27/2*s**2 + 21/5*s**5 - 2. Determine z, given that g(z) = 0.
-1, -2/7, 1
Let d(c) = c**3 - c**2 + c + 3. Let f(r) = -2*r**3 + r**2 - r - 4. Suppose 5*y - 9 = 2*y. Let m(h) = y*d(h) + 2*f(h). Find t, given that m(t) = 0.
-1, 1
Factor 2/3*j**2 + 2/9*j**3 + 2/3*j + 2/9.
2*(j + 1)**3/9
Let o be 2/(-7) - (-108)/(-14). Let n be (4/5)/(o/(-20)). Factor -1/4*l**n + 1/2*l - 1/4.
-(l - 1)**2/4
Suppose 34*w = 38*w - 8. Factor 2/3*l - 2/3*l**4 + 2/3*l**w + 0 - 2/3*l**3.
-2*l*(l - 1)*(l + 1)**2/3
Find d, given that 17 + 9 - 5*d**4 + 27 - 90*d**2 - 20*d + 67 + 45*d**3 = 0.
-1, 2, 6
Let o(n) = n**2 - 2*n. Let u be 220/50 - (-2)/(-5). Let q(k) = -k. Let l be (2/2)/((-2)/2). Let r(a) = l*o(a) + u*q(a). Determine d, given that r(d) = 0.
-2, 0
Let d(x) be the second derivative of -x**4/16 - x**3/8 - 6*x. Factor d(t).
-3*t*(t + 1)/4
Let y(k) be the third derivative of k**5/20 + 3*k**4/8 + 69*k**2. Factor y(p).
3*p*(p + 3)
Let z be (-9)/(-60) + 7/28. Determine x so that -1/5*x**3 - 4/5*x**2 - z - x = 0.
-2, -1
Let a(k) = 2*k + 4. Let j be a(-3). Let x = j - -4. Solve 1/2 - b**x + 1/2*b = 0 for b.
-1/2, 1
Let a(j) be the first derivative of j**5/270 - j**4/54 + j**3/27 - j**2 + 3. Let q(y) be the second derivative of a(y). Solve q(o) = 0.
1
Let m(x) be the first derivative of -x**5/60 - x**4/4 - 3*x**3/2 + x**2 - 6. Let v(z) be the second derivative of m(z). Solve v(o) = 0.
-3
Let s = 861 + -861. Factor 4/9*r**3 - 2/9*r**4 + 0*r + 0 + s*r**2.
-2*r**3*(r - 2)/9
Let j(k) be the first derivative of 3*k**5/5 + 3*k**4/4 - k**3 - 3*k**2/2 + 6. Suppose j(g) = 0. What is g?
-1, 0, 1
Let i(p) be the first derivative of p**6/24 - p**5/10 - 7*p**4/16 - p**3/3 + 12. Factor i(m).
m**2*(m - 4)*(m + 1)**2/4
Let b(n) be the second derivative of -n**4/30 - 2*n**3/3 - 5*n**2 - 13*n. Solve b(a) = 0 for a.
-5
Let g = 101 + -98. Factor -g*d + 1 + 5/4*d**2.
(d - 2)*(5*d - 2)/4
What is b in 3025*b**4 + 245*b**2 + 0 + 0 + 13*b - 23*b - 1760*b**3 = 0?
0, 1/11, 2/5
Let q(t) be the third derivative of -t**8/20160 + t**7/5040 - t**5/10 - 5*t**2. Let g(z) be the third derivative of q(z). Factor g(j).
-j*(j - 1)
Let q(j) be the second derivative of j**2 - 1/3*j**3 + 0 - j - 1/8*j**4 + 1/30*j**5. Let x(h) be the first derivative of q(h). Find a, given that x(a) = 0.
-1/2, 2
Let v = -33 + 33. Let u = 7/2 - 17/6. Factor 0 - u*q**2 + 1/3*q - 1/3*q**5 + v*q**3 + 2/3*q**4.
-q*(q - 1)**3*(q + 1)/3
Suppose 2*p + 16 = 3*a, 5*a = 10*a + 2*p - 16. Let 0*h**3 - 1/3*h + 0 - 2/3*h**a + 2/3*h**2 + 1/3*h**5 = 0. Calculate h.
-1, 0, 1
Let d(o) be the second derivative of 0*o**3 - 1/10*o**6 - 3*o + 0 - 1/12*o**4 + 0*o**2 - 1/42*o**7 - 3/20*o**5. Suppose d(u) = 0. What is u?
-1, 0
Let g = 44 - 54. Let a be 1/(-2)*(8 + g). Factor -19/4*m**3 - 25/4*m**2 - 1/4*m**5 - 7/4*m**4 - 4*m - a.
-(m + 1)**3*(m + 2)**2/4
Factor 4/13*h**3 + 0*h**2 - 4/13*h + 2/13 - 2/13*h**4.
-2*(h - 1)**3*(h + 1)/13
Find v, given that 2/3*v**4 + 2/9*v**5 - 2/9 - 4/9*v**2 - 2/3*v + 4/9*v**3 = 0.
-1, 1
Let x be 0/(3/6*(-2 - 0)). Let c = 0 - 0. Factor x*g + 4/3*g**2 - 2/3*g**3 - 2*g**4 + c.
-2*g**2*(g + 1)*(3*g - 2)/3
Let n(s) be the second derivative of 2*s + 4*s**2 - 2*s**3 + 1/2*s**4 + 0 - 1/20*s**5. Factor n(l).
-(l - 2)**3
Let d(r) be the third derivative of r**7/70 + r**6/40 - r**5/20 - r**4/8 - 7*r**2. Factor d(f).
3*f*(f - 1)*(f + 1)**2
Let v(f) be the second derivative of 0*f**3 - 1/36*f**4 - 1/90*f**6 - 4*f + 0*f**2 + 1/30*f**5 + 0. Factor v(u).
-u**2*(u - 1)**2/3
Factor 96/5 - 2/5*z**3 - 16*z + 22/5*z**2.
-2*(z - 4)**2*(z - 3)/5
Find a such that 15*a + 6*a**2 - 11*a - 10*a**2 = 0.
0, 1
Let h(y) be the second derivative of 0 + 1/12*y**4 + 1/3*y**3 + 3*y + 0*y**2. Factor h(s).
s*(s + 2)
Let n(g) be the second derivative of -5*g**5/4 - 5*g**4/6 + 25*g**3/6 + 5*g**2 - 5*g. Factor n(s).
-5*(s - 1)*(s + 1)*(5*s + 2)
Let x(o) = -o. Let q(a) = a**3 - 2*a**2 + a + 2. Let g(u) = -q(u) - 2*x(u). Suppose g(b) = 0. What is b?
-1, 1, 2
Let h be (2/70*2)/(25/125). Factor 0 + 0*s - h*s**2.
-2*s**2/7
Suppose -h - h = 0. Suppose 12 = -2*l + 6*l. Factor 0*d + d + h*d - d**l.
-d*(d - 1)*(d + 1)
Let x = 1179 + -1177. Determine u, given that 0*u**3 + 2/3*u**4 + 0 - 2/3*u**x + 0*u = 0.
-1, 0, 1
Let f(l) be the third derivative of l**5/210 + l**4/84 - 2*l**3/21 + l**2. Factor f(k).
2*(k - 1)*(k + 2)/7
Suppose 0 = 3*l - 4*l + 4. Factor -h**4 + l*h - 5 + 5 - 3*h**2 - 3*h**3 - 5*h.
-h*(h + 1)**3
Let n(z) be the third derivative of z**5/100 - z**4/10 + 3*z**3/10 - z**2. Solve n(s) = 0.
1, 3
Solve 169/2 - 13*a + 1/2*a**2 = 0.
13
Let t(s) be the first derivative of -s**6/10 + 27*s**5/25 - 9*s**4/2 + 46*s**3/5 - 99*s**2/10 + 27*s/5 + 4. Solve t(y) = 0 for y.
1, 3
Let r(t) be the third derivative of t**10/302400 - t**9/362880 + t**5/20 - 4*t**2. Let p(s) be the third derivative of r(s). Factor p(q).
q**3*(3*q - 1)/6
Factor 5/2*l**4 + 15/2*l**3 - 20 - 5*l**2 - 30*l.
5*(l - 2)*(l + 1)*(l + 2)**2/2
Let a(k) be the second derivative of k**5/10 - k**4/6 - 5*k**3/3 - 3*k**2 - 8*k. Factor a(x).
2*(x - 3)*(x + 1)**2
Let j(p) be the third derivative of p**7/70 - 3*p**5/20 - p**4/4 + 22*p**2. Suppose j(l) = 0. Calculate l.
-1, 0, 2
Determine n, given that -2*n**4 - 2*n + 2/3 + 2/3*n**5 + 4/3*n**3 + 4/3*n**2 = 0.
-1, 1
Let b = -62 + 64. Factor -3*u - 1/2 - 9/2*u**b.
-(3*u + 1)**2/2
Let l be (1 - 0)*(4 + -3). Let d(z) = 4*z**3 - 1. Let g be d(l). Let -2*v**2 - 15*v**3 + 9*v**2 + 15*v**2 - 12*v + g*v**4 + 2*v**2 = 0. What is v?
0, 1, 2
Let n(w) be the third derivative of -w**5/660 - 5*w**4/132 - 25*w**3/66 + 6*w**2. Factor n(r).
-(r + 5)**2/11
Let a be (-9)/(-45) + 1/(-5). Let s(b) be the second derivative of 1/45*b**6 + 0 + 0*b**5 - 2*b + 0*b**2 - 1/18*b**4 + a*b**3. Solve s(t) = 0.
-1, 0, 1
Factor 2/11*u**2 + 2/11*u + 0.
2*u*(u + 1)/11
Solve 2*u - 1/2*u**2 - 2 = 0.
2
Let c(a) be the third derivative of -a**7/6300 - a**6/300 - 3*a**5/100 - a**4/24 - 2*a**2. Let y(j) be the second derivative of c(j). Factor y(u).
-2*(u + 3)**2/5
Let q(b) be the first derivative of 5*b**6/18 - 4*b**5/5 + 3*b**4/4 - 2*b**3/9 - 5. Determine z, given that q(z) = 0.
0, 2/5, 1
Let d(q) be the second derivative of -q**4/84 + q**3/21 - q**2/14 - 6*q. Determine a, given that d(a) = 0.
1
Let b(f) be the first derivative of 6*f**5/55 - 6*f**3/11 + 6*f**2/11 + 16. Determine c so that b(c) = 0.
-2, 0, 1
Suppose 32 = h - 5*h. Let y = h + 11. Factor 2*q**2 + y*q**3 - 4*q**3 + 0*q**2 - q.
-q*(q - 1)**2
Let u(i) be the third derivative of 2*i**7/105 - 11*i**6/90 + 31*i**5/180 + 5*i**4/18 - 2*i**3/9 + 29*i**2 - i. Suppose u(f) = 0. Calculate f.
-1/2, 1/6, 2
Let q be 2/(-2)*(0 - 7/28). Determine p, given that -p**2 - 5/4*p**4 - 2*p**3 + 0 + 0*p - q*p**5 = 0.
-2, -1, 0
Let l(n) be the third derivative of -n**6/180 + n**5/45 - 4*n**2. Factor l(v).
-2*v**2*(v - 2)/3
Let z = -2 + 2. Let 8*k**2 + 12*k**3 + 10/3*k**4 - 16/3*k + z = 0. What is k?
-