n**4 - 1/4*n**3 + 0*n + 1/2*n**2 = 0.
-2, 0, 1
Let a(r) be the third derivative of -r**9/7560 - r**8/1680 - r**7/1260 + r**4/12 + 2*r**2. Let n(u) be the second derivative of a(u). Factor n(m).
-2*m**2*(m + 1)**2
Let x(h) be the first derivative of h**5/80 - h**4/24 - h + 2. Let m(j) be the first derivative of x(j). Factor m(t).
t**2*(t - 2)/4
Determine n so that 0*n**3 + 0 + 3/4*n**4 + 0*n - 3/4*n**2 = 0.
-1, 0, 1
Let l = -5/151 + 1384/755. Let j(k) be the first derivative of -3 - 3/2*k**4 + l*k**5 + 0*k + 3*k**2 - 3*k**3. Factor j(t).
3*t*(t - 1)*(t + 1)*(3*t - 2)
Let r = -11 - -23. Let w be 18/(-12) - (-22)/r. Find o, given that w*o**2 - 1/3 + 0*o = 0.
-1, 1
Let o = 231 - 231. Factor 0*w**2 - 1/4*w**5 + 0*w + o*w**4 + 1/4*w**3 + 0.
-w**3*(w - 1)*(w + 1)/4
Let b(o) = -9*o**5 - 27*o**4 - 23*o**3 - 3*o**2 + 2. Let w(v) = -v**4 - v**3 - v + 1. Let u be (2 - 1)/(-1 - -2). Let s(z) = u*b(z) - 2*w(z). Factor s(k).
-k*(k + 1)**3*(9*k - 2)
Factor 11/2*t + 11/4*t**2 + 1/8*t**3 + 3 - 1/8*t**4.
-(t - 6)*(t + 1)*(t + 2)**2/8
Let f(i) be the third derivative of 9*i**7/70 + 3*i**6/5 + 13*i**5/20 + i**4/4 + 4*i**2. Suppose f(n) = 0. Calculate n.
-2, -1/3, 0
Let h be 6/(0 + 6) + (0 - 1). Let m(q) be the second derivative of 3*q + 0*q**4 + h*q**2 - 1/90*q**5 + 0*q**3 - 1/45*q**6 - 2/189*q**7 + 0. Factor m(p).
-2*p**3*(p + 1)*(2*p + 1)/9
Let j(r) be the third derivative of -3*r**2 + 0*r + 1/66*r**5 + 7/660*r**6 + 0 - 1/66*r**4 + 0*r**3. Factor j(l).
2*l*(l + 1)*(7*l - 2)/11
Let u be (-3 - -3)/(-1 - -3). Suppose 5*w - 15 = -u*w. Factor -w*t**5 - 2*t**2 + 4*t**5 + t**5 + 6*t**3 - 6*t**4.
2*t**2*(t - 1)**3
Suppose -4*x + 1 = -7. Let -10 - x - 9*f**3 + 21*f**2 + 18*f**3 = 0. What is f?
-2, -1, 2/3
Factor -2/3*b - 4/9 - 2/9*b**2.
-2*(b + 1)*(b + 2)/9
Let y(n) be the first derivative of 0*n**2 - 1/2*n**4 - 1 + 0*n + 2/3*n**3. What is v in y(v) = 0?
0, 1
Let w be 6 + -1 - (-70)/(-20). Factor w*m - 3/2*m**2 - 1/2 + 1/2*m**3.
(m - 1)**3/2
Let o(s) be the third derivative of -s**7/945 + s**6/90 - 2*s**5/45 + 5*s**4/54 - s**3/9 + 9*s**2. Factor o(g).
-2*(g - 3)*(g - 1)**3/9
Let m be 2 - -3*(-4)/(-6). Let t(c) = -4*c**2 - c + 5. Let n(b) = 4*b - 3 + 3*b**2 - 1 - 3*b. Let o(x) = m*t(x) + 6*n(x). Factor o(h).
2*(h - 1)*(h + 2)
Let f(m) be the first derivative of m**3/12 + m**2/8 + 1. Factor f(v).
v*(v + 1)/4
Let v(k) be the first derivative of -k**4/20 - 2*k**3/15 - k**2/10 - 8. What is p in v(p) = 0?
-1, 0
Let k be 20/(-6)*24/(-10). Suppose k*q = 3*q. Solve 0 - 2/7*g**5 + 6/7*g**4 + q*g - 6/7*g**3 + 2/7*g**2 = 0 for g.
0, 1
Let a(p) be the third derivative of -2*p**2 + 0 + 0*p + 1/780*p**6 + 0*p**3 - 1/78*p**4 + 1/390*p**5. Let a(f) = 0. Calculate f.
-2, 0, 1
Let x be (16/(-84))/((-6)/9). Let m(c) be the first derivative of 2/7*c + 1 + 2/21*c**3 - x*c**2. Factor m(s).
2*(s - 1)**2/7
Factor -20*y**3 - 20*y**2 + 9*y + 8*y**2 + 4*y**2 + 3*y.
-4*y*(y + 1)*(5*y - 3)
Let a(k) be the second derivative of -k**4/21 + 2*k**3/21 + 4*k**2/7 + 4*k. Let a(q) = 0. What is q?
-1, 2
Let g(a) be the second derivative of -3*a - a**2 + 0 - a**3 - 1/2*a**4 - 1/10*a**5. Factor g(u).
-2*(u + 1)**3
Let n be (-4)/(-5)*20/8. Factor -2*w**2 - 5*w**3 - w**2 + 2*w**n + 3*w**3.
-w**2*(2*w + 1)
Let l(t) be the second derivative of t**3/2 - 3*t**2 - 3*t. Let k be l(5). Factor -3*j**2 + k*j**2 + 4*j**3 + 3*j - j**3.
3*j*(j + 1)**2
Let l(i) be the third derivative of 39*i**7/140 + 391*i**6/1200 - 23*i**5/60 - 7*i**4/60 + 2*i**3/15 - i**2 + 3*i. Suppose l(r) = 0. What is r?
-1, -2/9, 2/13, 2/5
Let u(o) = o**3 + 4*o**2 + o + 2. Let g be u(-4). Let i = 6 + g. Let 1/2*b - 1/2*b**i - 1/2*b**3 + 0 + 1/2*b**2 = 0. What is b?
-1, 0, 1
Let y = 15 + -13. Factor 3*m**3 - 3*m**3 + m**5 - y*m**4 + 2*m**5.
m**4*(3*m - 2)
Let d(n) = n - 2. Let f be d(-2). Let x be (-27)/(-12) - f/(-2). Factor 1/4*v**5 + 0 - 1/4*v**2 - x*v**3 + 1/4*v**4 + 0*v.
v**2*(v - 1)*(v + 1)**2/4
Let y be 9*(11 + 0/(-2)). Let w be 3/(-2)*(-12)/y. Suppose 0*g + w - 2/11*g**2 = 0. Calculate g.
-1, 1
Let t(n) be the first derivative of n**5/6 - n**4 + 35*n**3/18 - n**2 - 2*n/3 + 4. Factor t(o).
(o - 2)**2*(o - 1)*(5*o + 1)/6
Determine t, given that -19*t - t + 35 + 15 + 2*t**2 = 0.
5
Let y = 217 - 1955/9. Let w = y - -32/63. Factor w*n**2 + 4/7*n + 2/7.
2*(n + 1)**2/7
Let b(n) be the second derivative of -n + 0*n**4 + 0*n**6 - 1/5*n**5 + 1/21*n**7 + 0 + 1/3*n**3 + 0*n**2. Factor b(x).
2*x*(x - 1)**2*(x + 1)**2
Let o(y) = y**3 + 8*y**2. Let j be o(-8). Suppose 4*b - 2*r - r - 9 = j, -2*b = -3*r - 3. Find c such that -3*c + 1 + c**2 - b + 4*c = 0.
-2, 1
Let i(z) be the second derivative of -z**6/150 + 7*z**4/60 + z**3/5 + 62*z. Determine k so that i(k) = 0.
-2, -1, 0, 3
Let p(z) = -2*z**3 - 15*z**2 - 43*z + 3. Let h(w) = 2*w**3 + w**2 + w - 1. Let t(y) = 3*h(y) + p(y). What is j in t(j) = 0?
-2, 0, 5
Let r be 2500/14 + -10 + 9. Let d = -177 + r. Factor -10/7*g + d*g**2 - 4/7 + 10/7*g**3.
2*(g - 1)*(g + 1)*(5*g + 2)/7
Factor -5684*f**2 + 51 + 14*f + 5685*f**2 - 2.
(f + 7)**2
Factor 4 + 0*p + 2 - 3*p**2 - p - 2*p.
-3*(p - 1)*(p + 2)
Let j be (-1170)/(-91)*(-2)/(-5). Determine z, given that -38/7*z**4 - 16/7*z - 8/7*z**3 + j*z**2 + 2/7 + 24/7*z**5 = 0.
-1, 1/4, 1/3, 1
Let w(n) = -n**2 + 3*n - 1. Let o be w(1). Let r(p) be the first derivative of 0*p**3 - o + 1/7*p**2 - 1/14*p**4 + 0*p. Find t, given that r(t) = 0.
-1, 0, 1
Let n be -4*4/((-16)/(-6)). Let c be (-5)/(-2) + (-3)/n. Solve 1 + c*r + r**2 - 2*r - 3*r = 0 for r.
1
Let z(j) be the third derivative of j**9/1512 + j**8/420 - j**6/90 - j**5/60 - j**3/6 - 5*j**2. Let s(g) be the first derivative of z(g). Factor s(d).
2*d*(d - 1)*(d + 1)**3
Let o(g) = g**2 - g + 1. Let d(z) = 9*z**2 - 6*z + 9. Let w(j) = d(j) - 12*o(j). Solve w(f) = 0 for f.
1
Let u(h) = h**2 + h - 9. Let k be u(-7). Let s be (-2)/16 + k/72. Solve 0 - 2/3*a + s*a**3 + 1/3*a**2 = 0 for a.
-2, 0, 1
Let z(r) be the third derivative of r**6/240 - r**5/40 + r**4/24 - 3*r**2. Determine a so that z(a) = 0.
0, 1, 2
Suppose -b = 2*b + 3*z - 21, 13 = -b + 3*z. Factor -1/2*q**b - 1/4 + 3/4*q**4 + 1/4*q**5 + 1/2*q**3 - 3/4*q.
(q - 1)*(q + 1)**4/4
Factor 0*u**4 + 1/3*u**5 - 1/3*u**3 + 0 + 0*u**2 + 0*u.
u**3*(u - 1)*(u + 1)/3
Let h = -3 - -2. Let c = 9 + h. Find t, given that -t**3 - 2*t + 4*t**2 - t**3 - c*t**2 = 0.
-1, 0
Let q(k) be the third derivative of k**6/200 + 13*k**5/300 + 3*k**4/20 + 4*k**3/15 - 58*k**2. Factor q(p).
(p + 1)*(p + 2)*(3*p + 4)/5
Find v, given that -v**4 + 5*v**4 + 4*v**5 - 3*v**4 = 0.
-1/4, 0
Let m(r) be the first derivative of -2/15*r**3 + 5 + 6/5*r - 2/5*r**2. Factor m(v).
-2*(v - 1)*(v + 3)/5
Let x(b) be the second derivative of b**7/28 - b**6/20 - 3*b**5/40 + b**4/8 - b. Factor x(t).
3*t**2*(t - 1)**2*(t + 1)/2
Suppose l + 4 = 3*l. Let h(t) = -t**3 - 5*t**2 - t - 3. Let k be h(-5). Solve 2*g - g**l - k*g + g = 0 for g.
0, 1
Let z(c) be the first derivative of -c**5/90 - c**4/54 + c**3/27 - 4*c**2 + 8. Let h(y) be the second derivative of z(y). Determine n so that h(n) = 0.
-1, 1/3
Let i = -19/60 - -2/5. Let t(z) be the second derivative of 1/12*z**4 + z + 0 - 1/40*z**5 - i*z**3 + 0*z**2. Solve t(q) = 0 for q.
0, 1
Let v(m) be the third derivative of m**6/120 - m**5/20 + m**4/8 + m**3/2 - 5*m**2. Let q(y) be the first derivative of v(y). Solve q(g) = 0.
1
Suppose 2*m - 4*j = -32, -3*m - 2*j = 9 - 1. Let v be 38/20 - m/12. Solve -2/5*b**4 + v*b**3 - 8/5 + 24/5*b - 26/5*b**2 = 0 for b.
1, 2
Let f(s) be the third derivative of -s**7/840 - s**6/160 - s**5/80 - s**4/96 + s**2. Suppose f(p) = 0. What is p?
-1, 0
Suppose -12 + 12 = -3*x. Factor 2/5*j**2 + x + 4/5*j.
2*j*(j + 2)/5
Let h(d) = -d**2 - 1. Let i(p) = 4*p**4 + 12*p**3 + 8*p**2 + 4*p - 4. Let m(s) = 4*h(s) - i(s). Factor m(r).
-4*r*(r + 1)**3
Let i be -2 - -2 - -29 - -1. Factor 2*j**3 - j**3 + 32*j**2 - j**4 - i*j**2.
-j**2*(j - 2)*(j + 1)
Suppose -4*s + 24 = -0*s. Let r be ((-19)/s - -3)*-4. Suppose 2/3*c**2 + r*c + 0 = 0. What is c?
-1, 0
Let i(a) be the second derivative of a**5/10 + a**4/3 - 7*a**3/3 + 4*a**2 + 21*a. Let i(h) = 0. What is h?
-4, 1
Let j be 2/(4 - 3) - -2. Let z = 6 - j. Factor 13*a - 3 + 1 - 10*a - a**z.
-(a - 2)*(a - 1)
Suppose 4*n - 11 = k - 0*k, -5*n = -2*k - 7. Let u be (k/36)/(6/8). Factor 0*i - 1/3*i**2 + u.
-(i - 1)*(i + 1)/3
Let d be