1)/6
Let q = -5598/7 - -15506/21. Let h = q - -62. Suppose -h*c**2 + 2/3*c + 0 = 0. Calculate c.
0, 1
Let u = 15 - -64. What is m in 24*m - 25*m**3 + 4 + 3*m**2 + 54*m**4 - u*m**3 - 6*m**4 = 0?
-1/4, 2/3, 2
Suppose -1/7*r**5 + 0*r**3 + 1/7*r**4 + 0*r + 0*r**2 + 0 = 0. What is r?
0, 1
Let o(g) be the first derivative of -g**6/3 + 4*g**5/5 + g**4/2 - 4*g**3/3 - 11. Determine s so that o(s) = 0.
-1, 0, 1, 2
Factor -44*i**2 - 34 + 28*i**2 - 34*i - 18*i + 10 + 12*i**3.
4*(i - 3)*(i + 1)*(3*i + 2)
Suppose -a + 6 = 3. Factor 19*n + 4*n**2 + n**3 - a*n**2 - 19*n.
n**2*(n + 1)
Let h(y) = 4*y**5 - 7*y**4 + 3*y**3 + 3*y**2 - 3. Let c(t) = 8*t**5 - 15*t**4 + 7*t**3 + 7*t**2 - 7. Let r(u) = -3*c(u) + 7*h(u). Determine a so that r(a) = 0.
0, 1
Let y be (-12)/2 - (-56)/7. Suppose 3*s = -0*s. Solve 2/5*k**3 + 0*k - 2/5*k**y + s = 0.
0, 1
Let b be -2*(2 + 0 - 1). Let r be (-1)/b - (3 + -4). What is w in -r*w**2 + 3/2*w + 0 = 0?
0, 1
Let 4/17*u**3 + 0*u**2 - 2/17*u - 2/17*u**5 + 0*u**4 + 0 = 0. What is u?
-1, 0, 1
Suppose w - 4 = -3*v, 5*v - w + 4 = v. Solve -1/4*i**2 + v*i + 1/4 = 0.
-1, 1
Let d(r) be the second derivative of 0*r**2 + 3*r - 1/6*r**4 + r**3 + 0. Let d(q) = 0. Calculate q.
0, 3
Let q be 3 - (-4 - 146/(-21)). Let v(w) be the second derivative of q*w**3 + 2*w + 1/35*w**5 + 0 + 0*w**2 - 1/14*w**4. Find c such that v(c) = 0.
0, 1/2, 1
Find u such that 35 - 22*u - 6*u**2 - 156 + 5*u**2 = 0.
-11
Let j(m) = m**2 - m + 6. Let x be j(0). Let u(h) be the second derivative of 0*h**2 + 0*h**4 + 0 - 1/80*h**5 - 1/120*h**x + 0*h**3 + h. Solve u(z) = 0 for z.
-1, 0
Let v(m) be the first derivative of m**6/40 - m**5/8 - m**4/4 + 2*m**3/3 - 5. Let h(z) be the third derivative of v(z). Factor h(g).
3*(g - 2)*(3*g + 1)
Let w be 1/((-14)/4) + (-759)/(-231). Let p(o) be the first derivative of -2*o + 2/3*o**w - o**2 + 1/2*o**4 - 1. What is n in p(n) = 0?
-1, 1
Let 6/5 - 33/5*r + 48/5*r**2 - 21/5*r**3 = 0. What is r?
2/7, 1
Factor 831 + 5*r**2 - 831 - 5*r**4.
-5*r**2*(r - 1)*(r + 1)
Let t(m) be the first derivative of -4*m**3/3 + m**2 + 8. Factor t(q).
-2*q*(2*q - 1)
Let m be (-2954)/21*1/(-102). Let d = 31/17 - m. Factor -16/9*z**2 - 10/9*z**3 - 2/9*z + d.
-2*(z + 1)**2*(5*z - 2)/9
Suppose -2*s = 3*s - 2*s. Factor 0 + 0*k**2 - 4/3*k**3 + s*k + 0*k**4 + 4/3*k**5.
4*k**3*(k - 1)*(k + 1)/3
Factor -10*f**3 + 13*f**3 + 2 - f**5 - 2 + 5*f**2 - f**4 + 2*f.
-f*(f - 2)*(f + 1)**3
Let t(b) be the second derivative of 0 + 10*b - 1/15*b**3 - 1/15*b**4 + 2/5*b**2 + 1/50*b**5. Determine r, given that t(r) = 0.
-1, 1, 2
Let v(n) be the second derivative of n**4/28 + n**3/14 - 3*n**2/7 + 16*n. Determine d so that v(d) = 0.
-2, 1
Suppose -2 = -a + 3*a. Let d(t) = 3*t**2 + 3*t. Let u(v) = v**2 + v. Let l(r) = a*d(r) + 4*u(r). What is x in l(x) = 0?
-1, 0
Suppose -13*p - 6*p + 7*p = 0. Factor -14/9*s**2 + 10/3*s**3 + 2/9*s + p - 2*s**4.
-2*s*(s - 1)*(3*s - 1)**2/9
Suppose 4*c - c + 3*m = 21, 0 = -2*m + 10. Let p(a) be the first derivative of 0*a**c + 4 + 5/2*a**4 + 4/3*a**3 - 24/5*a**5 + 0*a. Factor p(w).
-2*w**2*(3*w - 2)*(4*w + 1)
Let 19*c**3 + 11*c**3 - 3*c**4 - 33*c**3 = 0. What is c?
-1, 0
Suppose -5*x = -4*x. Find b, given that 2/13*b**4 + 0*b + 6/13*b**3 + 4/13*b**2 + x = 0.
-2, -1, 0
Let m be (-6)/(-33)*99/63. Let r be 2 + ((-8)/(-14) - 2). Solve -r - 8/7*c**2 - m*c**3 - 10/7*c = 0 for c.
-2, -1
Let h(a) be the third derivative of -a**8/1848 + 4*a**7/1155 - a**6/132 + a**5/165 + 11*a**2. What is y in h(y) = 0?
0, 1, 2
Let c = 1131/10 - 113. Let r(z) be the second derivative of z + c*z**6 + 1/42*z**7 + 0*z**2 + 0*z**3 + 3/20*z**5 + 1/12*z**4 + 0. Factor r(l).
l**2*(l + 1)**3
Let h(i) be the first derivative of -1/6*i**6 + 1/2*i**4 - 1/2*i**2 + 0*i**3 + 0*i**5 + 0*i + 3. Find r, given that h(r) = 0.
-1, 0, 1
Let b(m) be the first derivative of 0*m + 1 + 1/3*m**4 - 2/15*m**5 + 0*m**2 - 2/9*m**3. Factor b(q).
-2*q**2*(q - 1)**2/3
Let k be 3*(186/(-21) + 9). Factor 3/7*j**4 - 3/7*j + 3/7*j**3 - k*j**2 + 0.
3*j*(j - 1)*(j + 1)**2/7
Factor 193 + 5*f**2 - 60*f - 37 + 24.
5*(f - 6)**2
Let p be 6 + 0 + 2/(-1). Factor -10*u**2 - 12*u - 8*u**2 - 7*u**3 - 3*u**p - 3 - 5*u**3.
-3*(u + 1)**4
Let k(q) be the first derivative of -q**6/12 + q**4/2 + q**3/3 - 3*q**2/4 - q + 1. Factor k(v).
-(v - 2)*(v - 1)*(v + 1)**3/2
Let t(u) = u**4 - 2*u**2 - 4*u. Let s(n) be the second derivative of -n**4/12 - n**3/2 + n. Let g(b) = -5*s(b) + 4*t(b). Factor g(o).
o*(o - 1)*(2*o + 1)**2
Let s be 4/(-22) - (1 + 70/(-22)). Factor 2*y + 1/2*y**s + 2.
(y + 2)**2/2
Let i(q) be the first derivative of -q**6/30 + 2*q**5/25 + 3*q**4/20 - 4*q**3/15 - 2*q**2/5 + 3. Factor i(p).
-p*(p - 2)**2*(p + 1)**2/5
Let f(w) be the first derivative of -2*w**3/5 + 3*w**2/10 + 3*w/5 + 16. Factor f(k).
-3*(k - 1)*(2*k + 1)/5
Let h(w) be the first derivative of -1 + w**2 + 2*w + 1/6*w**3. Factor h(r).
(r + 2)**2/2
Let j(b) be the third derivative of b**7/70 + 13*b**6/120 + 29*b**5/90 + b**4/2 + 4*b**3/9 + 4*b**2. Factor j(p).
(p + 1)*(p + 2)*(3*p + 2)**2/3
Let o(n) = 5*n - 1. Let m be o(1). Let k(u) be the second derivative of 0*u**3 + u**2 - 1/3*u**m + 1/15*u**6 + 0*u**5 + 2*u + 0. Factor k(x).
2*(x - 1)**2*(x + 1)**2
Let h(t) = t**3 + 2*t**2 - 2*t - 4. Suppose z = 3*f + 13, 20 + 10 = -5*z - 4*f. Let a be h(z). Factor 1/3*y**4 + 0 + 1/3*y**2 + 2/3*y**3 + a*y.
y**2*(y + 1)**2/3
Suppose 2*z = 3*z - 5. Suppose l - 7 = -2*l + 2*f, -z*l + 5*f + 10 = 0. Find n, given that -n**5 + 2*n**3 + n**3 - 5*n**l - 3*n**4 = 0.
-2, -1, 0
Suppose 2/3*k**2 + 32/3 + 16/3*k = 0. Calculate k.
-4
Let u(b) be the third derivative of b**6/180 - b**5/90 - b**4/36 + b**3/9 - 3*b**2. Factor u(w).
2*(w - 1)**2*(w + 1)/3
Let x(a) be the second derivative of 7*a**7/1440 + 7*a**6/720 + a**5/120 + a**4/12 - 2*a. Let g(h) be the third derivative of x(h). Factor g(m).
(7*m + 2)**2/4
Let m be 144/(-42) - (-6)/1. Suppose 0*c**3 + 24/7*c - 9/7 + 3/7*c**4 - m*c**2 = 0. What is c?
-3, 1
Let d be (-2 - 2)/(4/(-6)). Let x be (-1 - (-4)/(-2)) + d. Determine j so that 2*j**x - 1/2*j**2 + 0*j + 0 = 0.
0, 1/4
Solve 2/7*y**3 - 4/7*y**2 + 0 + 2/7*y = 0 for y.
0, 1
Let y be 16/40 + (1 - 8/(-5)). Factor -18/5*p**4 + 0 + 0*p**2 + 14/5*p**5 + 4/5*p**y + 0*p.
2*p**3*(p - 1)*(7*p - 2)/5
Let i = -6 - -10. Let c be i/3 + 1 + -2. What is y in 0 + 0*y + c*y**4 - 1/3*y**2 + 0*y**3 = 0?
-1, 0, 1
Factor 30*z**2 + 29*z**2 - 93*z**2 + 3*z + 35*z**2 + 2.
(z + 1)*(z + 2)
Suppose 1 = 4*x - 3*v, -5 = x - 0*x + v. Let n be x/4*(-2)/3. Find s, given that 2/3 + 1/3*s - n*s**2 = 0.
-1, 2
Let u be (-60)/(-35) + (-6)/(-21). Factor 1/3*g**3 + 4/3*g - 4/3*g**u + 0.
g*(g - 2)**2/3
Let r(t) = -28*t**4 + 36*t**3 - 8*t**2 + 20*t. Let c(l) = -4*l**4 + 5*l**3 - l**2 + 3*l. Let u(b) = -20*c(b) + 3*r(b). Factor u(o).
-4*o**2*(o - 1)**2
Factor 3*d + d**2 + 3*d - 22*d**2 - 14*d**3 - 15*d**4 + 3*d**5 + 41*d**3.
3*d*(d - 2)*(d - 1)**3
Let q be 3/6*0/1. Let y(h) be the second derivative of 0 - 1/147*h**7 + 0*h**2 + 1/35*h**6 + 2*h + q*h**3 + 1/42*h**4 - 3/70*h**5. Factor y(s).
-2*s**2*(s - 1)**3/7
Let 4/5*u - 6/5 + 2/5*u**2 = 0. What is u?
-3, 1
Let o(p) be the third derivative of p**6/132 + 7*p**5/330 + p**4/66 - 2*p**2. Determine s, given that o(s) = 0.
-1, -2/5, 0
Let q be 7/(-11)*(-48)/14 + -2. Factor 0*n + 2/11*n**2 + 0 + q*n**3.
2*n**2*(n + 1)/11
Suppose -56/9*l**5 + 0 - 2/9*l**4 + 4/9*l**3 + 0*l**2 + 0*l = 0. Calculate l.
-2/7, 0, 1/4
Let d = 177 - 879/5. Suppose 3/5*z**3 + d - 6/5*z**2 - 3/5*z = 0. What is z?
-1, 1, 2
Let p be 140/25 + (-4)/(-10). Suppose 2*l + 5*w + 21 = 0, w + p = -2*l - w. Factor a**2 - 4*a**3 - a**4 + a**3 - a - 4*a**l.
-a*(a + 1)**3
Let y be (3/12)/(5/(-240)*-4). Factor -2/9*d**y + 4/9*d + 2/9*d**2 + 0.
-2*d*(d - 2)*(d + 1)/9
Let y(f) be the third derivative of 0*f**7 + 0*f + 1/1344*f**8 + 0*f**3 - 1/480*f**6 + 0*f**5 + 0*f**4 + 0 + 2*f**2. Factor y(s).
s**3*(s - 1)*(s + 1)/4
Let b(p) = p**2 - 4*p + 2. Let r be b(4). Suppose -3*f**2 + 4 - 4 + f**r = 0. Calculate f.
0
Factor 2/9*g**3 - 2/9*g**2 + 2/9*g**4 + 0 - 2/9*g**5 + 0*g.
-2*g**2*(g - 1)**2*(g + 1)/9
Suppose 0 = 3*d - 0 - 6. Suppose -2*g = d*g - 12. Factor 2*m + 6*m**3 + 4*m**2 + m**g - 5*m**3 + 0*m.
2*m*(m + 1)**2
Suppose -x - 2 = -4*k, 4*x + k = -3*k - 8. Let f = 4 + x. Factor b - 1/2 - 1/2*b**f.
-(b - 1)**2/2
Let j(w) = w. Let q(