5 - 5*t**2. Determine c, given that o(c) = 0.
0
Let x(m) be the first derivative of -4*m - 5*m**2 + 14/3*m**3 - 3. Determine c, given that x(c) = 0.
-2/7, 1
Suppose v - r = -v + 6, -v + 2*r = 3. Solve v*g - 6*g - 2*g**2 + 5*g = 0 for g.
0, 2
Let v(m) be the third derivative of 0 + 0*m**3 + 0*m - 2*m**2 - 1/30*m**5 - 1/12*m**4. Factor v(o).
-2*o*(o + 1)
Let o(n) be the third derivative of -n**8/80640 + n**7/20160 + n**5/30 + 2*n**2. Let t(c) be the third derivative of o(c). Solve t(g) = 0 for g.
0, 1
Determine l so that -3*l**3 + 2 + l**3 + 3*l + l**3 = 0.
-1, 2
Let 0*r + 0*r + 2*r**2 - 4*r**2 + 8 = 0. Calculate r.
-2, 2
Let i be ((-16)/12)/(8/(-12)). Suppose s + 4 = b - 1, i*s + 14 = 4*b. Determine j so that 2/11*j**3 - 8/11*j**b + 8/11*j + 0 = 0.
0, 2
Let b be ((-12)/(-9))/((-10)/(-15)). Let 1/3*m**3 + 1/3*m**b + 0 + 0*m = 0. What is m?
-1, 0
Suppose -2*s + 6*s = 8, 0 = -2*w + 2*s. Let l(g) be the third derivative of 0 + 1/72*g**4 + 1/180*g**5 + w*g**2 - 1/360*g**6 - 1/18*g**3 + 0*g. Factor l(o).
-(o - 1)**2*(o + 1)/3
Suppose 8 = -6*k + 20. Solve 1/2*h + 0 + 1/2*h**k - 1/2*h**4 - 1/2*h**3 = 0 for h.
-1, 0, 1
Let q(f) be the third derivative of f**8/16 + 3*f**7/7 + 5*f**6/4 + 2*f**5 + 15*f**4/8 + f**3 - 15*f**2. Factor q(r).
3*(r + 1)**4*(7*r + 2)
Let s(l) be the first derivative of -l**6/27 + l**4/9 - l**2/9 - 2. Factor s(b).
-2*b*(b - 1)**2*(b + 1)**2/9
Let d(z) be the first derivative of 2*z**6/3 - 24*z**5/5 + 14*z**4 - 64*z**3/3 + 18*z**2 - 8*z + 22. Factor d(r).
4*(r - 2)*(r - 1)**4
Let r(c) = 64*c**2 + 59*c - 1. Let y(m) = 895*m**2 + 825*m - 15. Let q(g) = -55*r(g) + 4*y(g). Factor q(l).
5*(l + 1)*(12*l - 1)
Let d = 425 + -423. Let w be (-7)/(-2) + -2 + 1. Factor 1/2*x**3 + d*x**2 + 1 + w*x.
(x + 1)**2*(x + 2)/2
Let i(k) be the second derivative of -2*k**7/21 - 2*k**6/5 - 3*k**5/5 - k**4/3 + 11*k. Let i(b) = 0. Calculate b.
-1, 0
Let g = 370/7 + -53. Let i = g - -9/14. Find d such that 0 - i*d**5 + 0*d + 1/2*d**2 - 1/2*d**4 + 1/2*d**3 = 0.
-1, 0, 1
Let b(z) be the first derivative of 1/6*z**2 + 3 - 1/9*z**3 + 0*z. Factor b(d).
-d*(d - 1)/3
Let j(s) be the third derivative of -1/120*s**6 + 4*s**2 + 0 + 1/336*s**8 + 0*s - 7/60*s**5 + 1/70*s**7 + 2/3*s**3 + 0*s**4. Factor j(w).
(w - 1)**2*(w + 1)*(w + 2)**2
Let l(f) be the second derivative of -f**7/420 - f**6/120 + f**4/24 + f**3/12 + 5*f**2 - 5*f. Let s(x) be the first derivative of l(x). Factor s(t).
-(t - 1)*(t + 1)**3/2
Let r(x) be the third derivative of -x**6/60 - x**5/40 - x**3/2 - 4*x**2. Let w(l) be the first derivative of r(l). Factor w(v).
-3*v*(2*v + 1)
Factor 1/3*j**5 + 1/3*j**2 + 2/3*j - 1/3*j**4 + 0 - j**3.
j*(j - 2)*(j - 1)*(j + 1)**2/3
Let d(f) be the first derivative of 2*f**3/27 - f**2/9 - 4*f/9 + 2. Factor d(h).
2*(h - 2)*(h + 1)/9
Let m(t) be the second derivative of -5*t**6/24 + 9*t**5/16 - t**4/2 + t**3/6 - 15*t. Determine z so that m(z) = 0.
0, 2/5, 1
Suppose 3*y = 5*m + 16, 4 + 4 = -4*m. Let y*j - 6*j**2 - 4*j - 2*j**3 - 2*j = 0. What is j?
-2, -1, 0
Let y(x) be the third derivative of x**5/210 + x**4/14 + 3*x**3/7 - 10*x**2. Factor y(l).
2*(l + 3)**2/7
Suppose 1/3 + 2/3*m**2 - m = 0. Calculate m.
1/2, 1
Let x(s) be the second derivative of s**6/5 + 7*s**5/5 + 8*s**4/3 + 2*s**3/3 - 3*s**2 + 21*s. Find o, given that x(o) = 0.
-3, -1, 1/3
Let u be 5/(-4)*6/(-15). Factor 0 + 1/2*y**3 + y**2 + u*y.
y*(y + 1)**2/2
Let l = -103/3 + 35. Let n be (-4)/(-10)*(-10)/(-6). Factor 2/3*j**2 - n*j - l + 2/3*j**3.
2*(j - 1)*(j + 1)**2/3
Let w = 0 - 8. Let k be (-1)/(-2)*w/(-12). Solve 0 + 1/3*p - k*p**2 + 1/3*p**4 - 1/3*p**3 = 0 for p.
-1, 0, 1
Suppose 4*f - 12 = -y - 0*f, 10 = y + 3*f. Suppose t = -y*t. Factor 0 + t*w - 1/5*w**3 - 1/5*w**2.
-w**2*(w + 1)/5
Let q(u) be the second derivative of 0 + 1/30*u**6 - 1/12*u**4 + 0*u**2 + 2*u + 1/6*u**3 - 1/20*u**5. Suppose q(y) = 0. What is y?
-1, 0, 1
Let h be (-3*4/3)/(-14). Let c(p) = p**3 - 11*p**2 - 2*p + 22. Let v be c(11). Factor -4/7*s - h*s**3 + 6/7*s**2 + v.
-2*s*(s - 2)*(s - 1)/7
Let j(o) be the third derivative of -9*o**7/280 + o**6/60 - 5*o**3/6 - 5*o**2. Let h(q) be the first derivative of j(q). Find l, given that h(l) = 0.
0, 2/9
Let d = -4 + 7. Factor 2*w**3 - w**d + 0 + 1 - w - w**2.
(w - 1)**2*(w + 1)
Let r**3 - 1/3*r**2 - 1/3*r - 2/3*r**5 + 1/3*r**4 + 0 = 0. Calculate r.
-1, -1/2, 0, 1
Factor -6/17*t + 2/17*t**2 + 4/17.
2*(t - 2)*(t - 1)/17
Let i(r) be the second derivative of -r**3/6 - r**2/2 + 2*r. Let p be i(-3). Factor -p + f**2 + 4*f**2 - 3*f**2 + 0*f**2.
2*(f - 1)*(f + 1)
Let a be ((-2)/(-4))/(5/(-20)*-2). Let o(l) be the first derivative of -a + 0*l - 1/3*l**2 + 1/3*l**3 + 7/6*l**4. Factor o(n).
n*(2*n + 1)*(7*n - 2)/3
Let u = 3 - 6. Let y(g) = -5506*g + g**2 + 1 + 5506*g. Let h(k) = 12*k + 9. Let n(a) = u*y(a) - h(a). Determine j, given that n(j) = 0.
-2
Let x(f) be the third derivative of f**8/6720 + f**7/560 - f**5/60 + 5*f**2. Let a(k) be the third derivative of x(k). Determine b so that a(b) = 0.
-3, 0
Suppose -3*g + 18 = -0. Factor g*o**2 - o**2 - 10*o - 2*o**2 - 6 + 7*o.
3*(o - 2)*(o + 1)
Let w(b) = b**2 + 2*b + 1. Let f be w(-1). Let z(t) be the first derivative of -2/5*t**5 + 1/2*t**4 + 1 + 2/3*t**3 + 0*t - 1/3*t**6 + f*t**2. Factor z(k).
-2*k**2*(k - 1)*(k + 1)**2
Suppose -4*s + 7*s = 0. Let v(p) be the second derivative of s*p**5 + 0*p**3 - 2*p + 0 + 1/105*p**6 + 0*p**4 + 0*p**2. Factor v(u).
2*u**4/7
Let d = -1 + 1. Let m = 398 + -396. Let -2/9*j + d - 2/9*j**m = 0. What is j?
-1, 0
Suppose -3*i = 2*b, 3*b + 9 = 4*i - 8. Factor i - 4*f - 2 + 4*f**3.
4*f*(f - 1)*(f + 1)
Let w = -99 - -102. Let z(l) be the first derivative of w - 1/4*l**2 + 1/8*l**4 + 0*l**3 + 0*l. What is a in z(a) = 0?
-1, 0, 1
Let y(q) = q**5 - q**4 + q**3 + q. Let k(w) = 7*w**5 - 22*w**4 + 46*w**3 - 48*w**2 + 31*w - 6. Let o(d) = k(d) - 4*y(d). Factor o(a).
3*(a - 2)*(a - 1)**4
Let x(k) be the third derivative of 1/15*k**3 + 0*k + 0 + 1/10*k**4 - 3*k**2 + 3/50*k**5. Factor x(w).
2*(3*w + 1)**2/5
Let j be (-35)/(-60) - (-3)/12*3. Factor j*g + 0*g**2 + 2/3*g**4 - 4/3*g**3 - 2/3.
2*(g - 1)**3*(g + 1)/3
Let o = -8 + 12. Suppose o*j + 16 = 0, 3*t = 5*j + 13 + 28. Factor c**4 + 7*c**2 + c**5 - t*c**2.
c**4*(c + 1)
Suppose 19 = 5*h + 3*f, 5*h + 0*f = 4*f - 2. Factor -2*d**2 - 2*d - 21*d**3 - 8*d**4 - 10*d**h + 3*d**3.
-2*d*(d + 1)**2*(4*d + 1)
Let o be -2 + (41/82)/((-4)/(-18)). Suppose o*u**3 + 1/2*u + 0 - 3/4*u**2 = 0. What is u?
0, 1, 2
Let m(s) be the second derivative of 27*s**5/160 + 21*s**4/32 + s**3 + 3*s**2/4 - 22*s. Factor m(d).
3*(d + 1)*(3*d + 2)**2/8
Let p(c) be the first derivative of 1/10*c**5 - 2 - 1/4*c**2 + 0*c - 1/4*c**3 + 3/16*c**4. Factor p(y).
y*(y - 1)*(y + 2)*(2*y + 1)/4
Suppose -18 = -36*v + 33*v. Let r(f) be the second derivative of -1/42*f**4 + 0*f**2 + 1/70*f**5 + 0 - 1/147*f**7 + 1/105*f**v + 0*f**3 - f. Solve r(a) = 0.
-1, 0, 1
Let x(n) be the second derivative of 1/168*n**7 - 3*n + 3/40*n**5 + 1/24*n**3 + 1/30*n**6 + 0 + 1/12*n**4 + 0*n**2. Factor x(s).
s*(s + 1)**4/4
Let u(l) be the second derivative of 0*l**5 + 1/42*l**7 + 0*l**2 + 1/30*l**6 + 0*l**3 + 2*l + 0 + 0*l**4. Factor u(i).
i**4*(i + 1)
Suppose 0 + 27/5*v**3 + 21/5*v**4 + 6/5*v**2 + 0*v = 0. What is v?
-1, -2/7, 0
Let x be (-9)/15*20/(-48). Factor -x*a - 1/4 + 1/4*a**3 + 1/4*a**2.
(a - 1)*(a + 1)**2/4
Determine j so that -20/9*j**3 + 8/9*j - 16/9*j**4 + 28/9*j**2 + 0 = 0.
-2, -1/4, 0, 1
Let m(i) be the second derivative of -i**6/1800 - i**5/150 - i**4/30 - i**3/6 + 6*i. Let y(q) be the second derivative of m(q). Let y(n) = 0. Calculate n.
-2
Let l(z) = -z**3 - 9*z**2 + 11*z + 15. Let y be l(-10). Suppose -3*d = -y*d. Factor -3/2*u**5 + 0 + 2*u**4 - 1/2*u**3 + d*u**2 + 0*u.
-u**3*(u - 1)*(3*u - 1)/2
Let o(g) be the third derivative of -7*g**6/240 + 19*g**5/120 - g**4/6 - g**3/3 - 31*g**2. Let o(d) = 0. Calculate d.
-2/7, 1, 2
Factor 4*h**2 + 244*h - 4*h**3 - 244*h.
-4*h**2*(h - 1)
Factor 2/3 + p**2 - 5/3*p.
(p - 1)*(3*p - 2)/3
Factor -2/9*m**2 + 4/9*m - 2/9*m**3 + 0.
-2*m*(m - 1)*(m + 2)/9
Let z = 279/2 + -139. Find q, given that -z - 1/2*q**2 - q = 0.
-1
Factor 4*b**2 + 216 - 204 - 26*b + 157 - 3*b**2.
(b - 13)**2
Let o(s) be the second derivative of -2*s**5/5 - s**4/2 + s**3/3 - s. Suppose o(z) = 0. What is z?
-1, 0, 1/4
Let l(m) be the third