 Suppose -2*m - d*r = -m + 1, 0 = r + 2. Determine k so that 5*k**2 + 9*k**5 - 3*k**2 - 8*k**3 + k**2 - m*k**4 - k**3 = 0.
-1, 0, 1/3, 1
Let k(d) be the third derivative of d**5/300 - d**4/120 - d**3/15 + 18*d**2. Determine h, given that k(h) = 0.
-1, 2
Let b(c) = 2*c**3 + c**3 - 3*c**4 + 2*c - 1 - 4*c**3 - c**3. Let a(n) = -4*n**4 - 2*n**3 + 2*n - 2. Let j(w) = -2*a(w) + 3*b(w). Let j(k) = 0. Calculate k.
-1, 1
Let s(v) be the second derivative of v**5/10 + v**4/12 - v**3/6 - v. Factor s(c).
c*(c + 1)*(2*c - 1)
Let c = 437/2088 - -3/232. Let f be 4/6 + 20/(-45). Factor f*j**2 + c*j + 0 - 2/9*j**4 - 2/9*j**3.
-2*j*(j - 1)*(j + 1)**2/9
Let v be (6/(-21) + 0)/((-18)/84). Find w such that v*w**2 + 0*w**3 - 2/3 - 2/3*w**4 + 0*w = 0.
-1, 1
Let a(p) be the third derivative of -p**7/140 - p**6/40 - p**5/40 - 51*p**2. Factor a(q).
-3*q**2*(q + 1)**2/2
Suppose -2 - 16 = -6*o. Factor 0*v - 2/9*v**5 - 2/3*v**4 + 0 - 2/9*v**2 - 2/3*v**o.
-2*v**2*(v + 1)**3/9
Let z(o) be the second derivative of 2*o**7/147 + 4*o**6/35 + 2*o**5/5 + 16*o**4/21 + 6*o**3/7 + 4*o**2/7 + 2*o. What is x in z(x) = 0?
-2, -1
Let o(q) be the second derivative of -q**5/210 + q**4/42 - 12*q. Factor o(f).
-2*f**2*(f - 3)/21
Factor -11*g**2 + 3 - g**2 + 0 + 8*g + 1.
-4*(g - 1)*(3*g + 1)
Let b(l) = l**2 - 11*l + 5. Let z be b(11). Let w(a) be the second derivative of a + 1/10*a**2 + 1/20*a**4 - 1/10*a**3 + 0 - 1/100*a**z. Factor w(t).
-(t - 1)**3/5
Let u = -569/5 - -114. Solve 0 - 1/5*f**2 - u*f = 0 for f.
-1, 0
Let x(n) = 4*n**2 + 24*n + 32. Let w(g) = -12*g**2 - 72*g - 96. Let p(f) = -4*w(f) - 11*x(f). Let p(c) = 0. Calculate c.
-4, -2
Let t be 2 + (-48)/(-9) + -7. Suppose 2/3*n + 0 - t*n**2 = 0. What is n?
0, 2
Let u(c) = -6*c**5 - 10*c**4 - 2*c**3 + 3*c**2 + 3. Let v(t) = 6*t**5 + 11*t**4 + 2*t**3 - 4*t**2 - 4. Let b(g) = 4*u(g) + 3*v(g). Find l such that b(l) = 0.
-2/3, -1/2, 0
Factor 2/3*j - 8/9*j**2 + 2/9*j**3 + 0.
2*j*(j - 3)*(j - 1)/9
Let q = -8 + 2. Let p be 3 - (3 + 15/q). Factor -3/2*j**3 + 7/2*j**2 - p*j + 1/2.
-(j - 1)**2*(3*j - 1)/2
Let m(i) be the first derivative of -i**3/3 - 2*i**2 + 2*i - 3. Let o be m(-4). Factor 9*x**3 - 3*x**2 + 0*x**4 + o*x**5 - 3*x + 6*x**4 + 9*x**4 + 4*x**5.
3*x*(x + 1)**3*(2*x - 1)
Let f(w) be the second derivative of w**9/15120 + w**8/4200 + w**7/4200 + w**3/3 + w. Let y(c) be the second derivative of f(c). Factor y(n).
n**3*(n + 1)**2/5
Solve -6/5*v**4 - 3/5*v**3 + 0*v**2 + 0*v - 3/5*v**5 + 0 = 0.
-1, 0
Let k(z) = 4*z**2 + 6*z - 4. Let g(f) = -11*f**2 - 17*f + 11. Let h(s) = 6*g(s) + 17*k(s). Factor h(b).
2*(b - 1)*(b + 1)
Let r(t) be the second derivative of t**7/105 + t**6/75 - 3*t**5/25 + t**4/15 + t**3/3 - 3*t**2/5 - 2*t. Find q, given that r(q) = 0.
-3, -1, 1
Let p(v) = -v**4 + v**3 - v**2 - v. Let j(q) = 3*q**4 + 15*q**2 - 18*q + 12. Let t(b) = -j(b) - 6*p(b). Factor t(y).
3*(y - 2)*(y - 1)**2*(y + 2)
Let g(v) be the second derivative of v**6/30 - 3*v**5/20 + v**4/12 + v**3/2 - v**2 + 19*v. Find x such that g(x) = 0.
-1, 1, 2
Suppose 0 = 5*w - 16 + 6. Factor -v**5 + 1/4*v**2 + w*v**4 - 5/4*v**3 + 0 + 0*v.
-v**2*(v - 1)*(2*v - 1)**2/4
Suppose 0*n = 2*n. Let p = -8 + 11. Factor -4/5*g**p + 4/5*g - 2/5 + n*g**2 + 2/5*g**4.
2*(g - 1)**3*(g + 1)/5
Let w(s) be the first derivative of s**3 + 3*s**2 + 3*s - 9. Factor w(f).
3*(f + 1)**2
Suppose -5*x + 10*x = 0. Let l be 8/32 + 1/4. Factor -1/2*n + l*n**3 + 0 + x*n**2.
n*(n - 1)*(n + 1)/2
Let f(p) be the second derivative of -1/84*p**7 + 1/60*p**6 - 1/12*p**3 - 3*p + 1/20*p**5 + 1/4*p**2 - 1/12*p**4 + 0. Let f(z) = 0. What is z?
-1, 1
Let c(r) be the first derivative of -1280*r**6/3 + 576*r**5 - 270*r**4 + 45*r**3 - 18. Factor c(t).
-5*t**2*(8*t - 3)**3
Let k(s) be the first derivative of s**4/24 + s**3/18 - s**2/12 - s/6 - 9. Find z, given that k(z) = 0.
-1, 1
Let o(l) = l**2 - 6*l - 2. Suppose b + 4*q + 5 = 0, -3*b + 4*q - 3*q + 24 = 0. Let c be o(b). Suppose -3*y**3 + 4*y**3 - c*y**3 - 2*y - 6*y**2 = 0. What is y?
-1, -1/2, 0
Determine l, given that 0 - 1/9*l**2 - 1/9*l = 0.
-1, 0
Let r(c) be the first derivative of c**5/80 + c**4/48 - c**3/12 - 3*c - 1. Let k(o) be the first derivative of r(o). Factor k(l).
l*(l - 1)*(l + 2)/4
Let a(m) be the first derivative of -m**4/14 + 2*m**3/7 + 6*m**2/7 - 16*m/7 - 12. Solve a(s) = 0.
-2, 1, 4
Suppose 2 = -n, -4*n + 2 = -4*q - 9*n. Solve -7*f**3 - 4 - 68*f**2 - 3*f**3 - 14*f - q*f**4 + 50*f**2 = 0.
-2, -1
Let g = -2 - -4. Factor -5/3*m**4 - 2/3*m**3 + 5/3*m**g + 2/3*m + 0.
-m*(m - 1)*(m + 1)*(5*m + 2)/3
Let t = -3 + 6. Factor t*u**3 + 2*u**2 - 4*u**2 - u**2.
3*u**2*(u - 1)
Factor 4 + 35*q**2 + 7*q**3 - 13*q**2 - 10*q**2 + 12*q - 3*q**3.
4*(q + 1)**3
Let p = 13/2 + -31/6. Determine x, given that 0 + p*x - 2/3*x**2 = 0.
0, 2
Let r(b) be the third derivative of b**5/12 - 5*b**4/6 + 10*b**3/3 - 2*b**2. Find w such that r(w) = 0.
2
Factor 1/4*h**2 + 0 + 3/4*h.
h*(h + 3)/4
Let d = 119/3 - 39. Solve 1/3*z**2 + 0 - 5/3*z**3 + d*z + 2/3*z**4 = 0.
-1/2, 0, 1, 2
Suppose 0 = 3*x + 2*x - 10. Let j = -118/11 + 1502/99. Factor j*v + 8/9 + 50/9*v**x.
2*(5*v + 2)**2/9
Let i(g) be the first derivative of g**6/12 - 3*g**5/5 + 13*g**4/8 - 2*g**3 + g**2 - 16. Determine a so that i(a) = 0.
0, 1, 2
Let h(b) be the third derivative of -1/30*b**5 - b**3 + 0*b + 1/3*b**4 + 0 + 4*b**2. Find r, given that h(r) = 0.
1, 3
Factor 2/3*t - 4/3 + 2/3*t**2.
2*(t - 1)*(t + 2)/3
Let y = -22 - -244/11. Let b be 0/3 - (-1 - -1). Find f, given that b*f - y + 2/11*f**2 = 0.
-1, 1
Suppose 2/13*l - 12/13 + 2/13*l**2 = 0. Calculate l.
-3, 2
Let y be ((-6)/(18/(-21)))/(1 - -3). Determine o, given that 0 - 1/2*o**3 + 1/2*o - y*o**2 + 7/4*o**4 = 0.
-1, 0, 2/7, 1
Let w(g) = g + 1. Let j be w(1). Let n = 20 - 18. Factor n*d - j - 6*d**2 + 2.
-2*d*(3*d - 1)
Factor 1/2*u**3 - 5/4*u - 1/2 - 1/4*u**2.
(u - 2)*(u + 1)*(2*u + 1)/4
Let a(r) be the second derivative of r**7/70 - 3*r**5/100 - 2*r. Factor a(t).
3*t**3*(t - 1)*(t + 1)/5
Factor 32/15*x - 2/15*x**4 - 2/3 + 16/15*x**3 - 12/5*x**2.
-2*(x - 5)*(x - 1)**3/15
Let n(p) = 10*p**3 - 15*p**2 - 15*p + 10. Let r(x) = -30*x**3 + 45*x**2 + 45*x - 30. Let c(u) = -17*n(u) - 6*r(u). Suppose c(g) = 0. Calculate g.
-1, 1/2, 2
Factor -5*x**3 + x**2 + 62 - 62 + 19*x**2 + 20*x - 5*x**4.
-5*x*(x - 2)*(x + 1)*(x + 2)
Suppose f - 1 = 5*n - 3*f, -n - f = -7. Suppose 2 - 14 = -4*k - 4*z, -z = 5*k - 19. Determine c so that 2*c**4 - 2*c**4 - 4*c - 2*c**k + 4*c**n + 2 = 0.
-1, 1
Let l(k) be the first derivative of -k**5 - 5*k**4/2 + 5*k**2 + 5*k + 15. Factor l(p).
-5*(p - 1)*(p + 1)**3
Let a(m) be the first derivative of m**6/360 - m**5/90 + 2*m**2 - 4. Let u(c) be the second derivative of a(c). Factor u(n).
n**2*(n - 2)/3
Factor -5*p**2 + 4*p**3 - 2*p + 17*p**2 + 14*p + 4.
4*(p + 1)**3
Let d(s) be the first derivative of 0*s + s**2 - 1/2*s**4 + 0*s**3 - 5. Factor d(f).
-2*f*(f - 1)*(f + 1)
Let l(r) = 5*r**3 - 3*r**2 - 3*r. Let k(p) be the second derivative of 9*p**5/20 - 5*p**4/12 - 5*p**3/6 - p. Let w(s) = -3*k(s) + 5*l(s). Factor w(u).
-2*u**3
Let g(k) be the third derivative of k**7/210 - k**6/30 - k**5/20 + 7*k**4/12 - 4*k**3/3 + 2*k**2. Factor g(m).
(m - 4)*(m - 1)**2*(m + 2)
Factor -15*s + 3*s**2 - 1 + 8 + 1 + 4.
3*(s - 4)*(s - 1)
Let x(v) = -80*v**4 - 183*v**3 + 153*v**2 + 311*v - 192. Let c(i) = -20*i**4 - 46*i**3 + 38*i**2 + 78*i - 48. Let u(b) = 9*c(b) - 2*x(b). Solve u(z) = 0.
-2, 3/5, 1
Let d(i) be the second derivative of -1/10*i**2 + 0 - 1/60*i**4 + 3*i - 1/15*i**3. Factor d(o).
-(o + 1)**2/5
Suppose -3*b = -m + 69, b = -3*b - 5*m - 111. Let w = b - -26. Factor 4/3*v**w + 0 + 2/3*v**3 + 2/3*v.
2*v*(v + 1)**2/3
Factor -2/5*x + 0 + 0*x**2 + 2/5*x**3.
2*x*(x - 1)*(x + 1)/5
Let b be (7 - 3)*(-2)/(-4). Find r, given that -4*r**3 - b*r + 5 - 5 + r**4 + 5*r**2 = 0.
0, 1, 2
Let z(n) be the first derivative of -3*n**5/25 + n**3 - 12*n/5 - 1. Determine c, given that z(c) = 0.
-2, -1, 1, 2
Let n(w) be the second derivative of 0*w**3 + 0 + 0*w**2 + 3*w - 1/30*w**5 + 1/18*w**4. Factor n(k).
-2*k**2*(k - 1)/3
Factor 3/4*i**3 + 3/4*i**2 + 1/4*i + 1/4*i**4 + 0.
i*(i + 1)**3/4
Let b(h) be the third derivative of h**7/735 - h**6/60 + h**5/15 - 2*h**4/21 + 17*h**2. Let b(t) = 0. Calculate t.
0, 1, 2, 4
Let n(i) = -i**2 - 8*i + 24. Let b be n(-10). Solve -2/3*h**3 - b*h**2 - 16