a**6/360 + a**5/60 + a**4/24 - 2*a**2. Let o(p) be the second derivative of k(p). Factor o(q).
(q - 2)**2/2
Let r be ((-16)/(-84))/(60/42). Let i(m) be the first derivative of -2/3*m + r*m**5 + 2/3*m**2 + 2 - 1/3*m**4 + 0*m**3. Factor i(w).
2*(w - 1)**3*(w + 1)/3
Suppose 0 = 5*l - 1 - 14. Suppose -8 = -l*x - 2. Factor -6*k**x + 4/3 - 26/3*k**3 + 2/3*k - 10/3*k**4.
-2*(k + 1)**3*(5*k - 2)/3
Let s(u) = u + 19. Let g be s(-16). Let d(v) be the first derivative of 1/9*v**g + 1/3*v - 1 - 1/3*v**2. Find m, given that d(m) = 0.
1
Suppose 2*u = 6*u - 8. Suppose -u*z = z - 9. Factor -1/2*w**z - w**2 + 0 - 1/2*w.
-w*(w + 1)**2/2
Let o(r) be the second derivative of -37*r**4/12 - 49*r**3/6 - 17*r**2/2 + 5*r. Let m(i) = 18*i**2 + 24*i + 9. Let q(t) = -5*m(t) - 3*o(t). Factor q(b).
3*(b + 1)*(7*b + 2)
Find w such that -1/4*w**2 - 1/4*w + 1/4*w**3 + 0 + 1/4*w**4 = 0.
-1, 0, 1
Let m(z) be the second derivative of -3*z**5/20 + z**3/2 - 10*z. Let m(f) = 0. What is f?
-1, 0, 1
Let o be 1 - 0 - (3 - 36/16). Let q(x) be the second derivative of x - 7/80*x**5 - 1/24*x**4 + 7/24*x**3 + 0 + o*x**2. Determine v, given that q(v) = 0.
-1, -2/7, 1
Suppose -5*p = -9*p. Let o(u) be the second derivative of 1/21*u**3 + 0*u**2 + 2*u - 1/35*u**5 + 1/147*u**7 + 0 + p*u**6 + 0*u**4. What is r in o(r) = 0?
-1, 0, 1
Suppose -2*b**2 + 3*b**2 + 47 + 111 + 26*b + 11 = 0. What is b?
-13
Let w(q) = q**3 - q**2 + 1. Let i = -2 - -4. Let d be w(i). Determine z so that 2*z**4 + 4*z**2 - d*z**2 - z**4 = 0.
-1, 0, 1
Let y(k) = 5*k**3 + 5*k**2 - 13*k + 9. Let o(f) = 4*f**3 + 5*f**2 - 12*f + 8. Let p(b) = 6*o(b) - 5*y(b). Factor p(q).
-(q - 3)*(q - 1)**2
Let p(d) be the third derivative of 0 + 0*d - 3*d**2 + 2/945*d**7 - 1/135*d**5 + 0*d**3 - 1/108*d**4 + 0*d**6 + 1/1512*d**8. Find z, given that p(z) = 0.
-1, 0, 1
Let d be (1 + -2)*(1 - 1). Suppose -3*z = -0*z. Find c such that -c**3 + c**2 + d*c + z*c = 0.
0, 1
Let b(q) be the second derivative of -q**4/4 + 5*q**3 - 75*q**2/2 - 17*q. Factor b(t).
-3*(t - 5)**2
Let w(p) be the second derivative of 1/30*p**5 + 0 + 1/3*p**2 - 1/9*p**3 + 2*p - 1/18*p**4. Suppose w(j) = 0. What is j?
-1, 1
Suppose u = -3*u - 8. Let a be (-15)/(-9) - (3 + u). Factor -2/3*n**2 - 4/3*n - a.
-2*(n + 1)**2/3
Let u = 32 + -63/2. Factor -1 - r**2 + 5/2*r - 2*r**3 + 2*r**4 - u*r**5.
-(r - 2)*(r - 1)**3*(r + 1)/2
Let s(y) be the third derivative of -y**5/12 - 5*y**4/12 + 5*y**3/2 + 15*y**2. Factor s(q).
-5*(q - 1)*(q + 3)
Factor 1/5*z**3 - 1/5 - 1/5*z + 1/5*z**2.
(z - 1)*(z + 1)**2/5
Let 0*d + 4/7*d**2 + 0 - 6/7*d**3 - 10/7*d**4 = 0. Calculate d.
-1, 0, 2/5
Suppose -2*f + x = -2*x + 3, 5*x = f + 12. Factor -f*n**2 + 5*n**2 - 10*n**3 + 11*n**4 - 8*n**5 + 5*n**4.
-2*n**2*(n - 1)*(2*n - 1)**2
Suppose 0 = -4*k + 6 + 2. Let h(z) be the second derivative of 3*z + 2/3*z**3 + 1/6*z**4 + 0 + z**k. Find v such that h(v) = 0.
-1
Let w(b) be the second derivative of -b**7/21 + b**5/5 - b**3/3 - 5*b. Factor w(y).
-2*y*(y - 1)**2*(y + 1)**2
Let s(y) be the third derivative of 0*y**4 + 0 + 2*y**2 + 0*y + 1/80*y**6 - 1/40*y**5 + 0*y**3. Factor s(w).
3*w**2*(w - 1)/2
Suppose -3*a = -a. Suppose 3*c - 5*p + 3*p + 10 = a, -3*c + p = 5. Factor 2/7*s + c - 2/7*s**2.
-2*s*(s - 1)/7
Suppose 4*w - 3*b = 7, -4*w + 2 - 1 = -5*b. Let q(l) be the second derivative of -1/4*l**3 - 1/4*l**w + 0*l**2 + 0 + l - 3/40*l**5. Factor q(g).
-3*g*(g + 1)**2/2
Determine j, given that -53*j**2 - 3*j**5 - 27*j + 5*j**2 - 18*j**4 - 35*j**3 - 7*j**3 - 6 = 0.
-2, -1
Let m be (-18)/(-135) + (-9)/80. Let c(o) be the third derivative of -1/120*o**5 + 0 + 0*o + m*o**4 + 0*o**3 - 2*o**2. What is n in c(n) = 0?
0, 1
Factor -1/2*r**4 + 0 - 1/2*r**3 + 1/2*r + 1/2*r**2.
-r*(r - 1)*(r + 1)**2/2
Let l be ((-14)/(-84) - (-17)/6)*1. Let c(u) be the third derivative of 0*u**4 + 0*u**l + 1/540*u**6 + 0*u - 2*u**2 + 0 - 1/270*u**5. Let c(a) = 0. Calculate a.
0, 1
Let f(j) = j - 12. Let s be f(12). Factor 0 + 4/5*v**4 - 4/5*v**2 + 2/5*v + s*v**3 - 2/5*v**5.
-2*v*(v - 1)**3*(v + 1)/5
Let v = 18 + -20. Let b be (v/66)/((-3)/18). Factor -4/11 + 4/11*m**2 - b*m + 2/11*m**3.
2*(m - 1)*(m + 1)*(m + 2)/11
Let r be (-21)/(-504) + 4/(-2) + 2. Let d(h) be the second derivative of 0*h**2 - r*h**6 + 0 + 0*h**3 + 4*h - 1/12*h**4 - 1/10*h**5 - 1/168*h**7. Factor d(b).
-b**2*(b + 1)*(b + 2)**2/4
Factor -1/3*s**4 + 0 - 1/3*s + 1/3*s**3 + 1/3*s**2.
-s*(s - 1)**2*(s + 1)/3
Let n(a) be the third derivative of 0*a**3 + 0*a - 4*a**2 + 0 - 1/40*a**6 + 1/20*a**5 - 1/70*a**7 + 1/8*a**4. Factor n(k).
-3*k*(k - 1)*(k + 1)**2
Suppose -22*n**3 + 245*n**5 + 61*n**4 - 5*n**2 + 114*n**4 - 43*n**3 + 10*n**2 = 0. Calculate n.
-1, 0, 1/7
Let l(d) be the first derivative of -d**5/20 - 3*d**4/16 - d**3/4 - d**2/8 + 44. Factor l(a).
-a*(a + 1)**3/4
Let d(u) be the third derivative of u**8/560 + u**7/280 - u**6/120 - u**5/40 + u**3/3 - 6*u**2. Let h(k) be the first derivative of d(k). Solve h(l) = 0 for l.
-1, 0, 1
Suppose 4*v - 3*m = -6 - 1, 15 = 5*v + m. Let a(x) be the third derivative of -1/84*x**4 + 0 + 0*x + v*x**2 - 2/21*x**3 + 1/14*x**5. Factor a(z).
2*(3*z + 1)*(5*z - 2)/7
Let q(j) = j**3 + 10*j**2 - 12*j + 1. Let a(k) = -k**2 + k. Let u(f) = -44*a(f) - 4*q(f). Find m, given that u(m) = 0.
-1, 1
Let x(n) be the first derivative of -n**6/240 - n**5/30 - n**4/12 + n**2 + 2. Let s(t) be the second derivative of x(t). Find k, given that s(k) = 0.
-2, 0
Let c(t) be the first derivative of t**6/60 + t**5/20 - t**4/8 - t**3/3 + t**2 - 4*t - 2. Let m(s) be the first derivative of c(s). Factor m(x).
(x - 1)**2*(x + 2)**2/2
Suppose 0 = -a + 2*o - o + 1, -4*a = -5*o - 2. Let -4/7 + 6/7*j - 6/7*j**a + 2/7*j**2 + 2/7*j**4 = 0. What is j?
-1, 1, 2
Let n(s) = -27*s**2 - 30*s + 30. Let g(p) = -3*p - p**2 + 0 + 1 - 2*p + 4*p. Let v(c) = -18*g(c) + n(c). Factor v(a).
-3*(a + 2)*(3*a - 2)
Factor -1/4*p**2 + 1/4*p**4 + 1/4*p + 0 - 1/4*p**3.
p*(p - 1)**2*(p + 1)/4
Let x(c) be the third derivative of c**5/60 - c**3/6 - 36*c**2. Let x(r) = 0. Calculate r.
-1, 1
Let o(d) = -d**2 - 8*d + 2. Let j be o(-7). Suppose -3*b + 4*m = -j - 17, 0 = 4*b + 3*m + 7. Factor -4*u - u**2 + 1 + 2*u - b.
-(u + 1)**2
Let o(t) be the second derivative of -1/48*t**4 + 0 + 5*t + 1/120*t**6 + 0*t**2 + 0*t**3 + 1/168*t**7 - 1/80*t**5. Let o(m) = 0. Calculate m.
-1, 0, 1
Let l = 5 - 2. Let t = -1/425 - -681/425. What is y in -12/5*y**2 - t*y - 8/5*y**l - 2/5*y**4 - 2/5 = 0?
-1
Let p(n) be the third derivative of n**5/180 - n**4/24 - 5*n**3/9 - 13*n**2 - 3*n. Find o, given that p(o) = 0.
-2, 5
Suppose -11*g = -2*g. Let a(n) be the third derivative of -2/9*n**3 - 1/180*n**6 + 1/45*n**5 + 0 - n**2 + g*n + 1/36*n**4. Determine s so that a(s) = 0.
-1, 1, 2
Suppose -3*o = -r - 0 + 14, 0 = -4*r - 2*o. Factor 6*b - r*b**2 - 2*b + 2*b.
-2*b*(b - 3)
Factor 8/11*o + 4/11*o**2 - 16/11 - 2/11*o**3.
-2*(o - 2)**2*(o + 2)/11
Let y(n) be the first derivative of -2*n**5/95 - 3*n**4/19 - 26*n**3/57 - 12*n**2/19 - 8*n/19 + 8. Determine b, given that y(b) = 0.
-2, -1
Let m(a) = a**3 + 3*a**2 - 4*a + 2. Let t be m(-4). Let r be (6/(-9))/(t/(-6)). Factor 9/5*v**3 + 0*v - 6/5*v**r + 0.
3*v**2*(3*v - 2)/5
Let f(s) = s + 7. Let a(y) = 4*y + 3. Let q be a(-2). Let m be f(q). Solve -1/3*h**m + 0*h + 0 + 4/3*h**3 = 0 for h.
0, 1/4
Let r(v) be the second derivative of v**3 - 8*v + 0 + 1/4*v**4 + 3/2*v**2. Factor r(o).
3*(o + 1)**2
Let i(y) be the first derivative of 92/15*y**3 + 162/25*y**5 - 9*y**4 + 2/5*y + 2 - 11/5*y**2 - 9/5*y**6. Let i(h) = 0. What is h?
1/3, 1
Let -14*y**4 + 3*y**2 + 2*y**5 + 3*y**2 - 4*y**2 + 12*y**4 - 2*y**3 = 0. What is y?
-1, 0, 1
Let m be (-16)/(-20) - 643/(-15). Let x = m + -43. Let 1/3*n**2 + 1/3*n - x = 0. What is n?
-2, 1
Let x be 0/(((-5)/10)/(1/(-2))). Let u(q) be the first derivative of -1 + 2/3*q**3 - 2/5*q**5 + 1/3*q**6 + x*q - 1/2*q**4 + 0*q**2. Find w, given that u(w) = 0.
-1, 0, 1
Let j = -3482/37 + -136946/259. Let v = j + 624. Factor -2/7*t**2 - v*t - 8/7.
-2*(t + 2)**2/7
Let c be 5/(-15) + 4/3. Suppose u = -0*u + c. Factor u + n - 1 + n**2 + 0*n**2.
n*(n + 1)
Let v(m) be the second derivative of 0 + m + 0*m**2 + 0*m**3 - 1/50*m**5 - 1/30*m**4. Determine k so that v(k) = 0.
-1, 0
Factor 3*g + 2*g**2 + 18*g - 7*g.
2*g*(g + 7)
Factor -1/4*u**2 - 3/4 + u.
-(u - 3)*(u - 1)/4
Factor -8*k**2 + 3*k