0 - 2*d**3/3 - 5*d. Let n(i) be the second derivative of k(i). Suppose n(p) = 0. What is p?
0, 3
Let g(l) = 9*l**3 - 39*l**2 - 88*l - 36. Let m(b) = 9*b**3 - 39*b**2 - 87*b - 36. Let z(d) = -3*g(d) + 4*m(d). Factor z(x).
3*(x - 6)*(x + 1)*(3*x + 2)
Let z = 115 + -115. Let n(g) be the first derivative of 0*g + 1/9*g**3 - 2 + z*g**2. Factor n(h).
h**2/3
Let a be (3 - 1)*24/16. Factor -8*u**3 - 6*u**4 - 4*u**a - 2*u - 9*u**4 - 8*u**2 - 2*u**5 + 7*u**4.
-2*u*(u + 1)**4
Let s(y) = 28*y**4 - 125*y**3 + 143*y**2 - 71*y + 1. Let c(l) = -19*l**4 + 83*l**3 - 95*l**2 + 47*l - 1. Let x(a) = -8*c(a) - 5*s(a). Factor x(n).
3*(n - 1)**3*(4*n - 1)
Let v(j) be the third derivative of 0 + 0*j - 1/80*j**5 + 4*j**2 - 1/16*j**4 + 0*j**3. Suppose v(s) = 0. What is s?
-2, 0
Let k be (-2 - 138/(-75))*15/(-18). Factor 2/15*i**3 + 0 + k*i**2 + 0*i.
2*i**2*(i + 1)/15
Let b(z) be the second derivative of z**6/240 + z**5/160 - z**4/96 - z**3/48 + 12*z. Factor b(u).
u*(u - 1)*(u + 1)**2/8
Let m(b) be the first derivative of 9 - 1/16*b**4 + 1/4*b + 1/4*b**3 - 3/8*b**2. Factor m(h).
-(h - 1)**3/4
Let o(w) be the third derivative of 1/80*w**6 - 1/448*w**8 + 0*w**7 + 0 + 0*w - 1/32*w**4 + 0*w**3 + 3*w**2 + 0*w**5. Factor o(k).
-3*k*(k - 1)**2*(k + 1)**2/4
Let n(c) be the first derivative of -c**3/6 - 11*c**2/4 - 5*c - 13. Determine a, given that n(a) = 0.
-10, -1
Let o(q) = -q**2 - 4*q - 7. Let u be o(-3). Let t be (-14)/(-15) - u/6. Find y such that 2/5*y**2 + 8/5*y + t = 0.
-2
Let q = 19 - 15. Let a(f) be the first derivative of 0*f - 2/11*f**q + 0*f**2 + 6/55*f**5 - 2 + 2/33*f**3. Factor a(y).
2*y**2*(y - 1)*(3*y - 1)/11
Let u be ((-8)/10 - -1)/1. Let k(s) be the first derivative of 0*s - 1/10*s**4 + 0*s**2 - u*s**6 - 2 + 0*s**3 + 8/25*s**5. Factor k(f).
-2*f**3*(f - 1)*(3*f - 1)/5
Find l such that -1/3*l**3 - 1/6*l**4 + 1/3*l**2 - 1/6 + 1/6*l**5 + 1/6*l = 0.
-1, 1
Let p(o) = o**3 + 1. Suppose r - 1 = 6. Let u(v) = -2*v - 3*v + 2*v**3 + 7*v**2 - 3*v - r. Let b(c) = 3*p(c) + u(c). Solve b(h) = 0 for h.
-2, -2/5, 1
Factor 0*s + 0*s**2 + 1/3*s**3 + 0.
s**3/3
Let c(m) be the third derivative of -1/180*m**6 + 0*m**3 + 3*m**2 + 1/945*m**7 + 1/90*m**5 + 0 + 0*m - 1/108*m**4. Determine f, given that c(f) = 0.
0, 1
Let u(x) = 3*x**2 + 5. Let d(p) = -2*p**2 + p - 5. Let m(z) = 4*d(z) + 3*u(z). Factor m(v).
(v - 1)*(v + 5)
Factor 3*u**4 - 33*u**3 + 0*u**4 + 4*u**2 + 39*u**3 - u**2.
3*u**2*(u + 1)**2
Let s(u) be the second derivative of 81/28*u**4 + 0 + 5*u + 6/7*u**2 - 18/7*u**3. Factor s(y).
3*(9*y - 2)**2/7
Let x = 21 + -17. Factor q**3 - 7/5*q**x + 0*q + 0 - 1/5*q**2 + 3/5*q**5.
q**2*(q - 1)**2*(3*q - 1)/5
Let d(l) be the first derivative of 2/3*l**3 + 0*l**2 + 2/5*l**5 + l**4 - 3 + 0*l. Factor d(t).
2*t**2*(t + 1)**2
Let k(t) = -4*t**2 + 42*t - 17. Let w be k(10). Factor 9/2*c + 1/2*c**3 + w*c**2 + 0.
c*(c + 3)**2/2
Let g(x) be the first derivative of -2*x + 0*x**3 + 1/2*x**2 - 1/4*x**4 + 2. Let j(m) = -2*m**3 + 2*m - 5. Let b(d) = -5*g(d) + 2*j(d). Factor b(t).
t*(t - 1)*(t + 1)
Let w(p) be the second derivative of -4*p**2 + 16/3*p**4 + 2*p + 0 + 10/3*p**3 + 9/5*p**5. Factor w(k).
4*(k + 1)**2*(9*k - 2)
Let x(i) = i**2 + 11*i + 22. Let h be x(-9). Determine y, given that -16/9 + 124/9*y**2 - 14*y**h + 2/3*y**3 - 8/3*y = 0.
-1, -2/7, 2/3
Let b(i) be the first derivative of -i**2 + 1 + 0*i + 0*i**3 + 1/60*i**4 - 1/75*i**5. Let l(w) be the second derivative of b(w). Factor l(k).
-2*k*(2*k - 1)/5
Let w = 5 + 0. Suppose w*p = p. Factor -1/4*f + p + 1/4*f**2.
f*(f - 1)/4
Suppose 0 = 6*g - 14 - 10. Let j(c) be the first derivative of -1/12*c**g + 0*c + 1 + 0*c**2 - 2/15*c**5 + 1/9*c**3. Factor j(x).
-x**2*(x + 1)*(2*x - 1)/3
Suppose 2*y = -2*v - y + 35, 5*v - 75 = 5*y. Let b be (-14)/(-8) + 4/v. Factor -a**b + 5 - 5 - 2*a.
-a*(a + 2)
Let r(n) = -2*n**4 + 3*n**3 - 3*n**2 + 3*n. Let a(o) = -o**4 - o**3 + o**2 - o. Let g(y) = -3*a(y) - r(y). Let g(j) = 0. Calculate j.
0
Suppose -22 + 6 = -4*v. Suppose -v = 4*l - 6*l. Let -l*t**2 - 1 - 4 + 5 + 2*t**3 = 0. What is t?
0, 1
Let i(u) be the second derivative of -u**5/10 - 11*u**4/12 - 17*u**3/6 - 3*u**2 - 31*u. Find v, given that i(v) = 0.
-3, -2, -1/2
Let v(w) be the third derivative of 0*w - 1/30*w**5 + 1/105*w**7 + 0*w**6 + 1/24*w**4 - 1/336*w**8 + 0*w**3 - 5*w**2 + 0. Suppose v(a) = 0. What is a?
-1, 0, 1
Factor 0*a + 0 - 8*a**4 - 1/2*a**2 - 4*a**3.
-a**2*(4*a + 1)**2/2
Suppose -4*m = -m - 2*c - 6, -3*c - 9 = 4*m. Let x(b) be the third derivative of -1/240*b**6 + 0 + 3*b**2 - 1/48*b**4 + 0*b**3 - 1/60*b**5 + m*b. Factor x(p).
-p*(p + 1)**2/2
Let w be ((-10)/(-12) - 0)*12/40. Factor 0 + p**3 + 0*p + w*p**2 + 3/4*p**4.
p**2*(p + 1)*(3*p + 1)/4
Factor 1/3*u**2 - 1/6*u - 1/6*u**3 + 0.
-u*(u - 1)**2/6
Let w(a) = -a**3 - 7*a**2 + 2*a - 3. Let s be w(-8). Let n = 317/7 - s. Factor 0 - 8/7*h**3 + n*h**2 + 0*h.
-2*h**2*(4*h - 1)/7
Suppose 4*x - 4 = 2*m, -4*m - 15 + 7 = -x. What is c in 0*c - 10/11*c**3 + x + 4/11*c**2 = 0?
0, 2/5
Let d(o) = o + 1. Let w(s) = 3*s**2 - 7*s + 17. Let f(m) = -5*d(m) + w(m). Factor f(u).
3*(u - 2)**2
Find z, given that -6*z**2 + 3*z - z**2 - 5*z**4 + z**5 + 5*z**3 - z + 4*z**3 = 0.
0, 1, 2
Let j be (8/(-16))/(1 - 3). Let b = 110/3 - 205/6. Factor b*c**2 + 15/4*c**4 - j + 0*c + c**5 + 5*c**3.
(c + 1)**4*(4*c - 1)/4
Let w be -6 + (-2)/(36/(-16) + 2). Let -1/3 + 1/3*o**3 - o**w + o = 0. What is o?
1
Factor -t**3 + 11*t**2 - t**3 - 4*t**3 - t**2 + 4*t.
-2*t*(t - 2)*(3*t + 1)
Let w(p) be the second derivative of -p**5/20 - p**4/8 + 2*p**2 - p. Let i(z) be the first derivative of w(z). Factor i(o).
-3*o*(o + 1)
Let y = 45/148 + -2/37. Let b(c) = c**3 - 5*c**2 - 6*c + 2. Let m be b(6). Find p, given that 0*p - 1/4 + y*p**m = 0.
-1, 1
Let w(s) be the third derivative of 0*s + 3/40*s**6 + 0*s**3 - 9*s**2 - 1/20*s**5 + 0 + 0*s**4. Determine v so that w(v) = 0.
0, 1/3
Suppose -2*u - 5*u**2 + 3*u**2 - u**4 + 3*u**2 + 2*u**2 = 0. Calculate u.
-2, 0, 1
Let d be 3*(-1 - (-15)/9). Let b = 4 + -1. Factor -18*j**2 - d*j**5 + 4*j**3 - 2*j**b + 16*j**2 + 2*j**4.
-2*j**2*(j - 1)**2*(j + 1)
Let b(n) be the second derivative of -2*n**4/9 + 28*n**3/9 - 49*n**2/3 - 5*n. Find u, given that b(u) = 0.
7/2
Let a = -2 + -59. Let h = -181/3 - a. Factor 1/3*p - h*p**3 + 1/3*p**5 - 1/3*p**4 - 1/3 + 2/3*p**2.
(p - 1)**3*(p + 1)**2/3
Let h(t) = -t**5 + t**4 + t**3 - 1. Let q(d) = 7*d**5 - 14*d**4 + 18*d**3 - 34*d**2 + 23*d. Let x(b) = 6*h(b) + q(b). Factor x(i).
(i - 3)*(i - 2)*(i - 1)**3
Let g(n) be the third derivative of n**10/453600 - n**8/60480 - n**5/30 - n**2. Let m(q) be the third derivative of g(q). Factor m(w).
w**2*(w - 1)*(w + 1)/3
Let k(u) = 4*u + 11. Let q(h) = h + 1. Let o(c) = k(c) - 3*q(c). Let w be o(-6). Factor 2/7*a**w + 2/7 - 4/7*a.
2*(a - 1)**2/7
Suppose -5 - 3 = -4*p. Let w(m) be the first derivative of 0*m - 1/2*m**2 + 1/3*m**3 - p. Solve w(b) = 0.
0, 1
Let x(p) = 16*p - 3*p**2 - 3*p**2 + 4 + 4. Let u(g) = -g**3 + 3*g**2 - 4*g + 3. Let m be u(2). Let h(w) = w**2. Let c(y) = m*x(y) + 4*h(y). Factor c(o).
2*(o - 2)*(5*o + 2)
Let p(h) be the second derivative of -h**5/110 + 2*h**4/33 - 5*h**3/33 + 2*h**2/11 - 46*h. What is m in p(m) = 0?
1, 2
Let r(t) = t + 13. Let v be r(-11). Solve 0 + 0*u**v + 1/4*u**3 - 1/4*u = 0 for u.
-1, 0, 1
Let u(f) be the second derivative of 3*f + 3/40*f**5 - 3/4*f**2 + 1/8*f**4 + 0 - 1/4*f**3. Factor u(h).
3*(h - 1)*(h + 1)**2/2
Let b = 524/35 + -72/5. Determine s, given that 0*s**3 + 2/7*s - b*s**4 + 4/7*s**2 - 2/7*s**5 + 0 = 0.
-1, 0, 1
Let d be ((-6)/10)/(5/(-25)). Suppose -4*j = -4*o - 8, -j + d*j = -5*o - 10. Solve 0*n**4 - n**4 - n**5 + n**2 + n**3 + j*n**5 = 0 for n.
-1, 0, 1
Let t = -16 + 23. Let l(q) be the second derivative of -q + 0*q**2 + 1/10*q**5 + 0*q**3 + 0 - 1/6*q**4 + 1/15*q**6 - 1/21*q**t. Factor l(b).
-2*b**2*(b - 1)**2*(b + 1)
Let n(x) be the third derivative of -x**4/12 - 7*x**3/6 + 3*x**2. Let l be n(-5). Determine s so that 2*s**4 - 6*s**3 + l*s**3 - 3*s**4 - s - 3*s**2 = 0.
-1, 0
Let g(v) be the third derivative of v**7/70 - v**6/8 + 9*v**5/20 - 7*v**4/8 + v**3 + v**2. Factor g(i).
3*(i - 2)*(i - 1)**3
Let b(n) = -n**4 + n**3 + n. Let g(k) = -k**5 + 6*k**4 - 4*k**3 - k**2 - 5*k. Let z be (8/16)/((-1)/4). Let x(u) = z*g(u) - 10*b(u). Factor x(o).
2*o**2*(o - 1)**2*(o + 1)
What 