23. Let k(g) = -6*g**2 + 20*g - 70. Let j(o) = x*r(o) + 5*k(o). Factor j(d).
2*(d - 3)**2
Suppose -7*n**3 + 3*n**3 - 3*n**2 + 5*n**4 - 2*n**4 + n**3 + 3*n**5 = 0. Calculate n.
-1, 0, 1
Suppose -2*f + 2 = -0*f. Suppose -4 + f = -g. Factor -2/9*n**2 + 0*n + 0 + 4/9*n**g - 2/9*n**4.
-2*n**2*(n - 1)**2/9
Let q(l) be the second derivative of l**4/8 + l**3 + 9*l**2/4 + 10*l. Factor q(u).
3*(u + 1)*(u + 3)/2
Let a = 36 - 4. Let r = a + -63/2. Factor r + 0*d - 1/2*d**2.
-(d - 1)*(d + 1)/2
Let j(m) be the second derivative of -m**6/25 - 21*m**5/100 - 2*m**4/5 - 3*m**3/10 + 4*m - 1. Determine v, given that j(v) = 0.
-3/2, -1, 0
Let n(h) be the first derivative of 1/3*h**4 + 3 + 2/9*h**3 + 0*h**2 + 0*h + 2/15*h**5. Find s, given that n(s) = 0.
-1, 0
Let l(z) be the first derivative of 11/8*z**2 + 5 - 3/4*z**3 - 1/2*z. Suppose l(f) = 0. What is f?
2/9, 1
Let i(x) be the first derivative of -x**6/4 + 3*x**5/10 + 3*x**4/8 - x**3/2 + 7. Factor i(t).
-3*t**2*(t - 1)**2*(t + 1)/2
Find l, given that -1/5 + 2/5*l - 1/5*l**2 = 0.
1
Let p = -5795/97 + -3/388. Let i = 60 + p. Factor -1/4*n**2 - i*n + 0.
-n*(n + 1)/4
Factor -6*j**2 - 10*j - 2/3*j**3 + 50/3.
-2*(j - 1)*(j + 5)**2/3
Let o(g) be the second derivative of -g**10/90720 + g**9/15120 - g**8/6720 + g**7/7560 + g**4/12 + 2*g. Let i(m) be the third derivative of o(m). Factor i(k).
-k**2*(k - 1)**3/3
Let h(f) be the first derivative of f**4/16 - f**3/12 - 1. Let h(n) = 0. Calculate n.
0, 1
Factor 0 + 21/4*r - 3/4*r**2.
-3*r*(r - 7)/4
Let x(f) be the third derivative of -f**8/1176 + 2*f**7/735 + f**6/210 - 2*f**5/105 - f**4/84 + 2*f**3/21 - 5*f**2. Let x(d) = 0. What is d?
-1, 1, 2
Let v(k) = -k**4 - 2*k**3 - k**2 + 2. Let x(d) = 1. Suppose 4*a + 4 = 6*a. Let g(l) = a*v(l) - 4*x(l). Factor g(s).
-2*s**2*(s + 1)**2
Let p = -4 + 10. Let f(g) = -4*g**2 + 2*g. Let m(q) = 3*q**2 - q. Let a(u) = p*m(u) + 4*f(u). Suppose a(h) = 0. What is h?
-1, 0
Suppose -30*v + 24*v = -18. Let 1/4*n**4 + 0 - 5/4*n**v - n + 2*n**2 = 0. Calculate n.
0, 1, 2
Let t(r) be the third derivative of -r**7/420 - r**6/72 - r**5/30 + r**4/12 - 3*r**2. Let a(f) be the second derivative of t(f). Find d such that a(d) = 0.
-1, -2/3
Solve -3*k - 3*k**4 + 2*k**2 - k**3 + 3*k**3 + 0*k**2 + 1 - 3*k**5 + 4*k**5 = 0.
-1, 1
Let m be 2/3*((-15)/12 - -2). Suppose 1/2*q**2 - q + m = 0. What is q?
1
Suppose 12*o - 4 = 10*o. Let q(d) be the third derivative of 1/6*d**3 + 0 - 1/210*d**7 + 1/12*d**4 - d**o + 0*d**5 + 0*d - 1/60*d**6. Factor q(i).
-(i - 1)*(i + 1)**3
Let -1/3*u - 2/3*u**2 + 2/3*u**4 + 0 + 0*u**3 + 1/3*u**5 = 0. Calculate u.
-1, 0, 1
Let c(d) be the first derivative of d**3/3 + d**2 + d + 2. Let h(k) = -k**2 - 2*k - 1. Let s(v) = -5*c(v) - 6*h(v). Let s(o) = 0. What is o?
-1
Let c(x) be the first derivative of 27*x**4/4 + 2*x**3/3 - x**2/2 - 3. Let r be c(1). Factor -2*z**3 + 28 - r.
-2*z**3
Factor 5*d**4 - 2*d**4 - 2*d**4.
d**4
Factor -6*f - 20*f - 4*f**3 - f**3 + 20*f**2 + f + 10.
-5*(f - 2)*(f - 1)**2
Let r(w) = w**3 - 2*w**2 - 4*w + 3. Let d be r(3). Suppose 4*l + 28 = 2*v - 0*l, d = -5*l - 25. Factor 2/3*y**v + 0*y**3 + 0 - 2/3*y**2 - 1/3*y + 1/3*y**5.
y*(y - 1)*(y + 1)**3/3
Factor -1/3 + 2/3*r - 1/3*r**2.
-(r - 1)**2/3
Let a(b) be the first derivative of 5*b**5 + 45/2*b**4 + 0*b - 52/3*b**3 - 3 - 125/6*b**6 + 4*b**2. What is k in a(k) = 0?
-1, 0, 2/5
Let v = -1/19319 + 27162523/173871. Let h = -156 + v. Factor 0 - h*a**2 - 2/9*a.
-2*a*(a + 1)/9
Let f(j) be the second derivative of 0 + 1/10*j**5 + 1/12*j**4 + 1/30*j**6 - j + 0*j**2 + 0*j**3. Factor f(q).
q**2*(q + 1)**2
Suppose 2*c = 4, -6*c + c = -5*u + 5. Let -k**2 + 2*k**2 - 5*k**4 - 3*k**5 - u + 3 - k**3 = 0. Calculate k.
-1, 0, 1/3
Let m(q) = -5*q**5 + 10*q**3 - 25*q**2 + 5*q. Let t(d) = -d**4 - d**3 - d. Let y(g) = m(g) - 5*t(g). Suppose y(z) = 0. What is z?
-2, 0, 1
Let j(s) = 10*s**2 + 3*s - 7. Let q(z) = 7*z**2 + 2*z - 5. Let i(d) = d**2 - 7*d + 5. Let u be i(7). Let c(a) = u*j(a) - 7*q(a). Factor c(m).
m*(m + 1)
Let r(j) be the first derivative of 2*j**5/5 - j**4 - 2*j**3 + 4*j**2 + 8*j - 4. Solve r(p) = 0 for p.
-1, 2
Let b = 29 + -21. Let r be (-1 - 0)/((-2)/b). Find d, given that 0 + d - 9/2*d**5 - 7/2*d**2 + 15/2*d**r - 1/2*d**3 = 0.
-2/3, 0, 1/3, 1
Let j(s) be the third derivative of -s**5/150 - s**4/18 - s**3/15 - s**2. Factor j(m).
-2*(m + 3)*(3*m + 1)/15
Let c = -83 + 583/7. Determine r, given that 0 - 4/7*r**4 + 0*r - c*r**5 + 0*r**2 - 2/7*r**3 = 0.
-1, 0
Let l(b) = 7*b**4 + 6*b**3 + 4*b**2 + 5*b + 5. Let r(h) = -22*h**4 - 18*h**3 - 12*h**2 - 16*h - 16. Let t(y) = 16*l(y) + 5*r(y). Factor t(m).
2*m**2*(m + 1)*(m + 2)
Suppose x = 1, -3*j + 4*x = -x - 4. Let k(c) be the third derivative of -j*c**2 + 0*c + 1/180*c**5 + 1/9*c**3 + 0 + 1/24*c**4. Let k(b) = 0. What is b?
-2, -1
Let m(h) be the first derivative of 0*h - 1 + 0*h**3 + h**2 - 1/360*h**6 - 1/18*h**4 + 1/45*h**5. Let x(y) be the second derivative of m(y). Factor x(v).
-v*(v - 2)**2/3
Factor 32/13 + 0*d**2 - 2/13*d**3 + 24/13*d.
-2*(d - 4)*(d + 2)**2/13
Let g(m) be the second derivative of 5/24*m**4 + 1/20*m**5 + 0 - m + m**2 + 1/3*m**3. Let b(n) be the first derivative of g(n). Let b(s) = 0. Calculate s.
-1, -2/3
Determine g so that -4/9*g**5 - 8/9*g**2 + 4/9*g**3 + 2/9 + 0*g + 2/3*g**4 = 0.
-1, -1/2, 1
Let g be -1 - -1 - (-13 + 7). Let f(y) be the first derivative of 5*y**4 - 10/3*y**3 + y - 1 + 0*y**2 + 2/3*y**g - 3*y**5. Factor f(s).
(s - 1)**4*(4*s + 1)
Let o(t) be the third derivative of t**8/840 + t**7/525 - t**6/150 - t**5/75 + t**4/60 + t**3/15 + 10*t**2 + 2. Factor o(n).
2*(n - 1)**2*(n + 1)**3/5
Suppose -9/5*y**2 + 9/5 + 3/5*y - 3/5*y**3 = 0. Calculate y.
-3, -1, 1
Suppose -14 = -4*o - 158. Let p be (o/(-15) - 1) + -1. Factor 0*d + 0 + p*d**2 - 4/5*d**3 + 2/5*d**4.
2*d**2*(d - 1)**2/5
Let j(z) be the second derivative of -z**6/180 - z**5/30 + 4*z**3/9 + z**2 + 2*z. Let v(m) be the first derivative of j(m). Determine c, given that v(c) = 0.
-2, 1
Let n(d) be the second derivative of d**7/840 - d**6/180 + d**5/120 + 7*d**3/6 - 4*d. Let l(r) be the second derivative of n(r). Factor l(f).
f*(f - 1)**2
Let x(q) be the third derivative of 0 + 0*q**4 - 6/35*q**7 + 0*q**3 + 0*q - 1/5*q**6 - 9*q**2 - 1/15*q**5. Factor x(j).
-4*j**2*(3*j + 1)**2
Let j = -523/36 - -59/4. Factor 8/9*p**2 + 0 + j*p + 8/9*p**4 + 4/3*p**3 + 2/9*p**5.
2*p*(p + 1)**4/9
Suppose -4*i - q = -11, -5*i = 5*q + 2 - 27. Determine g so that 0 - 7/2*g**3 + g - 5/2*g**i = 0.
-1, 0, 2/7
Factor -5*t - 16/5*t**3 - 3/5 - 56/5*t**2.
-(t + 3)*(4*t + 1)**2/5
Solve -1/2*u**3 + 0*u + 0 + 2*u**2 = 0.
0, 4
Suppose 0 = 594*u - 590*u. Let 0*f**2 + 3/7*f + u - 3/7*f**3 = 0. Calculate f.
-1, 0, 1
Let d be 16/10*70/84. Solve 0 + d*v + 2*v**4 - 2*v**2 - 4/3*v**3 = 0 for v.
-1, 0, 2/3, 1
Let m(g) be the third derivative of -g**7/8820 + g**6/2520 + g**5/210 - g**4/8 - 3*g**2. Let i(c) be the second derivative of m(c). Find s, given that i(s) = 0.
-1, 2
Let s be 0 - (3 - (-4)/(-1)). Let h be (s/(-2))/(3/(-18)). Factor -11/4*o**h - 1/2*o**2 + 0*o + 0 - 9/4*o**4.
-o**2*(o + 1)*(9*o + 2)/4
Let x = 13 + -8. Determine c so that 3*c**2 + 2*c - x*c**2 - 2 - 4*c + 6*c = 0.
1
Suppose 4*f - 2 = 6. Let l be (-2)/(-4) + -16 + 16. Factor 1/2*q**f + q + l.
(q + 1)**2/2
Let c(j) be the third derivative of 0 + 0*j - 1/30*j**6 - 4/9*j**3 - 5*j**2 - 1/3*j**4 - 1/315*j**7 - 13/90*j**5. Factor c(x).
-2*(x + 1)**2*(x + 2)**2/3
Let o = -157 - -1885/12. Let s(g) be the second derivative of -1/3*g**2 - 2*g + 5/18*g**3 + 0 - o*g**4. Suppose s(x) = 0. What is x?
2/3, 1
Factor -3/5*s**3 + 0 + 12/5*s**2 - 12/5*s.
-3*s*(s - 2)**2/5
Let o be 2 - ((-2)/(-10) - -1). Let n = -3 + 5. What is a in o*a + 0*a**n - 4/5*a**3 + 2/5*a**4 - 2/5 = 0?
-1, 1
Let j(u) be the second derivative of 2/3*u**2 + 10/9*u**3 - 4*u + 0 + 25/36*u**4. Factor j(p).
(5*p + 2)**2/3
Factor -9/4*n - 3/4*n**2 - 3/2.
-3*(n + 1)*(n + 2)/4
Let l(h) be the third derivative of h**8/2688 - h**7/560 + h**6/480 + 2*h**2. Factor l(x).
x**3*(x - 2)*(x - 1)/8
Factor -2/5*a**3 + 0 + 1/5*a**2 + 0*a + 1/5*a**4.
a**2*(a - 1)**2/5
Let y be (-376)/(-24)*1/(-45). Let w = -2/135 - y. Find l such that -1/3*l**3 + w*l**2 + 0 + 1/3*l - 1/3*l**4 = 0.
-1, 0, 1
What is h in -1/6*h - 1/6*h**2 + 1/3 = 0?
-2, 1
Let u = 43 + -36. Let g(h) be the second deri