u(a). Factor c(f).
4*(f - 1)*(f + 1)
Let m(t) be the first derivative of 3*t**5 - 9*t**4/4 - 7*t**3 + 9*t**2/2 + 6*t - 31. Factor m(c).
3*(c - 1)**2*(c + 1)*(5*c + 2)
Let j(c) = -4*c**2 + c. Let q(v) = -5*v**2. Let z(s) = -6*j(s) + 5*q(s). Let k be z(-6). Suppose k*h - 2/13*h**2 - 2/13*h**4 - 4/13*h**3 + 0 = 0. Calculate h.
-1, 0
Factor 10/11*c**3 - 4/11 + 2/11*c + 16/11*c**2.
2*(c + 1)**2*(5*c - 2)/11
Let u(q) be the third derivative of -q**6/900 + q**5/150 - q**3/2 - q**2. Let d(f) be the first derivative of u(f). Factor d(i).
-2*i*(i - 2)/5
Let t(s) be the second derivative of -2*s**6/105 - 6*s**5/35 - 13*s**4/21 - 8*s**3/7 - 8*s**2/7 + 29*s. Factor t(o).
-4*(o + 1)**2*(o + 2)**2/7
Let m be -8 + 6 - (-2 - 0). Let s be (-16)/(-12)*3/8. Let -s*k**4 + m*k**2 - 2*k + 0 + 3/2*k**3 = 0. Calculate k.
-1, 0, 2
Factor 18*j - 12 + 3/4*j**3 - 27/4*j**2.
3*(j - 4)**2*(j - 1)/4
Let d(h) = -h - 1. Let y be d(-3). Find j such that -3*j**3 + 4*j**5 + 0*j**4 - 5*j**3 + y + 2*j**4 + 4*j - 4*j**2 = 0.
-1, -1/2, 1
Let z(d) be the second derivative of -d**6/30 - d**5/20 + d**4/12 + d**3/6 + 22*d. Suppose z(j) = 0. Calculate j.
-1, 0, 1
Let r(n) be the first derivative of -n**3/3 + 2*n**2 - 3*n + 6. Factor r(p).
-(p - 3)*(p - 1)
Let f(p) be the third derivative of p**9/30240 - p**8/10080 - p**7/2520 + p**6/360 - p**5/15 - 3*p**2. Let g(v) be the third derivative of f(v). Factor g(l).
2*(l - 1)**2*(l + 1)
Suppose -2/13 - 2/13*f**3 - 6/13*f - 6/13*f**2 = 0. What is f?
-1
Let v(t) = t + 19*t**2 + 2*t - 18*t**2. Let d(b) = b**2 + 4*b. Let z(a) = -2*d(a) + 3*v(a). Find i, given that z(i) = 0.
-1, 0
Suppose -8*k = -10*k + 4. Let j(p) be the third derivative of k*p**2 - 1/120*p**5 + 0 + 1/60*p**6 + 0*p**4 + 0*p**3 + 0*p. Factor j(f).
f**2*(4*f - 1)/2
Let p(v) be the third derivative of -v**6/840 - v**5/420 + 5*v**4/84 - 4*v**3/21 - 33*v**2. Factor p(o).
-(o - 2)*(o - 1)*(o + 4)/7
Let b(w) = w**3 + 3*w**2 - 3*w + 3. Let t(c) = 2*c**2 - 2*c + 2. Let p(k) = -k**2 - 5*k + 3. Let r be p(-6). Let o(v) = r*t(v) + 2*b(v). Factor o(j).
2*j**3
Let f(q) be the second derivative of 1/105*q**7 + 0*q**2 + 0*q**3 - 1/50*q**5 + 0*q**4 + 0*q**6 + q + 0. Factor f(j).
2*j**3*(j - 1)*(j + 1)/5
Let h(o) = -7*o**3 - 30*o**2 - 30*o - 6. Suppose 0*x - 3*x - 18 = 0. Let f(u) = u**3 - u + 1. Let p(b) = x*f(b) + 3*h(b). What is i in p(i) = 0?
-2, -2/3
Let y be (-1)/3 - 4/(-10). Let b(r) be the second derivative of 7/20*r**5 + 3/4*r**4 + 1/2*r**2 + 5/6*r**3 + y*r**6 + r + 0. Factor b(l).
(l + 1)**3*(2*l + 1)
Let p(o) be the third derivative of -o**6/120 + o**5/30 + o**4/24 - o**3/3 + 17*o**2 - 1. Let p(k) = 0. What is k?
-1, 1, 2
Let h(j) = -2*j - 30. Let u be h(-16). Factor u*y + 5/4*y**2 - 1.
(y + 2)*(5*y - 2)/4
Let a(q) be the first derivative of -1/12*q**3 - 1/2*q - 1 + 3/8*q**2. Suppose a(u) = 0. What is u?
1, 2
Let p = 127/10 + -61/5. Factor -p*a + 1/4*a**4 + 0*a**2 + 1/2*a**3 - 1/4.
(a - 1)*(a + 1)**3/4
Let u(d) be the first derivative of -4/3*d**3 - 1/2*d**4 - 2 + 0*d - d**2. Suppose u(s) = 0. Calculate s.
-1, 0
Let d be (20/(-16) + 2)/((-9)/(-6)). Find w such that 5/2*w**2 + 4*w + 2 + d*w**3 = 0.
-2, -1
Let g(c) be the first derivative of -2*c**3/3 - 4*c**2 - 6*c - 12. Solve g(d) = 0.
-3, -1
Let z = -14 - -29/2. Solve 1/2*f**3 + 3/2*f**2 - 1/2*f - 1 - z*f**4 = 0 for f.
-1, 1, 2
Suppose 0 = z + 3*z. Let u(c) be the second derivative of -1/24*c**4 + 0 + c - 3/40*c**5 + z*c**3 - 1/30*c**6 + 0*c**2. Factor u(v).
-v**2*(v + 1)*(2*v + 1)/2
Let q(m) = 4*m**5 - 3*m**4 + 2*m**3 - m**2 - 5. Let p(x) = -x**5 - x**3 + 1. Let a(k) = -5*p(k) - q(k). Solve a(i) = 0 for i.
-1, 0
Find x, given that 396*x**2 - 386*x**2 - 12*x**3 + 2*x**4 + x - x = 0.
0, 1, 5
Let i = 16 + -10. Let l = 8 - i. Factor 2/3*v - 1/3 - 1/3*v**l.
-(v - 1)**2/3
Let u(o) be the third derivative of 2*o**2 + 0 + 0*o - 1/10*o**5 - 1/12*o**4 + 2/3*o**3. Factor u(p).
-2*(p + 1)*(3*p - 2)
Let w = 11 + -11. Let a be (0 - (-3 + 3)) + 2. Factor -1/3*f**a - 1/3*f + w.
-f*(f + 1)/3
Let u(n) be the second derivative of -n**7/56 - 7*n**6/40 - 3*n**5/8 + 9*n**4/8 + 27*n**3/8 - 81*n**2/8 + n. Factor u(d).
-3*(d - 1)**2*(d + 3)**3/4
Let l(r) be the second derivative of -r**4/14 + 2*r**3/21 + 2*r. Let l(a) = 0. What is a?
0, 2/3
Let v = 51 - 48. Let u(o) be the third derivative of 1/30*o**5 + 0*o**v + 0*o + 3*o**2 + 0 + 1/6*o**4. Find s, given that u(s) = 0.
-2, 0
Let x(o) be the second derivative of 0 - 1/3*o**3 - 1/3*o**4 - 1/10*o**5 + o + 0*o**2. Solve x(n) = 0.
-1, 0
Let n(t) be the first derivative of 7/10*t**5 + 23/8*t**4 + 10/3*t**3 + t**2 + 8 + 0*t. Factor n(f).
f*(f + 1)*(f + 2)*(7*f + 2)/2
Factor -1/6*c**2 - c - 3/2.
-(c + 3)**2/6
Let u = 168/395 - 2/79. Solve -2/5*v + 0 + u*v**2 = 0.
0, 1
Let t be 2 - -2 - 24/24. Suppose 50/9*u**2 + 4/9 + 26/9*u + 28/9*u**t = 0. Calculate u.
-1, -1/2, -2/7
Let p(r) = -r**4 - r**3 + 3*r**2 - 1. Let m(a) = a - 1. Let v(g) = -2*m(g) - 2*p(g). Determine c so that v(c) = 0.
-2, -1, 1
Let v(d) = -d**4 + d**3 + d**2 + d. Let a(q) = -4*q**4 + 4*q**3 + 7*q**2 - q. Let l(u) = a(u) - 3*v(u). Factor l(z).
-z*(z - 2)*(z - 1)*(z + 2)
Let t(h) be the first derivative of -1/7*h**2 + 2/21*h**3 + 3 + 0*h. Factor t(o).
2*o*(o - 1)/7
Factor 21/4*v**3 - 9*v**2 + 0 - 3*v.
3*v*(v - 2)*(7*v + 2)/4
Factor 53*l + 3*l**2 - 20*l + 14 + 16.
3*(l + 1)*(l + 10)
Let l be (-4)/6 - (-40)/15. Let m = 2 + l. Factor f**m + 0*f**4 - f**3 + f**5 + 0*f**4 - f**2.
f**2*(f - 1)*(f + 1)**2
Factor 4*x**3 + 23/5*x**4 - 32/5*x**2 - 32/5*x + x**5 + 16/5.
(x - 1)*(x + 2)**3*(5*x - 2)/5
Let q(v) = v**2 - 34*v - 79. Let f(z) = -6*z**2 + 171*z + 396. Let l(w) = 4*f(w) + 21*q(w). Factor l(r).
-3*(r + 5)**2
Let w be 1/(1/(-4)*-2). Suppose 4 = 14*a - 12*a. Factor -i**5 - 5*i**3 + 3*i + 1 + 4*i**a - 3*i**4 + 3*i**3 - 2*i**w.
-(i - 1)*(i + 1)**4
Let g(v) be the second derivative of -1/3*v**2 + 1/9*v**4 + 0 + 4*v - 7/18*v**3. Factor g(p).
(p - 2)*(4*p + 1)/3
Let z(q) = -q**3 - 2*q**2 - 2*q. Let i be z(-2). Let l be ((-1)/(-4))/(9/36). Factor -3*f + i*f + l + 4*f**2 - 5*f**2 - f**3.
-(f - 1)*(f + 1)**2
Let k(y) be the first derivative of y**5/80 + y**4/16 + y**3/8 + 3*y**2/2 - 3. Let c(h) be the second derivative of k(h). Solve c(z) = 0 for z.
-1
Let k(z) be the first derivative of -z**6/36 - z**5/5 - 13*z**4/24 - 2*z**3/3 - z**2/3 + 6. Find g, given that k(g) = 0.
-2, -1, 0
Let i(l) = -l**3 - 11*l**2 - l - 7. Let r be i(-11). Let s = 8 - 5. Let s*v**2 + 3*v - v - r*v**2 = 0. What is v?
0, 2
Let x be (-1 + -5)*2/(-4). Factor -p - 2 + 2 + x*p + p**2.
p*(p + 2)
Factor 64/5*l + 32/5 + 48/5*l**2 + 2/5*l**4 + 16/5*l**3.
2*(l + 2)**4/5
Let q be ((-4)/(-20))/(-3 + 51/15). Factor -3/2*v + 3/2*v**2 - 1/2*v**3 + q.
-(v - 1)**3/2
Let o(y) be the second derivative of y**8/8400 - y**7/1400 + y**6/1800 + y**4/6 + 3*y. Let b(c) be the third derivative of o(c). Factor b(w).
w*(w - 2)*(4*w - 1)/5
Suppose -4 = -0*z - 2*z. Suppose 0 - 9*q - 4 + 9*q**2 + z + 4 = 0. What is q?
1/3, 2/3
Let y(u) be the second derivative of -1/90*u**6 - 1/9*u**3 + 1/30*u**5 + 0*u**4 + 2*u + 0 + 1/6*u**2. Determine c so that y(c) = 0.
-1, 1
Let l = -7633 + 23237/3. Let 8/3 + 104/3*t + l*t**2 = 0. Calculate t.
-2/13
Let r(h) be the second derivative of -h**5/30 + h**4/12 + 5*h**2/2 - 5*h. Let o(c) be the first derivative of r(c). Factor o(l).
-2*l*(l - 1)
Let i be (-1)/((-14)/46) - (-6)/(-21). Let v(z) be the third derivative of 1/60*z**4 + 0*z + 0*z**i - 3*z**2 - 1/150*z**5 + 0. Factor v(d).
-2*d*(d - 1)/5
Let v(w) be the third derivative of -5*w**8/112 - w**7/35 + w**6/4 + w**5/5 - 5*w**4/8 - w**3 + 4*w**2. Determine c so that v(c) = 0.
-1, -2/5, 1
Let m(a) be the third derivative of -a**8/25200 - a**7/5040 - a**6/3600 + 7*a**5/60 - 2*a**2. Let j(y) be the third derivative of m(y). Factor j(q).
-(q + 1)*(4*q + 1)/5
Let y(o) = 7*o**2 - 7. Let w(h) = -10*h**2 + 10. Let k(r) = -5*w(r) - 7*y(r). Factor k(b).
(b - 1)*(b + 1)
Let c(n) be the first derivative of 2*n**3/51 + 2*n**2/17 + 2*n/17 - 5. Determine k, given that c(k) = 0.
-1
Let l(t) be the first derivative of 2*t**3/3 + 3*t**2 + 15. Factor l(k).
2*k*(k + 3)
Suppose 0 = -s - 0*s + 4. Factor 2*t**2 + 2*t**3 - 3*t**s - t + t**5 - 3*t + 1 + t.
(t - 1)**4*(t + 1)
Determine l so that -2*l**3 + 845*l**4 - 12 + 2*l - 847*l**4 + 6*l**2 + 8*l**2 = 0.
-3