-17*b**2 + 16 - 2*b**3 + 14*b**2 + 15*b**2 - 24*b.
-2*(b - 2)**3
Let l(k) = -9*k**2 - 25*k. Let d(u) = 13*u**2 + 37*u. Let f(m) = -5*d(m) - 7*l(m). Factor f(o).
-2*o*(o + 5)
Let c(q) be the first derivative of -q**6/4 + 21*q**5/20 - 3*q**4/2 + q**3/2 + 3*q**2/4 - 3*q/4 + 2. Find m such that c(m) = 0.
-1/2, 1
Let y = 26 + -24. Let l(v) be the first derivative of 0*v - y + v**2 - 4/3*v**3 + 1/2*v**4. Factor l(z).
2*z*(z - 1)**2
Let n(d) be the third derivative of -d**9/3024 + d**7/840 + d**3/6 + 2*d**2. Let s(b) be the first derivative of n(b). Factor s(o).
-o**3*(o - 1)*(o + 1)
Let y be 3 - (6 + -4 + -1). Solve 2/5*z**3 - 2/5*z - 2/5 + 2/5*z**y = 0.
-1, 1
Let i be 126/45 - (3 + -1). Factor -2/5*w + i*w**3 + 0*w**4 - 2/5*w**5 + 0*w**2 + 0.
-2*w*(w - 1)**2*(w + 1)**2/5
Factor 0 + 1/4*v**4 + 0*v**3 + 0*v - 1/4*v**2.
v**2*(v - 1)*(v + 1)/4
Let n(g) be the third derivative of -g**9/241920 + g**8/40320 - g**7/20160 + g**5/15 + g**2. Let b(o) be the third derivative of n(o). Factor b(u).
-u*(u - 1)**2/4
Factor -8/3*y - 4 + 4/3*y**2.
4*(y - 3)*(y + 1)/3
Let k(q) be the first derivative of -5*q**6/6 - 2*q**5 + 5*q**4 + 40*q**3/3 + 65. Factor k(a).
-5*a**2*(a - 2)*(a + 2)**2
Let n(c) be the second derivative of 2*c**7/21 - 2*c**6/15 - c. Let n(l) = 0. What is l?
0, 1
Suppose -5*t = -21 - 4. Suppose -2*g = 3*o - t - 10, 0 = 3*g + 3*o - 15. Suppose -2/3*j + g + 1/3*j**2 + 5/3*j**4 + 8/3*j**3 = 0. Calculate j.
-1, 0, 2/5
Factor 4/3*w**3 - 4/3*w + 0*w**2 + 0.
4*w*(w - 1)*(w + 1)/3
Let c(h) be the first derivative of -10*h**3/27 - 2*h**2/9 - 11. Let c(p) = 0. Calculate p.
-2/5, 0
Let c(o) be the second derivative of o**3/6 - 4*o**2 + 3*o. Let j be c(12). Factor 0*g**j - 1/2*g + g**3 + 0 + 0*g**2 - 1/2*g**5.
-g*(g - 1)**2*(g + 1)**2/2
Solve 0*z + 0 + 1/7*z**2 = 0.
0
Let w(p) be the second derivative of p**7/5040 - p**6/1440 - p**5/120 + p**4/6 + 2*p. Let t(d) be the third derivative of w(d). Factor t(f).
(f - 2)*(f + 1)/2
Let t be (-2)/6 + 4/3. Let h = t + 1. Factor -h*f**2 - 9*f + 3*f**3 - 2*f**3 + 8*f + 2*f**4.
f*(f - 1)*(f + 1)*(2*f + 1)
Let a(g) = -g**2 - 3*g + 10. Let f be a(-5). Suppose 0 = 3*n - 6 - 0. Determine k, given that 2/7*k**3 + f*k**n - 2/7*k + 0 = 0.
-1, 0, 1
Let n(f) = 3*f - 3*f + f - 1. Let m be n(1). Let -2/7*a**3 + m - 4/7*a**2 - 2/7*a = 0. Calculate a.
-1, 0
Let n = 20 + -5. Let w be 13/n - (-2)/(-10). Factor 0 + 0*t**2 - 2/3*t**3 + w*t**5 + 0*t + 0*t**4.
2*t**3*(t - 1)*(t + 1)/3
Let u(t) be the third derivative of 0*t + 1/15*t**4 + 0*t**3 - 2*t**2 + 1/50*t**6 + 1/15*t**5 - 2/525*t**7 + 0 - 1/420*t**8. Solve u(l) = 0 for l.
-1, 0, 2
Let h(x) be the first derivative of 2*x**4/3 + 10*x**3/3 - 6*x**2 + 6*x + 5. Let k(g) be the first derivative of h(g). Determine l, given that k(l) = 0.
-3, 1/2
Let z = 43/12360 - -1/206. Let m(b) be the third derivative of 0*b - 1/240*b**5 + z*b**6 + 0 + 1/280*b**7 - 1/48*b**4 + 0*b**3 - 3*b**2. Factor m(i).
i*(i + 1)**2*(3*i - 2)/4
What is o in 7/3*o**3 - 5/3*o**5 + o**2 + 0 - 2/3*o - o**4 = 0?
-1, 0, 2/5, 1
Suppose -l = l - 4. Solve 0*w**2 + 18 - 20 - 4*w - l*w**2 = 0.
-1
Suppose 7*u - 12 = 3*u. Factor 3*c + 3*c**4 - 3*c**2 - 3*c**u + 0*c**3 + 0*c.
3*c*(c - 1)**2*(c + 1)
Determine c so that 1/3*c**2 - 1/3*c + 0 = 0.
0, 1
Find c, given that 3/4*c**3 + 3/2 + 3/4*c**4 - 9/4*c**2 - 3/4*c = 0.
-2, -1, 1
Factor 3*t**2 + 24*t**3 - 3*t**4 - 24*t**3.
-3*t**2*(t - 1)*(t + 1)
Let x(w) be the third derivative of 0 + w**2 + 0*w + 1/210*w**5 - 1/84*w**4 + 0*w**3. Factor x(y).
2*y*(y - 1)/7
Determine u so that -6 - 3/2*u**2 + 15/2*u**4 + 75/2*u**5 - 123/2*u**3 + 24*u = 0.
-1, 2/5, 1
Let g(l) = l**2 + 5*l - 6. Let y be g(-6). Factor 1/2*m**4 + 0 + 1/2*m**3 + y*m + 0*m**2.
m**3*(m + 1)/2
Let f(j) be the first derivative of 14*j**5/5 + 8*j**4 - 2*j**3 - 16*j**2 - 8*j - 2. Suppose f(r) = 0. Calculate r.
-2, -1, -2/7, 1
Let l(i) = -i**2 - 19*i + 31. Let a(h) = 10*h - 16. Let m(r) = -5*a(r) - 2*l(r). Factor m(p).
2*(p - 3)**2
Let a(g) be the second derivative of 3/10*g**5 + 3*g + 0*g**6 + 0 + 1/3*g**4 - 1/21*g**7 + 0*g**2 + 0*g**3. Find z such that a(z) = 0.
-1, 0, 2
Let o be 9/15*(-26)/(-39). Factor o*j**2 + 0 + 4/5*j.
2*j*(j + 2)/5
Suppose 12 + 38 = 5*t. Let o(j) = -j + t*j**2 + 0*j + 0*j - 6*j**2 - 3. Let y(a) = 3*a**2 - a - 2. Let r(v) = -2*o(v) + 3*y(v). Determine p so that r(p) = 0.
0, 1
Factor 12/7*q**4 + 0 + 4/7*q**2 + 0*q - 4/7*q**5 - 12/7*q**3.
-4*q**2*(q - 1)**3/7
Let v(j) = -18*j**4 + 69*j**3 - 75*j**2 + 15*j + 8. Let w(n) = -n**3 + n**2 + n. Let g(y) = -v(y) - w(y). Factor g(k).
2*(k - 2)*(k - 1)**2*(9*k + 2)
Let 6*g**2 - g**2 - 5*g**3 + 7*g - g + 4*g = 0. Calculate g.
-1, 0, 2
Suppose -4*f + 6 = -4*b - 10, -4*f = 3*b - 2. Determine i, given that 2/5*i**f + 4/5*i + 0 = 0.
-2, 0
Let v be 3/(2/6 + (-42)/(-36)). Let j(q) be the first derivative of -2/11*q + 0*q**v + 2/33*q**3 + 3. Factor j(l).
2*(l - 1)*(l + 1)/11
Let m = 211/495 - -1/55. Let y(r) be the first derivative of -m*r + 2/27*r**3 - 2 - 1/9*r**2. Find l, given that y(l) = 0.
-1, 2
Factor -15/4*v**2 + 21/4*v - 3/2.
-3*(v - 1)*(5*v - 2)/4
Suppose -8*g + 3*g = 0. Suppose 0 = q - 2 - g. Determine l so that 0*l + 0 - 2/7*l**q + 8/7*l**3 = 0.
0, 1/4
Let j(k) be the first derivative of -2*k**5/5 + k**4/2 + 2. What is r in j(r) = 0?
0, 1
Let b(c) be the third derivative of c**5/60 - 5*c**4/24 + 2*c**3/3 - 15*c**2. Factor b(g).
(g - 4)*(g - 1)
Solve 0*t**2 - 1/4*t + 0 + 1/4*t**3 = 0 for t.
-1, 0, 1
Factor t**5 - 55*t**3 - 4*t**5 - t**5 + 31*t**3 + 16*t**2 + 16*t**4 - 4*t.
-4*t*(t - 1)**4
Factor 8*m + 0*m + 5*m**3 - 18*m + 5*m**2 - 5*m**4 + 5*m.
-5*m*(m - 1)**2*(m + 1)
Let b(q) = q**2 + 12*q + 29. Let v be b(-9). Factor 1/2*t - 1/2*t**3 - 1/2*t**v + 0 + 1/2*t**4.
t*(t - 1)**2*(t + 1)/2
Let q(m) = m**2 + m. Let v be q(0). Factor 1/2*o**5 + v - o**2 + 0*o**3 + o**4 - 1/2*o.
o*(o - 1)*(o + 1)**3/2
What is n in 15*n**3 + 3/2*n**4 + 24 + 60*n + 99/2*n**2 = 0?
-4, -1
Factor 0*g + 1/5*g**2 - 1/5.
(g - 1)*(g + 1)/5
Let s(a) be the first derivative of -a**3 - 6*a**2 + 4. Determine y, given that s(y) = 0.
-4, 0
Let l be (-154)/(-35) - 2/5. Let x(p) be the second derivative of 4*p + 0*p**2 - 1/6*p**3 + 0 - 1/12*p**l. Solve x(a) = 0 for a.
-1, 0
Let p(b) = b**4 - b**3 + b**2 + 1. Let v(l) = 2*l**4 - 8*l**3 + 2*l**2 + 4. Let o(c) = -4*p(c) + v(c). Solve o(t) = 0 for t.
-1, 0
Let j = 2/17 - -9/68. Let r = 0 - -1/2. Factor -r*x + 0*x**2 - j + 1/2*x**3 + 1/4*x**4.
(x - 1)*(x + 1)**3/4
Let t be ((-4)/6)/((-4)/12). Factor -4*p**t + 3*p - 1 + 6*p**2 + 0*p + 2*p**2.
(p + 1)*(4*p - 1)
Let s be 4/(-1) - 25/(-6). Factor 0 - s*y + 1/6*y**3 + 0*y**2.
y*(y - 1)*(y + 1)/6
Solve 2/7*z**3 - 2/7*z**5 - 2/7*z**2 + 0 + 2/7*z**4 + 0*z = 0.
-1, 0, 1
Let j(d) be the second derivative of -d**6/150 + d**4/20 - d**3/15 - 20*d. Suppose j(x) = 0. Calculate x.
-2, 0, 1
Let y(k) be the second derivative of -k**9/1512 + k**7/210 - k**5/60 - 5*k**3/6 + 7*k. Let s(p) be the second derivative of y(p). Suppose s(g) = 0. Calculate g.
-1, 0, 1
Factor -2/3*b**2 + 0*b + 8/3.
-2*(b - 2)*(b + 2)/3
Let w(i) = -3*i**4 + 16*i**3 - 22*i**2 + 16*i - 3. Let u(y) = -12*y**4 + 63*y**3 - 87*y**2 + 63*y - 12. Let p(d) = 4*u(d) - 15*w(d). Factor p(g).
-3*(g - 1)**4
Let p(d) be the first derivative of -d**6/720 + d**5/360 + 2*d**2 + 2. Let o(g) be the second derivative of p(g). Find m, given that o(m) = 0.
0, 1
Factor -2/11*u**2 + 2/11*u**3 + 0 + 0*u.
2*u**2*(u - 1)/11
Suppose 11 + 25 = -2*m. Let u(s) = -7*s**2 - 13*s. Let b(j) = -j**2 - j. Let k(d) = m*b(d) + 2*u(d). Factor k(c).
4*c*(c - 2)
Let l be 80/45 + 2/9. Let z be (2 - l)*(0 - -1). Factor -32/3*y**3 + 16/3*y**2 - 2/3*y + z.
-2*y*(4*y - 1)**2/3
Let g(r) be the third derivative of r**5/300 - r**4/60 + 3*r**2. Suppose g(t) = 0. Calculate t.
0, 2
Let r be (-2)/7 + (-33)/7. Let b(u) = 19*u**3 - 3*u**2 + 7*u + 7. Let z(j) = 13*j**3 - 2*j**2 + 5*j + 5. Let k(a) = r*b(a) + 7*z(a). Let k(i) = 0. What is i?
0, 1/4
Let t(a) be the first derivative of -a**4/72 + a**3/6 - 3*a**2/4 - 5*a - 3. Let b(y) be the first derivative of t(y). What is p in b(p) = 0?
3
Factor -4*y**4 - 2*y**3 + 4*y**2 + 0*y**3 + 2*y - 5*y**4 + 5*y**2.
-y*(y - 1)*(y + 1)*(9*y + 2)
Let i(s) = s**5 - 2*s**4 - 3*s**3 + 2*s**2 + 2. Let n(o) = -3*o**5 + 9*o**4 + 12*o**3 - 9*o**2 - 9. Let c = -6 - -4. Let d(a) = c*n