(m) be the second derivative of -m**5/140 - m**4/7 - 8*m**3/7 - 32*m**2/7 + 2*m. Suppose a(y) = 0. Calculate y.
-4
Let r = 16 + -10. Let i(k) be the third derivative of 0 - 1/120*k**5 + 1/240*k**r - 3*k**2 + 0*k + 0*k**3 - 1/24*k**4. Let i(q) = 0. What is q?
-1, 0, 2
Let j = 45 + -128/3. Factor -j*b**2 + 0 - 2/3*b.
-b*(7*b + 2)/3
Let q(x) = x**2. Let g(l) = -l**2 - 6*l + 9. Let i(d) = -g(d) - 2*q(d). Let i(w) = 0. What is w?
3
Find q, given that -7 + 11 - 7 + 3*q**2 = 0.
-1, 1
Let x(o) = 32*o**4 - 171*o**3 + 338*o**2 - 264*o + 77. Let n(j) = 48*j**4 - 257*j**3 + 507*j**2 - 396*j + 115. Let d(r) = 5*n(r) - 7*x(r). Factor d(c).
(c - 2)**2*(4*c - 3)**2
Determine p so that 0 - 3/4*p - 1/4*p**2 = 0.
-3, 0
Factor 0*k + 0*k**3 + 0 - 2/7*k**5 + 0*k**4 + 0*k**2.
-2*k**5/7
Find m such that 1/2 - 3/4*m + 1/4*m**2 = 0.
1, 2
Let d(z) = -z**3 + 7*z**2 + 7*z + 10. Let o be d(8). Let k(i) be the first derivative of 2 - 3/4*i**o + 1/12*i**3 + 9/4*i. Suppose k(t) = 0. What is t?
3
Find i such that 1/4*i**3 + 5/4*i - i**2 - 1/2 = 0.
1, 2
Let j(t) = -10*t**2 + 16*t - 11. Let d(n) = -11*n**2 + 17*n - 10. Let z be ((-6)/(-5))/(-3)*-10. Let s(b) = z*j(b) - 5*d(b). Factor s(w).
3*(w - 1)*(5*w - 2)
Let b(f) be the first derivative of -f**4/18 - 4*f**3/9 - 4*f**2/3 + 4*f + 7. Let o(s) be the first derivative of b(s). Let o(a) = 0. What is a?
-2
Let g(a) = 4*a + 27. Let z be g(-6). Factor 5/4*t**2 + 7/4*t**z + 0 - 1/2*t.
t*(t + 1)*(7*t - 2)/4
Let r(k) = -k**3 + k**2 - k - 1. Let v(d) = -4*d**3 + 4*d**2 - 3*d - 3. Let z be 3/(1*(-3)/(-2)). Let u(p) = z*v(p) - 6*r(p). Factor u(o).
-2*o**2*(o - 1)
Let d be (2/(-1))/((-6)/(-3)). Let u(q) = q**2 - q - 1. Let v(t) = -28*t**3 + 30*t**2 - 2*t - 10. Let o(m) = d*v(m) + 10*u(m). Determine x, given that o(x) = 0.
-2/7, 0, 1
Let n(f) be the first derivative of -f**6/3 + f**4 - f**2 - 12. Factor n(p).
-2*p*(p - 1)**2*(p + 1)**2
Determine f so that 2*f**2 - f**5 + 0*f**2 - 217*f**3 + 220*f**3 = 0.
-1, 0, 2
Let u(i) = 2*i - 12. Let z be u(6). Let r(p) be the first derivative of 1/9*p**3 + z*p**2 + 1 - 1/5*p**5 + 1/6*p**4 + 0*p. Solve r(v) = 0 for v.
-1/3, 0, 1
Let i(x) be the first derivative of -x**7/1260 + x**6/324 + x**5/270 + x**3 - 7. Let j(u) be the third derivative of i(u). Factor j(l).
-2*l*(l - 2)*(3*l + 1)/9
Let h = -13 + -1. Let v be (h/3 - -2) + 3. Factor 1/3*b**2 - 1/3*b + v*b**3 - 1/3*b**4 + 0.
-b*(b - 1)**2*(b + 1)/3
Let h(m) be the second derivative of m**5/10 - m**4/12 - 2*m**3/3 - 5*m**2/2 - 3*m. Let y(d) be the first derivative of h(d). Factor y(w).
2*(w - 1)*(3*w + 2)
Let m(d) be the first derivative of 9*d**5/5 - 15*d**4/8 - 3*d**3 + 9*d**2/4 + 3*d - 13. Solve m(r) = 0.
-2/3, -1/2, 1
Let x be (-3)/(42/10) - (4 - 5). Let 0*k + 2/7*k**5 + 0 + 4/7*k**4 + 0*k**2 + x*k**3 = 0. What is k?
-1, 0
Let t(s) be the second derivative of s**7/14 - 3*s**6/10 + 3*s**5/10 + s**4/2 - 3*s**3/2 + 3*s**2/2 - s. Factor t(y).
3*(y - 1)**4*(y + 1)
Let f(u) be the second derivative of u**7/21 - u**6/5 + u**5/5 - 11*u. Factor f(w).
2*w**3*(w - 2)*(w - 1)
Let q(c) be the third derivative of -c**7/15 + c**6/12 + 3*c**5/10 - 5*c**4/12 - 2*c**3/3 - 14*c**2. Solve q(d) = 0.
-1, -2/7, 1
Let f(d) be the first derivative of -4/5*d**5 + 2*d**2 + 2*d**4 + 2/15*d**6 + 7 - 4/5*d - 8/3*d**3. Factor f(q).
4*(q - 1)**5/5
Let t(r) = -5*r**2 + 0*r**2 + 4 - 5. Let u(y) = -9*y**2 - 1. Let q(c) = -5*t(c) + 3*u(c). Solve q(o) = 0 for o.
-1, 1
Find j, given that 2/9*j**3 - 2/9*j**5 + 0*j - 2/3*j**4 + 2/3*j**2 + 0 = 0.
-3, -1, 0, 1
Let u(g) = g**2 + 19*g + 18. Let z be u(-18). Let h(l) be the second derivative of 0*l**3 + 0 + 0*l**2 + 3*l + z*l**5 + 1/105*l**6 - 1/42*l**4. Factor h(m).
2*m**2*(m - 1)*(m + 1)/7
Let g(m) be the first derivative of 4*m**5/35 + 6*m**4/7 + 52*m**3/21 + 24*m**2/7 + 16*m/7 + 24. Factor g(p).
4*(p + 1)**2*(p + 2)**2/7
Let w(i) be the first derivative of 5*i**5 + 35*i**4/4 - 5*i**3 - 35*i**2/2 - 10*i + 1. Solve w(y) = 0.
-1, -2/5, 1
Let g be -3 - (-2 - -5 - 3). Let w = -1 - g. Find c such that -4*c**2 + 3*c**2 - 4*c**w + 2*c + 3*c**2 = 0.
0, 1
Suppose j - 5 = 0, -5*f + 31 = 5*j - 9. Determine n so that -n**4 + f*n**4 - 5*n**2 + 3*n**2 = 0.
-1, 0, 1
Let i be (-5)/(10/(-4)) + 1. Suppose -3*b + b = 0. Let -f**4 - f**i + 0 + b = 0. What is f?
-1, 0
Let b(s) be the second derivative of s**4/30 - 14*s**3/15 + 49*s**2/5 - s. Let b(o) = 0. Calculate o.
7
Let a(l) be the second derivative of l**6/15 - l**5/5 + 2*l**3/3 - l**2 + 23*l. Factor a(o).
2*(o - 1)**3*(o + 1)
Let r(i) = i**3 + i**4 - 4*i**2 + 3*i**4 - 3*i - 3 - i. Let l(o) = -3*o**4 - o**3 + 3*o**2 + 3*o + 2. Let f(b) = -3*l(b) - 2*r(b). Factor f(p).
p*(p - 1)*(p + 1)**2
Let s(y) = 31*y**3 + 65*y**2 + 23*y + 11. Let c(q) = 15*q**3 + 33*q**2 + 12*q + 6. Let k(m) = 11*c(m) - 6*s(m). Find j, given that k(j) = 0.
-1, -2/7, 0
Let y(p) be the first derivative of -2*p - 1/2*p**3 + 1/4*p**4 + 0*p**2 + 2. Let m(s) be the first derivative of y(s). Factor m(a).
3*a*(a - 1)
Let p(q) = q**3 - 3*q**2 - 4*q. Let b be p(4). Let h be -6*(2 + (-5)/2). Solve -6*w - 2 - 1 - h*w**2 + b*w**2 = 0.
-1
Let y(v) be the second derivative of -7*v**6/30 + v**5/10 + 7*v**4/12 - v**3/3 - 4*v. Factor y(z).
-z*(z - 1)*(z + 1)*(7*z - 2)
Let d be (-2604)/40 + 2/(-5). Let b = -64 - d. Factor b*q - 1 - 1/2*q**2.
-(q - 2)*(q - 1)/2
Let x(t) = 2*t**2 - 16*t - 40. Let h be x(10). What is u in 16/5*u**4 - 11/5*u**3 + 0*u - 7/5*u**5 + 2/5*u**2 + h = 0?
0, 2/7, 1
Let p(f) = 6*f**2 + 4. Let b(k) = 5*k**2 + 3. Suppose 8 + 12 = 4*r. Let m(n) = r*b(n) - 4*p(n). Factor m(t).
(t - 1)*(t + 1)
Let u = 2 + -8. Let q be ((-1)/u)/((-4)/(-8)). Factor 1/3*g - q*g**3 + 1/3*g**2 - 1/3.
-(g - 1)**2*(g + 1)/3
Let g(a) be the second derivative of a**5/75 - a**4/12 + 2*a**3/15 - a**2 + 7*a. Let r(v) be the first derivative of g(v). Solve r(s) = 0 for s.
1/2, 2
Suppose -3*o - 5*y - 2 - 17 = 0, 5*y = -o - 23. What is c in 5*c**2 - 4*c**2 + 0*c**2 - 3*c**o + 2*c = 0?
0, 1
Factor 60/13*c**4 - 22/13*c**3 + 8/13*c - 24/13*c**2 + 50/13*c**5 + 0.
2*c*(c + 1)**2*(5*c - 2)**2/13
Suppose 0 = -a + 16*a. Determine s, given that 1/3*s**2 + a - 2/3*s = 0.
0, 2
Let u = -5/6593 - 25666504/59337. Let t = u + 433. Solve 0 + t*r**2 - 2/9*r**3 - 2/9*r = 0 for r.
0, 1
Let k be 9/24*8/12. Suppose -4*q - 2*z + z = -5, -4*q + 5*z = -23. Determine u so that 1/4 + k*u**3 - 1/4*u - 1/4*u**q = 0.
-1, 1
Suppose -4*g = 5*m - 23, 3*g = 2 + 4. Let v(n) be the third derivative of 1/60*n**5 + 1/6*n**m + 0 + 0*n + 1/12*n**4 + n**2. Suppose v(t) = 0. What is t?
-1
Let y(w) = w**5 - w**4 - w**3 - w**2 - w + 1. Let z(n) = -16*n**5 + 8*n**3 + 24*n**2 + 20*n - 12. Let k(s) = -12*y(s) - z(s). Suppose k(g) = 0. Calculate g.
-2, -1, 0, 1
Determine v so that 2 - 1 - 3 + 3*v + 4*v**2 - 5*v**2 = 0.
1, 2
Let v(l) be the third derivative of -1/336*l**8 + 1/120*l**6 - 2*l**2 + 0*l**4 - 1/210*l**7 + 0*l + 1/60*l**5 + 0 + 0*l**3. Find k, given that v(k) = 0.
-1, 0, 1
Suppose -2*u + 4*u = 0. Let a(x) be the second derivative of x - 1/90*x**5 + u - 1/27*x**4 + 0*x**2 - 1/27*x**3. What is j in a(j) = 0?
-1, 0
Let s = 10 + -119/12. Let w(x) be the second derivative of 2*x - 1/2*x**2 + 0 + s*x**4 - 1/10*x**5 + 1/3*x**3. Factor w(m).
-(m - 1)*(m + 1)*(2*m - 1)
Let d = -3 - -25. Suppose -3 = c - 5*k - d, -5*c + k = -23. Factor -15*a**3 - 9*a**4 - 7*a**2 + 4 - c - a.
-a*(a + 1)*(3*a + 1)**2
Let g(x) be the third derivative of -2*x**2 + 2/75*x**5 + 1/12*x**4 + 1/15*x**3 + 0*x + 0. Factor g(h).
2*(h + 1)*(4*h + 1)/5
Let v(a) be the first derivative of a**7/1680 - a**5/240 - a**3/3 - 3. Let o(s) be the third derivative of v(s). Factor o(d).
d*(d - 1)*(d + 1)/2
Let x be ((-4)/6)/((-2)/9). Let n = -10 + 13. Factor -l**n + l**x + l**3.
l**3
Let v = 14 + -12. Find g such that g - 4*g**2 + 2 - g**3 + 2*g**v + 0*g**3 + 0 = 0.
-2, -1, 1
Let g(k) be the first derivative of -2*k**3/33 + 6*k**2/11 + 32*k/11 + 22. Factor g(r).
-2*(r - 8)*(r + 2)/11
Factor -5*u**2 + u + u**4 - 3*u**3 - u - 2*u + u**5.
u*(u - 2)*(u + 1)**3
Suppose 0 = 6*a - 40 + 28. Factor 0*c + 0 - 2/7*c**a.
-2*c**2/7
Let k(l) be the first derivative of -l**5/100 - l**4/60 + l**3/30 + l**2/10 - 2*l - 4. Let s(u) be the first derivative of k(u). Factor s(b).
-(b - 1)*(b + 1)**2/5
Let c(r) be the first derivative of -6*r**4 - 22*r**3 - 4 - 36*r**2 - 27