culate k.
-3, -2, 2/7, 1
Let p(a) be the first derivative of a**5/10 - a**4/8 - 3*a**3/2 - 11*a**2/4 - 2*a + 6. Factor p(r).
(r - 4)*(r + 1)**3/2
Let y(b) = -b**3 - 7*b**2 - 2*b - 2. Suppose 5*x + 16 = x. Let i(u) = -u**3 - 8*u**2 - u - 2. Let h(l) = x*y(l) + 3*i(l). Determine r, given that h(r) = 0.
-2, -1
What is a in 132/5*a - 48/5 - 6*a**2 = 0?
2/5, 4
Let v(s) be the second derivative of s**4/16 + 11*s**3/8 + 2*s - 4. Factor v(r).
3*r*(r + 11)/4
Let q(u) be the third derivative of u**5/100 - u**4/20 - 12*u**2. Determine b so that q(b) = 0.
0, 2
Let w(s) be the first derivative of s**3/6 - s**2/2 + 1. Determine n, given that w(n) = 0.
0, 2
Let c(j) = 6*j**2 + 9*j - 3. Let s(z) = -z**3 + 5*z**2 + 8*z - 2. Let q(g) = -2*c(g) + 3*s(g). Solve q(f) = 0.
-1, 0, 2
Let z(r) be the third derivative of r**5/80 - 7*r**2. Factor z(a).
3*a**2/4
Suppose 0*r - 2*r = 10. Let k = -1 - r. Factor 2*b + 3 - k*b - 1 - 7*b + 4*b**2.
(b - 2)*(4*b - 1)
Let a(w) be the first derivative of w**6/39 + 2*w**5/65 - 3*w**4/13 - 28*w**3/39 - 11*w**2/13 - 6*w/13 + 6. Factor a(m).
2*(m - 3)*(m + 1)**4/13
Let s(u) be the first derivative of -u**4/8 + 3*u**2/4 + u + 32. Factor s(g).
-(g - 2)*(g + 1)**2/2
Let a be (-2295)/150 - 1/(-2). Let l = a + 15. Solve l - 1/5*h**3 + 1/5*h - 1/5*h**2 = 0.
-1, 1
Let a(k) = -6*k**3 + 12*k - 3. Let q(n) = 5*n**3 - 11*n + 4. Let s(l) = -2*a(l) - 3*q(l). Factor s(w).
-3*(w - 1)**2*(w + 2)
Find m such that 15 + 13 + m**2 - 32 = 0.
-2, 2
Let g(i) be the third derivative of i**6/660 - i**5/330 - 5*i**4/132 - i**3/11 - 4*i**2. Determine f, given that g(f) = 0.
-1, 3
Factor -1/2*b**3 + 1/2*b**4 + 0 + 0*b**2 + 0*b.
b**3*(b - 1)/2
Let r(q) be the first derivative of -q**4/10 + 4*q**3/5 - 9*q**2/5 + 8*q/5 - 25. Factor r(g).
-2*(g - 4)*(g - 1)**2/5
Let a(l) = -2*l**2 - 7*l - 4. Let c = -5 + 3. Let d(g) = -g**2 - 6*g - 5. Let m(s) = c*d(s) + 3*a(s). Factor m(o).
-(o + 2)*(4*o + 1)
Let g be 2/(-1 + 3 - 1). Let r(i) be the first derivative of 2 + 2/9*i**3 + 2/3*i - 2/3*i**g. Find k, given that r(k) = 0.
1
Let t(q) be the third derivative of 4*q**2 + 1/540*q**6 + 0*q - 1/90*q**5 + 0 + 1/6*q**3 + 1/36*q**4. Let x(l) be the first derivative of t(l). Solve x(d) = 0.
1
Let b(v) be the second derivative of v**4/3 + 10*v**3/3 + 12*v**2 - v. Factor b(a).
4*(a + 2)*(a + 3)
Let r(p) be the first derivative of -1/8*p**4 + 0*p**3 - 3 + 1/4*p**2 + 0*p. Factor r(i).
-i*(i - 1)*(i + 1)/2
What is s in s + 9*s**3 - 6*s + 5*s + 6*s**2 = 0?
-2/3, 0
Suppose -1/2 + 1/2*i**2 - 1/6*i**3 + 1/6*i = 0. Calculate i.
-1, 1, 3
Let s = 20 - 14. Suppose -s + 4 = -2*f. Let q(i) = -10*i**3 - 2*i**2 - 6*i - 6. Let t(u) = -u**3 - u**2 - 1. Let y(h) = f*q(h) - 8*t(h). Factor y(d).
-2*(d - 1)**3
Factor 15/2*w**2 + 25/2*w - 5/2*w**3 - 5/2*w**4 + 5.
-5*(w - 2)*(w + 1)**3/2
Let k(t) = -t**2 - 10*t - 9. Let w(l) = l**3 - 10*l**2 - 9. Let i be w(10). Let d be k(i). Factor d*n + 1/4*n**2 - 1/4.
(n - 1)*(n + 1)/4
Suppose -2*p = -4*n + 18 + 4, 5*n - 11 = -3*p. Factor 0*g + 0 + 4/3*g**3 - 2/3*g**n - 2/3*g**2.
-2*g**2*(g - 1)**2/3
Let r(b) be the third derivative of -b**5/30 + b**4/12 + 2*b**3/3 + 8*b**2. Factor r(t).
-2*(t - 2)*(t + 1)
Let j(m) be the first derivative of 1/10*m**5 - 1 + 1/3*m**3 - 1/3*m**4 + 0*m**2 + 2*m. Let y(p) be the first derivative of j(p). Factor y(x).
2*x*(x - 1)**2
Suppose -2*w - 5*d + 14 = 5, 3*w = -3*d + 9. Factor 0 + 1/3*r**3 + 0*r**w - 1/3*r.
r*(r - 1)*(r + 1)/3
Let o(c) be the second derivative of -c**4/5 + 3*c**3/2 + 6*c**2/5 + 7*c. Factor o(r).
-3*(r - 4)*(4*r + 1)/5
Suppose p + 10 = 4*z, 0 = -p - 2*z - 5 - 17. Let y = 22 + p. Find g such that 0*g**y - 2/3*g**3 + 1/3*g**5 + 0 + 0*g**2 + 1/3*g = 0.
-1, 0, 1
Let q = 2 - -2. Factor -q*j**2 + j**2 + 2*j**2.
-j**2
Let j(z) be the third derivative of z**7/210 - z**6/30 + z**5/10 - z**4/6 + z**3/6 - 9*z**2. Determine m, given that j(m) = 0.
1
Let j(y) be the third derivative of y**10/60480 - y**8/13440 + 5*y**4/24 - 5*y**2. Let t(b) be the second derivative of j(b). Determine v so that t(v) = 0.
-1, 0, 1
Suppose -3*o = -3*b, o - 3 = -3*b + 5. Let y(q) be the first derivative of 1 + 0*q**b - 2/21*q**3 + 0*q - 2/35*q**5 + 1/7*q**4. Factor y(x).
-2*x**2*(x - 1)**2/7
Suppose -3 = -2*d + 1. Let f(m) be the first derivative of 7/8*m**6 + 0*m - d + 17/12*m**3 + 11/4*m**5 + 49/16*m**4 + 1/4*m**2. Solve f(k) = 0 for k.
-1, -1/3, -2/7, 0
Let z be (2/(-4))/(-6 + 4). Let k(a) be the first derivative of -2 - 3/8*a**2 + z*a + 1/4*a**3 - 1/16*a**4. Find f such that k(f) = 0.
1
Let i be (64/5)/((-2)/(-10)). Suppose -4*q**2 - 11 - i*q + 5 + 73*q + q**2 = 0. What is q?
1, 2
Suppose 3*u + 4*v = 16, 5*u + 4*v - v = 23. Factor 12*m**3 + 24 + 27*m**u + 165*m**2 + 9*m**2 + 89*m**3 + 16*m**3 + 108*m.
3*(m + 1)*(m + 2)*(3*m + 2)**2
Let h(z) be the third derivative of -1/18*z**4 - 1/3*z**3 - 2*z**2 + 0*z - 1/540*z**6 + 0 - 1/60*z**5. Let n(v) be the first derivative of h(v). Factor n(g).
-2*(g + 1)*(g + 2)/3
Let w be -11 + -2 + (0 - -1). Let n be (w/32)/(6/(-4)). Factor -n*p**3 - 1/4*p**4 + 1/4*p**2 + 0 + 1/4*p.
-p*(p - 1)*(p + 1)**2/4
Let x = 219/908 + 2/227. Factor -x*l + 0 + 1/4*l**3 + 0*l**2.
l*(l - 1)*(l + 1)/4
Let q(d) be the third derivative of d**6/40 - d**5/20 + 4*d**2. Factor q(u).
3*u**2*(u - 1)
Let s(z) = z**3 + 5*z**2 - 5*z + 8. Let m be s(-6). Let u = 211/321 - -1/107. Determine j so that u*j**m - 2/3*j + 0 = 0.
0, 1
Let r(k) be the first derivative of -2 + 2/7*k + 0*k**2 - 2/21*k**3. Factor r(n).
-2*(n - 1)*(n + 1)/7
Factor 8/9 + 2/9*u**2 + 8/9*u.
2*(u + 2)**2/9
Suppose -541 - 739 = -5*x. Let m = x + -1267/5. Let -m*l - 11/5*l**2 - 2/5 = 0. What is l?
-1, -2/11
Let r be (-92)/(-35) + (-16)/(-28). Let b(j) be the first derivative of 8/5*j - 2 + 5/2*j**4 - r*j**2 + 2/3*j**3. Factor b(v).
2*(v + 1)*(5*v - 2)**2/5
Let k(i) = 15*i**4 - 7*i**4 - 26*i**2 - 10*i**3 - 12*i**4 - 14*i. Let t(z) = z**3 - z**2 - z. Let j(o) = -k(o) + 6*t(o). Factor j(h).
4*h*(h + 1)**2*(h + 2)
Suppose 0*c + 10 = 5*c. Factor -5*r + r - c*r**2 - 2*r**2 - 2*r**3 + 2*r.
-2*r*(r + 1)**2
Let y = 121/2 + -829/14. Factor 6/7 - 9/7*t**2 - 6/7*t**3 + y*t.
-3*(t - 1)*(t + 2)*(2*t + 1)/7
Let g(r) = r**2 - 1. Suppose -i + 3 = -1. Let k(f) = 3*f - f - i + 2*f + 0*f + 4*f**2 - 4*f**3. Let a(b) = 6*g(b) - 2*k(b). Factor a(n).
2*(n - 1)*(n + 1)*(4*n - 1)
Let z(y) be the third derivative of -y**7/1680 + y**6/480 - y**4/96 + y**3/48 - 8*y**2. Suppose z(s) = 0. Calculate s.
-1, 1
Let s(f) = 9*f - 1. Let y be s(1). What is t in 0*t**3 - 8*t - y*t - 8 - 10*t**2 - t**3 - t**3 = 0?
-2, -1
Let g = 63 - 61. Factor 1/3 + 1/3*o**g + 2/3*o.
(o + 1)**2/3
Let l(i) be the first derivative of -1/2*i**3 + 1/2*i**2 + 1/12*i**4 - 1 + i + 3/20*i**5 - 1/15*i**6. Let a(v) be the first derivative of l(v). Factor a(p).
-(p - 1)**2*(p + 1)*(2*p - 1)
Let l(c) be the second derivative of 0 - 2/15*c**6 + 1/2*c**2 + 1/4*c**4 + 1/4*c**5 - 5/6*c**3 - c. Solve l(g) = 0.
-1, 1/4, 1
Let o(k) be the second derivative of -9*k**4/4 - 3*k**3 - 3*k**2/2 - 9*k. Solve o(d) = 0.
-1/3
Suppose -2*x + 1 + 3 = 0. Let y be (1 + 1)/(x/4). Suppose 1/2*o**2 + 1/4*o**5 + 1/4*o - 1/4 - 1/2*o**3 - 1/4*o**y = 0. What is o?
-1, 1
Let -2/13 - 12/13*j**2 + 10/13*j = 0. What is j?
1/3, 1/2
Suppose 2*i = -4*h + 22, 6*i - 27 = i - 3*h. Determine m so that -m + 0 + m**i - 8*m**2 + 1 + 6*m**4 + 1 + 0*m**4 = 0.
-1, -2/3, 1/2, 1
Let u = 2 - -2. Let x(s) be the first derivative of 2 + 0*s**u - 1/5*s**5 + 0*s**3 + 0*s**2 + 0*s. Determine g so that x(g) = 0.
0
Let f(r) be the second derivative of -5*r**7/189 - 2*r**6/135 + r**5/30 + 2*r + 1. Suppose f(h) = 0. Calculate h.
-1, 0, 3/5
Let d = 2/89 - -884/267. Find c, given that 0 + d*c**3 - 8/3*c - 4/3*c**2 - c**4 = 0.
-2/3, 0, 2
Let z(t) be the first derivative of t**6/60 + t**5/40 - t**4/24 - t**3/12 + 4*t - 3. Let s(r) be the first derivative of z(r). Factor s(g).
g*(g - 1)*(g + 1)**2/2
Let n(r) = r**5 + r**4 + r**2 - r + 1. Let z(k) = 2*k**5 + 30*k**4 + 76*k**3 + 61*k**2 + 3*k - 19. Let l(g) = -3*n(g) - z(g). Factor l(u).
-(u + 1)*(u + 2)**3*(5*u - 2)
Suppose -1 = i - 3. Suppose 4*r**i - 2*r**2 + 0*r + 2*r = 0. Calculate r.
-1, 0
Let i be (13 - 872/64)*(-18)/5. Suppose 1/4*d**2 + i - 3/2*d = 0. What is d?
3
Suppose 6*m**2 + 350*m**3 - 8*m - 314*m**3 + 22*m**4 - 6 + 10*m**2 + 4*m**5 = 0. Wha