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Let g be (-1268)/(-210) + (-2)/3. Let i = -24/5 + g. Determine c, given that i*c - 2/7*c**2 + 0 = 0.
0, 2
Let l(d) be the second derivative of 7/6*d**4 + 0 + 4*d - 3*d**3 + 2*d**2. Suppose l(u) = 0. What is u?
2/7, 1
Let p(f) be the third derivative of 1/210*f**7 + 4*f**2 - 1/30*f**5 + 0*f + 0*f**3 + 0 + 0*f**4 - 1/120*f**6. Let p(n) = 0. What is n?
-1, 0, 2
Let s(i) be the first derivative of -i**3 + 3*i**2/2 - 15. Factor s(m).
-3*m*(m - 1)
Let w(a) be the third derivative of a**8/1176 + 2*a**7/735 - a**5/105 - a**4/84 + 4*a**2. Let w(x) = 0. Calculate x.
-1, 0, 1
Let w(u) be the second derivative of u**6/60 + 10*u. Factor w(n).
n**4/2
Let b(q) be the second derivative of -q**5/70 - q**4/14 + 10*q**3/21 - 44*q. Let b(j) = 0. What is j?
-5, 0, 2
Let l(h) be the second derivative of -h**6/120 + h**5/16 - 7*h**4/48 + h**3/8 + h. Suppose l(z) = 0. What is z?
0, 1, 3
Factor q**2 - 1/2 - 1/2*q**4 + 1/2*q**5 + 1/2*q - q**3.
(q - 1)**3*(q + 1)**2/2
Let k(v) = -v. Let y be k(-14). Let z(t) = -2*t**2 + 29*t - 13. Let h be z(y). Determine o, given that o - h - 1/4*o**2 = 0.
2
Solve 1/3*r + 1/6 + 1/6*r**2 = 0.
-1
Let 32/3*j - 4/3*j**2 + 0 = 0. What is j?
0, 8
Let q(w) be the second derivative of 0 + 2*w + 1/30*w**4 - 2/15*w**3 + 1/5*w**2. Factor q(y).
2*(y - 1)**2/5
Let g(u) = -u**2 - 5*u - 2. Let z be g(-2). Suppose -12 = -5*v + 3*r - 6*r, r - 4 = z*v. Factor v*d**3 - 2/3*d**2 + 0 + 2/3*d**4 + 0*d.
2*d**2*(d - 1)*(d + 1)/3
Let l(w) be the second derivative of 4*w + 0*w**2 - 1/10*w**5 + 1/15*w**6 + 0 + 0*w**4 + 0*w**3. Factor l(f).
2*f**3*(f - 1)
Let x(q) be the first derivative of q**4/5 - 7*q**3/15 + q**2/5 + q/5 - 10. What is w in x(w) = 0?
-1/4, 1
Let y(h) be the second derivative of -7/12*h**4 - 3/2*h**3 - h**2 + 0 - 2*h. Let i(q) = 20*q**2 + 26*q + 6. Let r(t) = -6*i(t) - 17*y(t). Factor r(u).
-(u + 1)*(u + 2)
Suppose 0 = -9*k + k. Let m(n) be the second derivative of k + 3*n - 1/36*n**4 + 0*n**3 + 0*n**2 + 1/60*n**5. Factor m(c).
c**2*(c - 1)/3
Let p(h) be the first derivative of h**6/42 + h**5/35 - h**4/14 - 5. Suppose p(d) = 0. Calculate d.
-2, 0, 1
Let m(o) be the second derivative of o**4/12 - o**3/6 - 4*o. Determine j so that m(j) = 0.
0, 1
Let q(h) be the first derivative of h**5/30 - h**4/3 + 4*h**3/3 - 8*h**2/3 - h - 2. Let j(s) be the first derivative of q(s). Determine x, given that j(x) = 0.
2
Suppose 17 = p - 3*s - 2*s, -5*s - 25 = -5*p. Let n(a) be the second derivative of 0*a**3 + 0 + p*a + 1/30*a**4 + 0*a**2. Factor n(z).
2*z**2/5
Suppose -10 = -u - 4*u. Let v be (10 - 18)*(-2)/4. Factor v*d**u - 1 - 3*d**2 + 2 - 2*d.
(d - 1)**2
Let t(p) be the third derivative of -p**10/604800 + p**8/80640 - p**5/60 - p**2. Let j(z) be the third derivative of t(z). Factor j(m).
-m**2*(m - 1)*(m + 1)/4
Let c(x) = -4*x**3 - 2*x**2 - 2*x. Let y(k) = -12*k**3 - 7*k**2 - 7*k. Let b(n) = -7*c(n) + 2*y(n). Suppose b(z) = 0. Calculate z.
0
Let a(z) = 7*z**3 + 17*z**2 + 11*z + 1. Let w(s) = -20*s**3 - 50*s**2 - 34*s - 4. Let m(t) = 8*a(t) + 3*w(t). Find f such that m(f) = 0.
-2, -1, -1/2
Let a(z) = 11*z**4 + 16*z**3 + 12*z**2 - 7. Let n(x) = -6*x**4 - 8*x**3 - 6*x**2 + 4. Let m(l) = 3*a(l) + 5*n(l). Let m(f) = 0. What is f?
-1, 1/3
Let m be 24/(-16)*10/(-75). Let 1/5*h + 0 + m*h**2 = 0. Calculate h.
-1, 0
Factor 0*v - 4*v + v + v**2.
v*(v - 3)
Let r(v) be the second derivative of v**4/4 - v**3 - 8*v. Find u, given that r(u) = 0.
0, 2
Let l be 3 + (-5)/(10/(-6)). Suppose -4*c + 10*c - l - 2*c**2 + 2 = 0. Calculate c.
1, 2
Let y(p) be the third derivative of -2*p**2 + 0 + 0*p**4 + 1/15*p**5 + 0*p - 1/21*p**7 + 0*p**3 + 1/20*p**6. Find q, given that y(q) = 0.
-2/5, 0, 1
Let w(u) = -u**3 - 5*u**2 - u - 2. Let d be w(-5). Find a, given that -5*a - 21*a**2 + 4*a - 2*a + 6 + 15*a**2 + 3*a**d = 0.
-1, 1, 2
Let -3*h**4 + 20*h**2 - 3*h**5 + 25*h**2 - 42*h**2 + 3*h**3 = 0. What is h?
-1, 0, 1
Let y(a) be the first derivative of a**4/20 - 3*a**2/10 - 2*a/5 + 16. Factor y(u).
(u - 2)*(u + 1)**2/5
Let w = 1 - -2. Suppose 0 = -3*k - 3*d, w*k + 5*d = -8 + 2. Factor 3*p**2 - 2*p**4 - p - 6*p**3 + 4*p**3 - p**2 + k*p.
-2*p*(p - 1)*(p + 1)**2
Let h be 0 + 0 + (-2)/(-1). Factor -8*y + 4*y**4 - 2*y**5 + 20*y**2 + h - 2*y - 20*y**3 + 6*y**4.
-2*(y - 1)**5
Let n(c) = 15*c**3 + 9*c**2 + 9*c - 15. Let o(y) = y**3 + y - 1. Let p(a) = n(a) - 18*o(a). Solve p(b) = 0 for b.
1
Let y = -443 + 445. Solve 0*j + 2/11 - 4/11*j**y + 0*j**3 + 2/11*j**4 = 0.
-1, 1
Let w(c) be the second derivative of c**7/42 - c**6/15 - c**5/10 + 2*c**4/3 - 7*c**3/6 + c**2 + 8*c. Let w(g) = 0. Calculate g.
-2, 1
Let 20/3*o + 14/9*o**2 + 16/9 = 0. Calculate o.
-4, -2/7
Let h(a) = a**2 - a + 1. Let r(q) = 2*q**2 + 1. Let j(k) = -6*h(k) + 2*r(k). Determine i so that j(i) = 0.
1, 2
Let r be 20/9 + 88/(-396). Factor -4/13*t + 0 + 4/13*t**3 + 6/13*t**r.
2*t*(t + 2)*(2*t - 1)/13
Let p(x) = -x**3 + 8*x**2 - 7*x + 3. Let d be p(7). Let d*a**2 + 4*a**3 + 3/2*a**4 - 1/2 + 0*a = 0. What is a?
-1, 1/3
Let d(k) = -k**3 - 2*k**2 + 7*k. Let o be d(-5). Let z be (-8)/60 + 12/o. Factor 1/3 - 1/6*r**2 - z*r.
-(r - 1)*(r + 2)/6
Let j be (0/4)/(-2 + 0). Let u(v) be the third derivative of 0 + v**2 + 1/28*v**4 + j*v + 1/210*v**5 + 2/21*v**3. Find b such that u(b) = 0.
-2, -1
Let 0*m + 0*m**2 - 4/3*m**3 + 0 - 4/3*m**5 - 8/3*m**4 = 0. What is m?
-1, 0
Let z(s) be the third derivative of 0*s**6 - 1/105*s**5 + 0*s + 0*s**3 - 1/1176*s**8 + 0 + 1/84*s**4 + 2/735*s**7 + 2*s**2. Factor z(b).
-2*b*(b - 1)**3*(b + 1)/7
Let a(y) be the first derivative of 0*y**3 + 1/27*y**6 + 0*y - 1/9*y**4 + 0*y**5 + 1/9*y**2 + 5. Find v, given that a(v) = 0.
-1, 0, 1
Suppose -8*t - 12 = -12*t. Factor z**2 + 0*z + 0 + 1/2*z**t.
z**2*(z + 2)/2
Let 4/3*j**3 + 2 + 16/3*j + 14/3*j**2 = 0. What is j?
-3/2, -1
Suppose -7*r = -6*r - 0*r. Let x(s) be the third derivative of 2/9*s**3 + 1/90*s**5 + 2*s**2 + 0*s + r - 1/12*s**4. Find k such that x(k) = 0.
1, 2
Let v(h) be the first derivative of 3*h**4/4 + 18*h**3 + 162*h**2 + 648*h - 19. Determine t, given that v(t) = 0.
-6
Let q(v) be the third derivative of -1/240*v**6 + 0*v**5 + 0 + 0*v**4 + 1/840*v**7 + 0*v + 0*v**3 - 4*v**2. Find s such that q(s) = 0.
0, 2
Factor -2/3*a - 1/6*a**2 - 1/2.
-(a + 1)*(a + 3)/6
Let m(t) be the third derivative of -t**8/25200 + t**7/6300 + t**6/450 + 7*t**5/60 + 9*t**2. Let j(k) be the third derivative of m(k). What is g in j(g) = 0?
-1, 2
Let t(a) = -a**4 + 5*a**3 - 4*a**2 - 34*a + 30. Let i(m) = 5*m**4 - 24*m**3 + 19*m**2 + 171*m - 149. Let d(o) = -4*i(o) - 22*t(o). Suppose d(u) = 0. What is u?
-2, 1, 4
What is p in 6*p - 14 + 14 + 10*p**2 - 7*p**2 = 0?
-2, 0
Let l(w) = w**2. Let h(r) = -r**3 + r**2 - 2*r. Let q(m) = -h(m) - 2*l(m). Factor q(y).
y*(y - 2)*(y - 1)
Factor 25*u**5 + 14*u**5 - 36*u**4 - 23*u**5 + 8*u**3.
4*u**3*(u - 2)*(4*u - 1)
Let a(x) be the first derivative of -x**3 + 9*x**2 - 27*x - 20. Factor a(j).
-3*(j - 3)**2
Let s(b) = b**3 - 41*b**2 + 59*b - 19. Let w(u) = 2*u**3 - 61*u**2 + 88*u - 29. Let f(k) = 7*s(k) - 5*w(k). Factor f(h).
-3*(h - 4)*(h - 1)**2
Let g(c) be the first derivative of 7*c**5/30 + c**4/12 - 7*c**3/6 - 5*c**2/3 - 2*c/3 + 3. Factor g(x).
(x - 2)*(x + 1)**2*(7*x + 2)/6
Let p(t) be the second derivative of -4*t**6/5 + 23*t**5/10 - 13*t**4/6 + 2*t**3/3 + 2*t. Suppose p(z) = 0. What is z?
0, 1/4, 2/3, 1
Let h(v) be the first derivative of -v**9/4536 + v**7/1260 + v**3/3 - 2. Let f(t) be the third derivative of h(t). Factor f(a).
-2*a**3*(a - 1)*(a + 1)/3
Let k = 27/23 + -112/115. Find c, given that 0*c**2 + 0 + 1/5*c - k*c**3 = 0.
-1, 0, 1
Find k, given that 2/9*k**2 + 8/9*k + 2/3 = 0.
-3, -1
Let q = 552/5 + -110. Factor 8/5*g + q*g**2 + 8/5.
2*(g + 2)**2/5
Factor -4*g**2 - 10*g**2 + 1 + 16*g**2 + 3*g.
(g + 1)*(2*g + 1)
Let p(i) be the first derivative of 5*i**3/3 + 10*i**2 + 15*i + 10. Solve p(d) = 0 for d.
-3, -1
Suppose -6/5*w + 3/5*w**2 + 0 = 0. What is w?
0, 2
Suppose -n + p = -p + 10, -4*n + 3*p - 15 = 0. Suppose 1 = -0*o + o, 3*s = 5*o + 7. Factor 4/5*c**3 + 0*c**s + 0*c**2 - 2/5*c - 2/5*c**5 + n.
-2*c*(c - 1)**2*(c + 1)**2/5
Let d(m) be the second derivative of -m**5/30 - m**4/18 - 2*m. Factor d(b).
-2*b**2*(b + 1)/3
Suppose 0 = 2*y + 2*y. Let g(j) be the third derivative of 0*j**3 - 1/240*j**5 + 0 + y*j + j**2 - 1/96*j**4. Factor g(o).
-