k(-5). Let m(d) = -7*d**2 + 3*d - 3. Let l(i) = -4*i**2 + i - 1. Let c(t) = u*l(t) + 3*m(t). Suppose c(p) = 0. What is p?
2
Let z(m) be the third derivative of m**5/15 - m**4/3 + 10*m**2. Suppose z(x) = 0. What is x?
0, 2
Let k be 6*10*(-1)/(-4). Let w = k - 15. Factor w*p**3 - 2/7*p**5 + 0 + 0*p + 2/7*p**4 + 0*p**2.
-2*p**4*(p - 1)/7
Let h = 89/2 + -43. Factor 0 + h*p**2 + 0*p - 3/2*p**5 + 3/2*p**3 - 3/2*p**4.
-3*p**2*(p - 1)*(p + 1)**2/2
Suppose -92 = -4*u - 0*u. Let y = -113/5 + u. Determine m, given that -3/5*m**4 + 1/5*m**2 + 0 + 0*m + y*m**3 = 0.
-1/3, 0, 1
Let a(t) be the first derivative of -t**6/3 - 4*t**5/5 + t**4 + 8*t**3/3 - t**2 - 4*t + 52. Suppose a(f) = 0. Calculate f.
-2, -1, 1
Let i(m) = -m**2 + 7*m - 6. Let q be i(5). Let o(f) be the second derivative of 2*f + 0 + 1/18*f**3 + 1/20*f**5 + 0*f**2 - 1/12*f**q - 1/90*f**6. Factor o(w).
-w*(w - 1)**3/3
Let u = 10 - 7. Factor -37*p + 0*p**3 - 3*p**u + 24 + p + 18*p**2.
-3*(p - 2)**3
Suppose -3/2*t**5 + 1/2 - t**3 + 5/2*t - 7/2*t**4 + 3*t**2 = 0. Calculate t.
-1, -1/3, 1
Let j(f) be the third derivative of -f**8/30240 - f**7/7560 + f**5/15 - 6*f**2. Let t(g) be the third derivative of j(g). Factor t(b).
-2*b*(b + 1)/3
Let m(s) be the third derivative of -s**7/10080 + s**6/1440 - s**5/480 - s**4/8 + 2*s**2. Let b(w) be the second derivative of m(w). Let b(l) = 0. What is l?
1
Determine y so that 2*y**2 + 8*y - 616 + 616 = 0.
-4, 0
Suppose 3 = -0*r + r. Suppose -2*u = -r*u. Solve 2*v**3 + 2*v**5 + u*v**4 + 3*v**4 - 7*v**4 = 0 for v.
0, 1
Let v(u) be the first derivative of -1/15*u**5 - 8/9*u**3 + 1 + 0*u + 5/12*u**4 + 2/3*u**2. What is k in v(k) = 0?
0, 1, 2
Let h = -296 - -298. Factor h*r**3 + 10/3*r**2 + 2/3*r - 2/3.
2*(r + 1)**2*(3*r - 1)/3
Suppose -35 - 37 = -2*g. Suppose 6 = 3*x - g. Find v, given that 3*v**3 - 15*v**4 + x*v**5 - 9*v**4 + 4*v**2 + 3*v**3 = 0.
-2/7, 0, 1
Let s(m) = -14*m**2 + 5*m - 8. Let g(d) = -9*d**2 + 3*d - 5. Let o = -48 + 76. Let p = 20 - o. Let q(a) = p*g(a) + 5*s(a). Factor q(i).
i*(2*i + 1)
Let y(m) = m**4 + m**2 + 2*m. Let h(c) be the first derivative of 4*c**5/5 + 5*c**3/3 + 9*c**2/2 + 3. Let w(k) = 2*h(k) - 9*y(k). Find i such that w(i) = 0.
-1, 0, 1
Let o(t) be the second derivative of t**7/21 + t**6/3 + 3*t**5/5 - t**4/3 - 7*t**3/3 - 3*t**2 + 10*t. Factor o(b).
2*(b - 1)*(b + 1)**3*(b + 3)
Let q(a) = -a**3 + 1. Let o(i) = 16*i**2 - 8*i + 10. Let v(h) = -2*o(h) + 20*q(h). Find u such that v(u) = 0.
-2, 0, 2/5
Let f be 3/((-12)/(-4)) + 7. Let r(g) = -6*g**3 + 6*g**2 - 2*g - 14. Let x(o) = -2*o**3 + 2*o**2 - o - 5. Let t(u) = f*x(u) - 3*r(u). Factor t(q).
2*(q - 1)**2*(q + 1)
Solve 23*n + 33*n - 75*n - 20*n**2 + 34*n = 0.
0, 3/4
Let g(o) = 3*o - 3. Let q be g(5). Suppose 5*u - u = q. What is z in 0*z - 5*z**3 + 6*z**u + 2*z - 3*z = 0?
-1, 0, 1
Let d(k) be the second derivative of k**7/14 + k**6/5 - k**4/2 - k**3/2 + k. Solve d(i) = 0 for i.
-1, 0, 1
Let i be 1794/621 + 1/9. Find z, given that -5/4*z**i - 11/2*z**2 - 3/2 - 23/4*z = 0.
-3, -1, -2/5
Let h(f) be the third derivative of -f**7/280 + f**6/45 - 7*f**5/120 + f**4/12 - 5*f**3/6 - 7*f**2. Let o(c) be the first derivative of h(c). Factor o(b).
-(b - 1)**2*(3*b - 2)
Let k = -3/2 + 25/14. Factor 10/7*q**4 + k*q**5 + 18/7*q**3 + 4/7*q + 2*q**2 + 0.
2*q*(q + 1)**3*(q + 2)/7
Let c(y) be the third derivative of 4*y**2 + 0*y + 1/11*y**4 - 7/330*y**5 + 0 + 4/33*y**3. Factor c(j).
-2*(j - 2)*(7*j + 2)/11
Suppose -2*h - 8 = 5*s + 14, 3*h + 3*s + 15 = 0. Let i be h/(-4)*(-36)/(-27). Let -2/3*n**2 + 1/6*n**3 - i + 5/6*n = 0. Calculate n.
1, 2
What is f in 0*f + 0*f**2 + 0 - 2/11*f**4 - 2/11*f**5 + 4/11*f**3 = 0?
-2, 0, 1
Let g(x) be the second derivative of x**4/27 + 2*x**3/27 + 17*x. Factor g(h).
4*h*(h + 1)/9
Suppose 17/4*h**2 + 21/4*h**4 - 1/2 + 41/4*h**3 - 5/4*h = 0. What is h?
-1, -2/7, 1/3
Let a(r) be the third derivative of -1/18*r**4 - 1/9*r**5 + 0 + 9*r**2 + 0*r + 8/9*r**3. Factor a(t).
-4*(t + 1)*(5*t - 4)/3
Let w(y) = 5*y**4 - 18*y**3 + 31*y**2 - 22*y + 2. Let d(l) = 21*l**4 - 73*l**3 + 125*l**2 - 89*l + 7. Let m(k) = -4*d(k) + 18*w(k). Suppose m(c) = 0. What is c?
1/3, 1, 2
Let -3*a**4 + 10*a**2 + 8*a - 7*a**2 + 4 - 2*a**3 + 2*a**4 = 0. Calculate a.
-2, -1, 2
Let o(x) be the third derivative of -x**7/210 - x**6/40 + x**4/6 + 24*x**2. Factor o(p).
-p*(p - 1)*(p + 2)**2
Let h(r) be the first derivative of -r**6/120 + r**5/60 + r**4/24 - r**3/6 + r**2 - 4. Let o(g) be the second derivative of h(g). Factor o(m).
-(m - 1)**2*(m + 1)
Let i(u) be the second derivative of u**4/20 + u**3/5 - 9*u**2/10 - 2*u. Factor i(n).
3*(n - 1)*(n + 3)/5
Let t(p) = -p**2 + 25*p - 22. Let l be t(24). Factor -1/2*c - l*c**3 + 0 - 2*c**2.
-c*(2*c + 1)**2/2
Factor 3*x**4 + x**5 - 4*x**3 + 3*x + 2 - 8*x**2 + 6*x**2 - 3*x**4.
(x - 2)*(x - 1)*(x + 1)**3
Let g(p) be the second derivative of -p**4/48 + p**2/2 - 2*p. Determine m, given that g(m) = 0.
-2, 2
Suppose -2*z = -5 + 1. Suppose 0 = -5*p - z*p. Factor -1/2*n**3 - 1/2*n + p - n**2.
-n*(n + 1)**2/2
Let a(h) = -4*h**2 - 5*h - 9. Let s(r) = -6*r**2 - 8*r - 14. Let i(l) = 8*a(l) - 5*s(l). Let w(f) = -4*f**2 - 3. Let c(q) = 7*i(q) - 4*w(q). Factor c(o).
2*(o - 1)*(o + 1)
Let b(q) be the third derivative of -q**6/780 + q**5/390 - 2*q**2. Factor b(y).
-2*y**2*(y - 1)/13
Let w = 26 + -13. Determine r, given that -3*r**2 - 3 - 11*r + 4*r + w*r = 0.
1
Let s(c) be the third derivative of 2*c**2 + 0 + 0*c**3 - 1/270*c**5 + 0*c + 0*c**4 - 1/540*c**6. Let s(v) = 0. What is v?
-1, 0
Let j(v) be the second derivative of 1/3*v**3 - 2/7*v**2 - 4*v - 5/42*v**4 + 0. Determine q, given that j(q) = 0.
2/5, 1
Let t = 2014/3 - 666. Find x, given that -t - 4/3*x**2 + 16/3*x = 0.
2
Let t(m) = m**2 - 14*m + 44. Let j be t(10). Factor 0*d**3 + 1/4*d**j + 0*d - 1/2*d**2 + 1/4.
(d - 1)**2*(d + 1)**2/4
Let w(m) be the third derivative of m**6/90 + m**5/45 - m**4/9 + 5*m**2. Let w(o) = 0. What is o?
-2, 0, 1
Let r = 68/3 + -22. Solve 0 - 2/3*l**2 + r*l = 0 for l.
0, 1
Let v be 2/12 - 3/18. Let n = 2 - v. Solve -n*j**4 - 2*j**3 - 2*j**4 + 5*j**4 + j**2 = 0.
0, 1
Let u(h) = -4*h + 39. Let y be u(9). Let -1/6*v**y + 1/3*v**2 + 0*v + 0 = 0. What is v?
0, 2
Let a be (4 + -7)/(-3) + 2. Let g(q) be the third derivative of 2*q**2 - 1/330*q**5 + 0*q**4 + 1/33*q**a + 0*q + 0. Factor g(s).
-2*(s - 1)*(s + 1)/11
Let b(z) be the third derivative of -z**8/1008 - z**7/630 + z**6/180 + z**5/90 - z**4/72 - z**3/18 + 7*z**2. Factor b(l).
-(l - 1)**2*(l + 1)**3/3
Suppose 8*p**2 - 4*p**5 - 4*p**4 + 0*p - 4*p**4 + 3*p + p = 0. Calculate p.
-1, 0, 1
Let o be 386/8 + (-2)/(-4). Let m = 49 - o. Factor -1/4*n + 0 + 1/4*n**4 + m*n**3 - 1/4*n**2.
n*(n - 1)*(n + 1)**2/4
Let f(k) be the third derivative of 2*k**2 + 5/96*k**6 + 0*k + 1/24*k**4 + 0 + 1/12*k**5 + 0*k**3. Factor f(o).
o*(5*o + 2)**2/4
Let o(t) be the third derivative of -27/4*t**3 - 36/5*t**5 + 9*t**4 - 64/105*t**7 + 0 + 0*t - 4*t**2 + 16/5*t**6. Find j, given that o(j) = 0.
3/4
Factor -16/3*d - 32 - 2/9*d**2.
-2*(d + 12)**2/9
Suppose 24*r - 2*t - 16 = 22*r, 3*t = 2*r - 20. Solve -4/5*y - 6/5*y**2 + 0*y**3 + 2/5*y**r + 0 = 0 for y.
-1, 0, 2
Let d be (1/3)/(-23 + 83). Let h(l) be the third derivative of 0*l + l**2 + 1/18*l**4 - 2/9*l**3 - d*l**5 + 0. Determine b, given that h(b) = 0.
2
Let k(p) be the second derivative of 2/3*p**2 + 0 + 4/3*p**3 - 3*p + 5/4*p**4 + 5/12*p**5. Solve k(y) = 0.
-1, -2/5
Let h = 5 - 4. Let p = 1 - h. What is y in p*y**2 + 3*y + 3*y**2 - y**3 - 3*y**4 - 6*y + 4*y**3 = 0?
-1, 0, 1
Let r(b) be the third derivative of -1/90*b**6 + 0*b**3 + 0 + 0*b - 4/945*b**7 - 1/1512*b**8 - b**2 - 2/135*b**5 - 1/108*b**4. Factor r(a).
-2*a*(a + 1)**4/9
Factor 5*p**2 + 0*p**2 + 5*p**4 + 0*p**2 + 7*p**3 + 3*p**3.
5*p**2*(p + 1)**2
Let o = 0 - 0. Let l(f) be the second derivative of -f - 1/36*f**4 + 0*f**3 + o*f**2 + 0 - 1/20*f**5. Determine s, given that l(s) = 0.
-1/3, 0
Let x = -2/255 + 269/1785. Factor 0*b - 1/7*b**5 + 1/7*b**2 + 0 - 1/7*b**4 + x*b**3.
-b**2*(b - 1)*(b + 1)**2/7
Let n be (-2)/(-4) + (-7)/(-14). Factor -4 - 16*z + 14 + 7 - n + 4*z**2.
4*(z - 2)**2
Let b(s) = s**5 + 11*s**4 - 11*s**2 - 4*s - 3. Let g(x) = 8*x**5 + 100*x**4 - 100*x**2 - 36*x - 28. Let r(k) = 28*b(k) - 3*g(k). Factor r(a).
4*a*(a - 1)*(a + 1)**3
Let b(k) = 4*k**3 + 9*k**2 + 9*