 + 8*s**7/105 - s**6/10 - 10*s**2. Suppose w(m) = 0. What is m?
0, 1, 3
Factor -125/4*y**2 - 245/4 - 175/2*y.
-5*(5*y + 7)**2/4
Let c(n) = -5*n**4 + 53*n**3 + 131*n**2 + 100*n. Let f(r) = 2*r**4 - 26*r**3 - 66*r**2 - 50*r. Let w(x) = -4*c(x) - 9*f(x). Find a such that w(a) = 0.
-5, -1, 0
Let w(o) be the third derivative of o**7/189 - o**6/45 + o**5/30 - o**4/54 - 5*o**2. What is c in w(c) = 0?
0, 2/5, 1
Let h = -65813/9 + 7929. Let t = 618 - h. Factor -10/9*r - 2/3*r**3 - 2/9 - t*r**2.
-2*(r + 1)**2*(3*r + 1)/9
Let v(d) be the first derivative of 2 + 0*d + 0*d**4 - 1/15*d**5 + 1/36*d**6 - 1/12*d**2 + 1/9*d**3. Solve v(i) = 0 for i.
-1, 0, 1
Suppose 2*q - 10 = 4*q. Let x be q*8/(-20) + -2. Factor 1/5*d**5 - d**2 + x + 1/5*d**4 - 2/5*d - 3/5*d**3.
d*(d - 2)*(d + 1)**3/5
Let n(i) = -i**3 + i**2 - 1. Let v(q) = -3*q**3 + 7*q**2 - 7*q + 1. Let p be (9/6)/3*4. Let k(h) = p*n(h) - v(h). Find b, given that k(b) = 0.
1, 3
Let q = -176 - -177. Factor -1/2*a**3 - a**2 + 1/2*a + q.
-(a - 1)*(a + 1)*(a + 2)/2
Let r(k) be the third derivative of k**8/112 + k**7/70 - k**6/40 - k**5/20 - k**2. Factor r(h).
3*h**2*(h - 1)*(h + 1)**2
Let o(k) = k**3 + 4*k**2 - 5*k + 3. Let t(y) = 4*y**3 + 20*y**2 - 24*y + 16. Let i(w) = -16*o(w) + 3*t(w). Let i(p) = 0. What is p?
-2, 0, 1
Let r = 1 - -1. Determine z, given that 7*z**2 - 3*z**r + 2*z**2 - z - 2*z = 0.
0, 1/2
Let f be (-34)/(-8) - 14/56. Let h(c) be the second derivative of -1/54*c**f + 3*c - 4/27*c**3 + 0 - 4/9*c**2. Factor h(u).
-2*(u + 2)**2/9
Suppose -8*o + 7*o = -5. Suppose o*x = -x + 12. Determine i, given that -1/4*i**x + 0 + 1/4*i = 0.
0, 1
Let d(o) be the second derivative of -3*o**5/20 + o**4/4 + o**3/2 - 3*o**2/2 - 12*o. Suppose d(m) = 0. What is m?
-1, 1
Let i(q) be the third derivative of 2*q**2 + 0 + 1/48*q**4 + 0*q + 1/240*q**5 + 1/24*q**3. Factor i(y).
(y + 1)**2/4
Let h be ((-8)/(-14))/(1/2). Let 0 - 2/7*z**4 + 0*z**2 + 6/7*z**3 - h*z = 0. What is z?
-1, 0, 2
Suppose s - 24 = -4*h, -5 - 7 = -3*s + 3*h. Factor -s*o**2 + 2*o**4 + 4 - o**4 + 21*o**2 + 2*o + 6*o**3 + 10*o.
(o + 1)**2*(o + 2)**2
Let i(l) be the first derivative of 2*l**3 - 3*l - l**3 - 1 + 0*l**3. Solve i(u) = 0 for u.
-1, 1
Let y = 1697/7 - 242. Suppose 3/7 - 3/7*o**2 - y*o + 3/7*o**3 = 0. Calculate o.
-1, 1
Let y be ((-2)/(-2))/(2/24). Let o be (-1)/4 + 51/y. Factor -4*i**2 - i**3 + i**4 - i**3 + i**o.
2*i**2*(i - 2)*(i + 1)
Let l(x) = 5*x**5 + 7*x**4 - 6*x**3 - 6. Let z(v) = -3*v**3 - 4*v**3 + 11*v**5 + 2*v**4 - 6*v**3 - 13 + 13*v**4. Let u(c) = 13*l(c) - 6*z(c). Solve u(s) = 0.
0, 1
Let u(h) be the third derivative of 1/420*h**7 + 1/672*h**8 + 0*h**4 + h**2 + 0*h - 1/240*h**6 + 0*h**3 - 1/120*h**5 + 0. Suppose u(v) = 0. What is v?
-1, 0, 1
Factor -1/2 + 1/4*u**4 + 3/4*u**3 + 1/4*u**2 - 3/4*u.
(u - 1)*(u + 1)**2*(u + 2)/4
Let t be (-2)/(-5) + 69/15. Suppose t*n + 4*y + 5 = 20, -5*n = -4*y - 15. What is k in -8/5*k**n + 0 + 0*k + 2/5*k**2 = 0?
0, 1/4
Let x = 124 + -495/4. Suppose -4*p + 8 = -0*p. Let 0*c + 1/4*c**3 + 0 + 0*c**p + x*c**4 = 0. What is c?
-1, 0
Suppose 0 = 3*t + 3 - 0. Let d = 1/5 - t. Factor -2/5*x**4 + d*x**3 + 0 - 6/5*x**2 + 2/5*x.
-2*x*(x - 1)**3/5
Let c = 15/2 - 71/10. What is o in c*o**3 - 4/5*o + 2/5*o**2 + 0 = 0?
-2, 0, 1
Let f(q) be the second derivative of -1/60*q**6 + 0 + 1/168*q**7 + 1/24*q**4 - 1/24*q**3 + 0*q**5 + 0*q**2 - 3*q. Factor f(h).
h*(h - 1)**3*(h + 1)/4
Let y(p) be the first derivative of -p**5/50 + 3*p - 1. Let j(a) be the first derivative of y(a). Factor j(h).
-2*h**3/5
Let q(s) be the first derivative of -s**4/2 - 2*s**3/3 + s**2 + 2*s + 9. Factor q(z).
-2*(z - 1)*(z + 1)**2
Let m = -158 + 476/3. What is w in -2/3*w**2 + m - 1/3*w**3 + 1/3*w = 0?
-2, -1, 1
Suppose -6/7 + 4/7*o + 2/7*o**2 = 0. Calculate o.
-3, 1
Let x(m) = m**2 - m + 3. Let g be x(2). Suppose 3*t - 5*o - 6 = 0, -3*t + 8*t - 10 = -g*o. Factor -2/3*q**t - 2/3 + 4/3*q.
-2*(q - 1)**2/3
Let g(s) be the first derivative of -5*s**3/9 + s**2/2 + 2*s/3 + 12. Find d, given that g(d) = 0.
-2/5, 1
Let y = -5 + 8. Factor -n**3 - 5*n**2 + 0*n**2 - n**2 + 4*n**y.
3*n**2*(n - 2)
Let y(n) be the third derivative of -n**7/420 + n**6/40 - n**5/10 + 5*n**4/24 - n**3/4 + 12*n**2 - 1. Factor y(j).
-(j - 3)*(j - 1)**3/2
Let h(i) = 4 - i**2 + 3 - 3 + 7*i. Let v be h(7). Factor 10*d**2 - 4*d**2 - 14*d**v + 6*d**5 + d**3 + 5*d**3 - 4*d.
2*d*(d - 1)**3*(3*d + 2)
Factor -h**2 + 4 + 5*h**4 + 2*h**4 - 3*h**4 - 7*h**2.
4*(h - 1)**2*(h + 1)**2
Let h(l) be the third derivative of -l**6/540 + l**5/270 + l**4/54 + 24*l**2. Find n such that h(n) = 0.
-1, 0, 2
Let m(y) be the third derivative of -y**7/350 - 13*y**6/600 - 7*y**5/150 + y**4/30 + 4*y**3/15 + y**2. Solve m(h) = 0.
-2, -1, 2/3
Let f(g) be the second derivative of -g**5/10 + g**4/3 - 17*g. Factor f(b).
-2*b**2*(b - 2)
Suppose -6*j = -5*j - 4. Find o, given that -2*o**2 + 4/7 + 6/7*o + 10/7*o**j - 6/7*o**3 = 0.
-1, -2/5, 1
Let r be (-34)/12 - (-9 - -5 - -1). Factor 0 + 0*c + 0*c**2 + r*c**3.
c**3/6
Suppose 1 - 4*f + 4*f**3 - 2*f**3 + 2*f - f**4 = 0. Calculate f.
-1, 1
Determine j so that -1/2*j**2 + j - 5/2*j**3 + 1/2*j**4 + 0 + 3/2*j**5 = 0.
-1, 0, 2/3, 1
Let z(k) be the first derivative of 1/300*k**5 - 1/2*k**2 - 1/600*k**6 + 0*k**4 + 0*k**3 + 0*k - 1. Let q(j) be the second derivative of z(j). Factor q(f).
-f**2*(f - 1)/5
Let z(d) be the second derivative of d**7/2940 + d**6/630 + d**5/420 - d**3/2 - 2*d. Let g(o) be the second derivative of z(o). What is h in g(h) = 0?
-1, 0
Let x(v) be the third derivative of -3*v**8/112 - v**7/70 + 19*v**6/60 - 4*v**4/3 + 16*v**2. Determine d, given that x(d) = 0.
-2, -1, 0, 4/3
Let w be (-1)/(-1) + (-12)/(-3). Let j(f) = -f**2 + 3. Let k(i) = -3*i**2 - i + 7. Let h(d) = w*j(d) - 2*k(d). Suppose h(t) = 0. What is t?
-1
Let g(z) = z**2 + z + 1. Let j(o) = 2*o**3 + 18*o**2 + 18*o + 18. Let c(q) = -36*g(q) + 2*j(q). Find t, given that c(t) = 0.
0
Let a(z) be the first derivative of -7*z**3/3 + 9*z**2/2 - 2*z + 8. Factor a(r).
-(r - 1)*(7*r - 2)
Let h(s) be the first derivative of -5*s**3/12 + s**2/4 + 3. Determine g, given that h(g) = 0.
0, 2/5
Factor -1/6*i**2 - 1/6 - 1/3*i.
-(i + 1)**2/6
Suppose 5*s = s. Let o(b) be the second derivative of 1/10*b**2 + 0*b**3 - 1/30*b**4 + s*b**5 + 1/150*b**6 + 0 - 2*b. Determine i so that o(i) = 0.
-1, 1
Let c be -6*(-2)/8*8/48. Factor 0*d - 1/4*d**2 + c.
-(d - 1)*(d + 1)/4
Let k(i) = -16 + 3*i - 22 + 3*i**2 + 40. Let d be k(-1). Find a, given that d*a**5 + 16/5*a**4 - 2/5*a - 4*a**2 - 8/5*a**3 + 4/5 = 0.
-1, 2/5, 1
Let s be (-32)/(-10) + 1/(-5). Factor -1 + 4*m**2 + 3*m**s + 3 - 2*m**3 + 5*m.
(m + 1)**2*(m + 2)
Let m = 4 - 0. Determine c, given that 2*c**3 - 2*c**2 - c**3 - c + c**2 + c**m = 0.
-1, 0, 1
Let n(d) be the first derivative of -1/4*d + 5 - 1/20*d**5 - 1/2*d**3 + 1/4*d**4 + 1/2*d**2. Solve n(z) = 0 for z.
1
Let p = -756 - -756. Determine d so that p*d**2 - d + 2/3 + 1/3*d**3 = 0.
-2, 1
Let z(w) be the second derivative of w**9/7560 + w**8/3360 - w**4/6 + 3*w. Let s(k) be the third derivative of z(k). Factor s(a).
2*a**3*(a + 1)
Let z(n) = n**2 - 8*n + 10. Let u be z(7). Factor -9/4*v**u - 1/2 - 5/4*v**2 + 7/4*v**4 + 9/4*v.
(v - 1)**2*(v + 1)*(7*v - 2)/4
Find w, given that 0 - 2/7*w**4 + 2/7*w**2 + 2/7*w**5 - 6/7*w**3 + 4/7*w = 0.
-1, 0, 1, 2
Let r(j) = -j**3 - 2*j**2 + 2*j - 3. Let l be r(-3). Factor -1/2 + 0*w + w**2 - 1/2*w**4 + l*w**3.
-(w - 1)**2*(w + 1)**2/2
Let k(t) be the second derivative of 4/27*t**3 + 0 - 1/18*t**5 + 1/135*t**6 + 11*t + 1/9*t**4 - 8/9*t**2. Factor k(q).
2*(q - 2)**3*(q + 1)/9
Let x(r) be the first derivative of -r**4/26 - 2*r**3/13 + 3. Suppose x(h) = 0. Calculate h.
-3, 0
Suppose -12 = -p - 3*p - 4*q, -p + 18 = -4*q. Suppose -8*l**4 - 6 - 2*l - 18*l**3 - 12*l**2 + p = 0. What is l?
-1, -1/4, 0
Let d = -4 + 11. Suppose -9*n + 4 = -d*n. Factor 3/2*p - 3 + 3/2*p**n.
3*(p - 1)*(p + 2)/2
Let z(u) be the third derivative of 13*u**5/60 + 25*u**4/24 + 19*u**3/6 + 7*u**2. Let b(o) = 6*o**2 + 12*o + 9. Let v(x) = -7*b(x) + 3*z(x). Factor v(s).
-3*(s + 1)*(s + 2)
Solve -6/11*z**3 - 8/11*z - 10/11*z**4 + 0 + 24/11*z**2 = 0.
-2, 0, 2/5, 1
Let h(w) be the second derivative of 0*w**2 - 63/20*w**5 - 4*w**4 + w - 9/10*w**6 - 2*w**3 + 0. Let h(g) = 0. Calculate g.
-1, -2/3, 0
Let k be (-5 + 0)/(5/(-5)) -