- 3/5*h**5 + 0 + 3/5*h**3 + 0*h**4 = 0. What is h?
-1, 0, 1
Let g(q) be the second derivative of q**7/21 + q**6/15 - q**5/10 - q**4/6 - 15*q. Factor g(z).
2*z**2*(z - 1)*(z + 1)**2
Determine z so that 6/7*z**3 + 3/7*z**4 + 0 + 0*z**2 + 0*z = 0.
-2, 0
Let p = 5 + -3. Suppose 4*s - s + 7*s - 4*s - 3*s**p = 0. What is s?
0, 2
Let y = 24 - 22. Suppose 4*v + 15 = 3*b, -y*v + 5*b - 22 = 3. Factor v + 0*p**2 + 3/5*p**3 - 3/5*p.
3*p*(p - 1)*(p + 1)/5
Suppose 0 = -5*o + 20 + 5. Let l(u) = -u**3 - u**2 + u - 1. Let c(p) = 2*p**3 + 14*p**2 - 5*p - 7. Let v(g) = o*l(g) + c(g). Factor v(d).
-3*(d - 2)**2*(d + 1)
Let z(f) be the second derivative of f**4/6 - 4*f**3/3 + 4*f**2 - 2*f. Factor z(n).
2*(n - 2)**2
Let h(w) be the second derivative of -w**7/28 - 3*w**6/10 - 39*w**5/40 - 3*w**4/2 - w**3 + 9*w. Factor h(m).
-3*m*(m + 1)**2*(m + 2)**2/2
Suppose 0 = 212*l - 220*l. Let -1/2*n**2 + 1/2*n**4 + 0 + l*n + n**3 - n**5 = 0. Calculate n.
-1, 0, 1/2, 1
Suppose 4*q = 88 - 80. Find n, given that 1/2*n - n**3 - n**q + 1/2*n**5 + 1/2*n**4 + 1/2 = 0.
-1, 1
Let x(c) = c - 4. Let o be x(4). Suppose 4*d - d = o. Factor d + 1/3*r**2 - 1/3*r**4 + 0*r**3 + 0*r.
-r**2*(r - 1)*(r + 1)/3
Let h(r) be the third derivative of -r**7/630 - r**6/90 - r**5/30 - r**4/18 - r**3/18 + 3*r**2. Factor h(o).
-(o + 1)**4/3
Let k(m) = -2*m**2 + 12*m - 10. Let f(a) = 3*a**2 - 13*a + 10. Let i(j) = -3*f(j) - 4*k(j). Let v be i(-10). Factor v*c + 3/2*c**2 - 9/2*c**3 + 0.
-3*c**2*(3*c - 1)/2
Let z(s) be the third derivative of -1/3*s**3 + 0 + 0*s - 1/6*s**4 - 3*s**2 - 1/24*s**5 - 1/240*s**6. Determine g, given that z(g) = 0.
-2, -1
Let x = 10 + -5. Factor -3*o**3 + 4*o**2 + x*o**4 - 4*o**4 - 2*o**2.
o**2*(o - 2)*(o - 1)
Let o be (-95)/(-20) - 2/(-8). Suppose 9 = o*j - 6. Solve -s + 2*s**2 - s**3 + j*s**3 - 2*s**4 - 3*s**5 + 2*s**3 = 0 for s.
-1, 0, 1/3, 1
Let f be (-15)/(-13) - (-2)/(-13). Suppose n - 4 = -f. Factor 4*j**2 + 6*j**n - 2*j**4 - 6*j + 8*j - 10*j**2.
-2*j*(j - 1)**3
Find s such that -2*s**2 + 0*s**3 + 2*s**3 - 2*s - 406*s**4 + 408*s**4 = 0.
-1, 0, 1
Let s(r) = 6*r**4 + 9*r**3 - 3*r**2 - 9*r - 6. Let z(x) = -x**4 - x**3 + x**2 + x + 1. Let l(m) = -s(m) - 3*z(m). Factor l(n).
-3*(n - 1)*(n + 1)**3
Let x(w) be the second derivative of w**4/90 + 2*w**3/9 + 3*w**2/5 - w + 12. Find g, given that x(g) = 0.
-9, -1
Find x such that -3/7*x**3 + 0 + 4/7*x + 1/7*x**5 - 2/7*x**4 + 4/7*x**2 = 0.
-1, 0, 2
Let a(t) = 2*t - 2. Let g be a(1). Let h(n) be the second derivative of -3*n - 1/7*n**2 + 1/42*n**4 + g + 0*n**3. Factor h(p).
2*(p - 1)*(p + 1)/7
Let g = -1211/8558 + 2/389. Let k = 4/11 - g. Solve -k*n - 1/4*n**2 - 1/4 = 0 for n.
-1
Let j be (-3 - (-17)/4)*-12. Let v be ((-6)/4)/(j/6). Let 4/5*t + v*t**2 + 1/5 = 0. Calculate t.
-1, -1/3
Let y(v) = v + 7. Let b be y(-4). Suppose 8*o = 4*o + 8. Factor q**o + q**b + 0 + 1/3*q + 1/3*q**4.
q*(q + 1)**3/3
Suppose -a = -2*a + 2*i + 8, -5*i = 15. Let a + 25*k**4 - 8*k**5 + 19*k**3 + k - 4*k**5 - 8*k**3 - 27*k**2 = 0. What is k?
-1, -1/4, 1/3, 1, 2
Let b = -7 - -11. Solve 4*n**b - 12 + 2*n**2 + 12 + 6*n**3 = 0 for n.
-1, -1/2, 0
Let o(g) = -29*g + 174. Let h be o(6). Factor 0*q + 0*q**2 + h + 2/7*q**3.
2*q**3/7
Let b(c) be the first derivative of c**6/180 + c**5/60 - 2*c**3/3 - 3. Let l(h) be the third derivative of b(h). Factor l(q).
2*q*(q + 1)
Let n(w) be the third derivative of -w**8/1680 + w**7/210 - 2*w**5/15 - w**4/8 + 7*w**2. Let f(r) be the second derivative of n(r). Factor f(k).
-4*(k - 2)**2*(k + 1)
Let z(q) be the third derivative of 0*q + 0 + 1/3*q**3 + 2/15*q**5 + 1/3*q**4 + q**2. Factor z(k).
2*(2*k + 1)**2
Let v be (-9)/(-3) - (-59 - 0). Factor 2 + 0*n - 3*n + 48*n**2 - v*n**2.
-(2*n + 1)*(7*n - 2)
Let v(u) be the third derivative of 3/14*u**5 + 3*u**2 + 5/84*u**6 + 0*u + 2/7*u**4 + 0 + 4/21*u**3. Factor v(r).
2*(r + 1)*(5*r + 2)**2/7
Factor 6/5*r + 1/5*r**5 - 7/5*r**3 + r**2 - r**4 + 0.
r*(r - 6)*(r - 1)*(r + 1)**2/5
Let p = 13/24 + -1/2. Let a(y) be the third derivative of -p*y**3 + 0*y - y**2 + 0 + 1/240*y**5 + 1/96*y**4 - 1/480*y**6. What is q in a(q) = 0?
-1, 1
Let m = 89 - 711/8. Let u(z) be the second derivative of -z + 1/2*z**2 - 1/40*z**5 + m*z**4 + 5/12*z**3 + 0 - 1/60*z**6. Factor u(i).
-(i - 2)*(i + 1)**3/2
Let n(q) = -7*q**5 + 7*q**4 - 5. Let z(t) = -4*t**5 + 4*t**4 - 3. Suppose 0*j = j - 3*d - 7, j = d - 1. Let v(l) = j*z(l) + 3*n(l). Factor v(h).
-h**4*(h - 1)
Let l(k) be the first derivative of -9*k**5/20 - k**4/2 + k**3/2 + 3*k - 3. Let c(f) be the first derivative of l(f). Factor c(a).
-3*a*(a + 1)*(3*a - 1)
Let m = -12 - -37/3. Determine l so that 2/3*l**2 + 1/3*l + 1/3*l**5 - m - 2/3*l**3 - 1/3*l**4 = 0.
-1, 1
Let v(k) be the third derivative of -k**9/211680 + k**7/17640 - k**5/15 + 3*k**2. Let i(o) be the third derivative of v(o). Factor i(w).
-2*w*(w - 1)*(w + 1)/7
Let i(x) = 2*x**3 + x**2 - 4*x. Suppose -5*m = 5*b + 5, -2*m + 4*b = -15 - 7. Let f(u) = u**3 - 3*u. Let s(a) = m*f(a) - 2*i(a). Factor s(h).
-h*(h + 1)**2
Let y = -17690/11 - -108760/77. Let q = y - -196. Factor -q*s**5 - 2/7 + 4/7*s**3 - 2/7*s - 2/7*s**4 + 4/7*s**2.
-2*(s - 1)**2*(s + 1)**3/7
Let h = 4 + -1. Solve h - 5 - 19*y**2 + 17*y**2 - 4*y = 0.
-1
Let k(t) be the third derivative of -t**5/300 - t**4/120 + 3*t**2. Find q, given that k(q) = 0.
-1, 0
Factor 2/3*w**2 + 4*w + 6.
2*(w + 3)**2/3
Let i(b) = -6*b**2 + 31*b - 11. Let f(r) = r**2 - 6*r + 2. Let p(t) = 11*f(t) + 2*i(t). Factor p(c).
-c*(c + 4)
Let v(z) = -2*z**2 - 14*z - 12. Let q be v(-6). Find y such that 2/3*y**2 - 2/3*y**3 + 0*y + q = 0.
0, 1
Let v(i) = -12*i**3 - 56*i**2 - 56*i + 8. Let f(l) = 4*l**3 + 19*l**2 + 19*l - 3. Let j(p) = -8*f(p) - 3*v(p). Solve j(c) = 0.
-2, 0
Let h(b) be the second derivative of 4*b**7/147 + 4*b**6/105 - 3*b**5/70 - 2*b**4/21 - b**3/21 + 9*b. Suppose h(s) = 0. Calculate s.
-1, -1/2, 0, 1
Let q(a) = a**5 + a**4 + a**3 - a**2 - a + 1. Let o(z) = 9*z**5 + 9*z**4 + 18*z**3 - 12*z**2 - 12*z + 12. Let v(y) = -o(y) + 12*q(y). Factor v(m).
3*m**3*(m - 1)*(m + 2)
Let p(h) = -h**5 - 5*h**4 + 6*h**3 - 7*h**2 - 7. Let o(u) = -2*u**4 + 2*u**3 - 2*u**2 - 2. Let z(s) = -7*o(s) + 2*p(s). Factor z(x).
-2*x**3*(x - 1)**2
Let w(t) be the third derivative of t**5/60 + t**4/6 + 7*t**2. Factor w(q).
q*(q + 4)
Let w(f) be the third derivative of f**5/105 - 2*f**4/21 + 2*f**3/7 - 3*f**2 + 4. Find q such that w(q) = 0.
1, 3
Let o be -1*(0/1 + 0). Suppose 0 = -o*j - 2*j. Suppose j - 1/3*l - 1/3*l**2 = 0. Calculate l.
-1, 0
Let h be (-36)/(-40) + (-3)/6. Determine z so that h*z**2 + 0 - 2/5*z = 0.
0, 1
Let c = -79177/5 + 15890. Let n = c - 54. Factor n*p**2 - 3/5 + 3/5*p**3 - 3/5*p.
3*(p - 1)*(p + 1)**2/5
Let c(v) be the third derivative of 0*v**4 + 0 + 0*v**3 - 1/30*v**5 + 1/168*v**8 + 9*v**2 - 1/60*v**6 + 1/105*v**7 + 0*v. Suppose c(n) = 0. What is n?
-1, 0, 1
Let j(g) be the second derivative of 9*g + 3/20*g**5 + 0*g**3 + 0 + 0*g**2 + 3/4*g**4. Factor j(q).
3*q**2*(q + 3)
Factor 0*y - 5/3*y**2 + 5/3.
-5*(y - 1)*(y + 1)/3
Find g, given that -2/15*g**4 + 0 + 2/15*g**2 - 4/15*g**3 + 4/15*g = 0.
-2, -1, 0, 1
Let m = 88 + -85. Determine i so that 8/11*i - 4/11*i**2 - 2/11*i**m + 16/11 = 0.
-2, 2
Let m(d) be the first derivative of -3*d**4/2 - d**3 + 3*d**2 + 3*d + 27. Solve m(b) = 0.
-1, -1/2, 1
Let f(b) = -b**4 + b**3 + b. Let m(s) = s**5 + 2*s**4 - 6*s**3 + s**2 - s. Let l(y) = 15*f(y) + 5*m(y). Solve l(q) = 0.
-1, 0, 1, 2
Let c(j) = -j**2 - 27*j - 26. Let m be c(-26). Factor 2/11*z**2 + m*z + 0 - 2/11*z**3.
-2*z**2*(z - 1)/11
Let w(y) be the first derivative of -4*y**5/5 - 2*y**4 - 8. Factor w(i).
-4*i**3*(i + 2)
Let c(a) be the second derivative of 0*a**2 - 1/42*a**7 + 7*a + 2/15*a**6 - 3/10*a**5 - 1/6*a**3 + 1/3*a**4 + 0. Find d such that c(d) = 0.
0, 1
Let y(d) be the first derivative of -d**4/4 + d**3 - 4*d - 7. What is c in y(c) = 0?
-1, 2
Let i(t) be the third derivative of -t**6/160 - t**5/160 - t**3/6 + 2*t**2. Let w(d) be the first derivative of i(d). Let w(s) = 0. Calculate s.
-1/3, 0
Let v be -1 - -4 - (2 - 2). Suppose -11 = 2*o - 5*m, -v*m = m - 12. Factor 1 + 7*h + 1 - 3*h**2 - o*h.
-(h - 2)*(3*h + 1)
Let a be (-1 + -35)/(-3) - 2. Suppose -5*j = -a*j. Factor 0*y + 1/4*y**3 + j - 1/4*y**2.
y**2*(y - 1)/4
Suppose -3*h - 422 - 493 = 0. Let o = h + 1539/5. Factor -o*j