00 + n**6/400 + n**5/300 + n**4/8 - n**2. Let z(y) be the second derivative of m(y). Solve z(o) = 0.
-1, -2/7
Let v(u) be the first derivative of -u**6/6 - 3*u**5/5 - 3*u**4/4 - u**3/3 - 24. Find h, given that v(h) = 0.
-1, 0
Let d be 368/(-188) - 2 - -4. Let x = 37/235 + d. What is l in 3/5*l**2 + x - 3/5*l - 1/5*l**3 = 0?
1
Let f(l) be the second derivative of -l**2 + 2/3*l**3 + 3*l + 0 - 1/6*l**4. Let f(g) = 0. What is g?
1
Let j(n) be the first derivative of n**7/420 - n**6/240 - n**5/40 + n**4/48 + n**3/6 + 2*n**2 - 4. Let g(m) be the second derivative of j(m). Factor g(r).
(r - 2)*(r - 1)*(r + 1)**2/2
Factor 3 + 6*d**2 - 3/2*d**3 - 15/2*d.
-3*(d - 2)*(d - 1)**2/2
Let n(l) be the first derivative of -4*l**3/21 - 8*l**2/7 - 16*l/7 - 16. Factor n(f).
-4*(f + 2)**2/7
Let a = 64 + -64. Let k(j) be the second derivative of 0*j**2 + 0 + 0*j**3 + 2*j - 1/75*j**6 + a*j**5 + 0*j**4 + 1/105*j**7. Determine o so that k(o) = 0.
0, 1
Let z be (-8)/6*1*-3. Suppose -6*c + 6 = -z*c. Factor -4*a**2 + 0*a**2 - 2*a**3 + c*a + 4*a**4 - a.
2*a*(a - 1)*(a + 1)*(2*a - 1)
Let d be ((-2)/3)/((-6)/18). Factor -6*v**2 + 4*v**d + 2*v + 0*v**2.
-2*v*(v - 1)
Let t(l) be the second derivative of -l**5/4 + 5*l**4/3 - 5*l**3/2 - 39*l. Solve t(i) = 0 for i.
0, 1, 3
Suppose i - 2*i - 2*t + 14 = 0, -i + 2 = -2*t. Let r be i/4 + (5 - 7). Factor q**3 + r + 1/2*q**2 + 1/2*q**4 + 0*q.
q**2*(q + 1)**2/2
Let k be 32/(-336)*(-2 - 5). Solve 5*x**3 - 11/3*x**4 + x**5 + k*x - 3*x**2 + 0 = 0.
0, 2/3, 1
Let z = 7 + -4. Let q be -3 - z/((-36)/39). Solve -q*a**2 + 0 + 0*a + 1/4*a**3 = 0.
0, 1
Let p(i) = i. Let d(k) = 6*k + 7. Let f(h) = -d(h) + 3*p(h). Let v be f(-5). Factor -64*g**2 - 56*g**3 - 4*g**2 - 22*g**2 - v + 98*g**4 + 56*g.
2*(g - 1)*(g + 1)*(7*g - 2)**2
Let v(q) = 3*q**2 - 4*q + 5. Let p = 136 - 86. Let j be p/(-15)*(-6)/4. Let o(b) = b**2 - 2*b + 2. Let u(z) = j*o(z) - 2*v(z). Suppose u(a) = 0. Calculate a.
-2, 0
Determine n so that -25/11 - 6/11*n**2 - 40/11*n - 1/11*n**4 + 8/11*n**3 = 0.
-1, 5
Let l(m) be the first derivative of -3*m**4/8 + m**3/2 + 3*m**2/4 - 3*m/2 + 18. Factor l(n).
-3*(n - 1)**2*(n + 1)/2
Let l be (-25269)/(-108) - 3/4. Let b = l - 233. Factor b + 2/9*t**4 + 2/9*t + 2/9*t**5 - 4/9*t**2 - 4/9*t**3.
2*(t - 1)**2*(t + 1)**3/9
Let b(o) = -o**3 - 5*o**2 + 5*o - 1. Let t be b(-6). Let -2*f**3 + 5*f**t - 5*f**4 - 3*f**5 + 5*f**4 = 0. Calculate f.
-1, 0, 1
Suppose -38*q + 62 = -52. Factor 2/7 + 4/7*j**2 - 6/7*j + 2/7*j**5 + 4/7*j**q - 6/7*j**4.
2*(j - 1)**4*(j + 1)/7
What is b in 0*b**2 + 1/9*b**3 + 0*b**4 + 0 - 1/9*b**5 + 0*b = 0?
-1, 0, 1
Suppose -g = g - 7*g. Factor 0*x**4 + 0*x**2 + g*x + 0 + 1/2*x**3 - 1/2*x**5.
-x**3*(x - 1)*(x + 1)/2
Let i(n) be the second derivative of -n**6/135 - n**5/45 + n**4/54 + 2*n**3/27 - 14*n. Determine z, given that i(z) = 0.
-2, -1, 0, 1
Suppose 42*s**2 + 1862*s**3 - 1956*s**3 + 14*s**5 + 3 - 18*s**4 + 80*s - 27 = 0. What is s?
-2, -1, 2/7, 1, 3
Let l(t) = -5*t**2 + 5*t + 4. Let a(r) = -10*r**2 + 10*r + 9. Let d(y) = 6*a(y) - 11*l(y). Determine n, given that d(n) = 0.
-1, 2
Let m(r) be the third derivative of r**6/210 - r**5/35 + r**4/21 - r**2. Find v, given that m(v) = 0.
0, 1, 2
Let j(r) be the first derivative of 1/2*r**2 - 2/3*r - 1/9*r**3 - 4. What is h in j(h) = 0?
1, 2
Suppose -3*c + 13 + 2 = 0. Suppose c*a - 6*a = 0. Find j, given that -2/5*j**4 + 4/5*j**2 - 2/5 + 0*j**3 + a*j = 0.
-1, 1
Let c(q) be the second derivative of q**4/12 - 5*q**3/3 - 9*q**2/2 + q. Let v be c(11). Factor b**3 + v*b**5 + 2*b**5 - 3*b**5 - 2*b**3.
b**3*(b - 1)*(b + 1)
Let p(k) = -k**4 - k. Let v(j) = 2*j**4 + 13*j**3 - 9*j**2 + 6*j + 2. Let u(n) = -n - 11. Let o be u(10). Let l(x) = o*p(x) - 3*v(x). Find s such that l(s) = 0.
-2/5, 1
Let a = -17 + 25. Suppose -2*v + 5*j = -12, -v = -2*v - 2*j + 6. Factor 5*u**2 + 4*u - v*u**3 + a*u**3 + u**2.
2*u*(u + 1)*(u + 2)
Let g = -31/11 - -3. Find w such that -10/11*w - 4/11 - 8/11*w**2 - g*w**3 = 0.
-2, -1
Let y(c) be the second derivative of c**4/72 - 4*c**3/9 + 16*c**2/3 - 25*c. Factor y(h).
(h - 8)**2/6
Let l(z) = -5*z**3 - 5*z**2 + 5*z - 5. Let d(g) = -g**5 + 6*g**3 + 4*g**2 - 5*g + 4. Let a(s) = -5*d(s) - 4*l(s). Find k such that a(k) = 0.
-1, 0, 1
Let s = -92 - -92. Let m(p) be the second derivative of -1/50*p**5 + s*p**3 + 0 + 1/30*p**4 + 4*p + 0*p**2. Factor m(b).
-2*b**2*(b - 1)/5
Let x(v) be the first derivative of -v**8/1260 + v**7/252 - v**6/180 - v**5/180 + v**4/36 - v**3 - 2. Let b(w) be the third derivative of x(w). Factor b(d).
-2*(d - 1)**3*(2*d + 1)/3
Let z(m) be the third derivative of 0*m - 2*m**2 + 0 - 1/84*m**7 + 0*m**3 - 1/20*m**6 - 3/40*m**5 - 1/24*m**4. Factor z(f).
-f*(f + 1)**2*(5*f + 2)/2
Let r(n) = -4*n**4 - 13*n**3 - 9*n**2 - 5*n - 5. Let h(g) = -g**3 - g**2 - g - 1. Let l(v) = -5*h(v) + r(v). Let l(z) = 0. What is z?
-1, 0
Let i(u) = -u**4 + u**3 + u**2 - u + 1. Let n(h) = 3*h + h**2 + 5*h**3 - h**2 + h**2 + h**4 - 8*h**3 + 1. Let f(z) = -3*i(z) + n(z). Factor f(v).
2*(v - 1)**2*(v + 1)*(2*v - 1)
Suppose 4*h - 2 = 2*h + 2*q, -q = -3*h + 1. Find u such that -2/3*u**2 + 2/3*u + h = 0.
0, 1
Let r(c) = 21*c**3 - 49*c**2 + 60*c - 26. Let i(a) = a**3 + a**2 - 1. Let g(o) = -6*i(o) + r(o). Let g(h) = 0. What is h?
2/3, 1, 2
Let h(i) be the second derivative of -i**5/180 + i**4/72 - 2*i**2 - 3*i. Let y(m) be the first derivative of h(m). Factor y(n).
-n*(n - 1)/3
Let n(m) be the first derivative of -4/15*m**3 - 7 + 0*m + 2/25*m**5 + 0*m**2 - 1/10*m**4. Factor n(i).
2*i**2*(i - 2)*(i + 1)/5
Let u = 616 - 2437/4. Determine v, given that u - 1/4*v**3 - 27/4*v + 9/4*v**2 = 0.
3
Let k(b) be the second derivative of -8*b**6/15 - b**5 - b**4/3 + 16*b. Factor k(s).
-4*s**2*(s + 1)*(4*s + 1)
Let l(k) be the second derivative of -k**4/28 + k**3/7 - 7*k. What is h in l(h) = 0?
0, 2
Let p be ((-1)/(-3))/((-7)/(-42)). Suppose p*b = 4*b. Factor b - 1/3*n + 1/3*n**3 + 0*n**2.
n*(n - 1)*(n + 1)/3
Let a(s) be the third derivative of -s**6/120 + 11*s**5/20 - 121*s**4/8 + 1331*s**3/6 - 25*s**2. Factor a(h).
-(h - 11)**3
Let c be -2 + ((-27)/3 - 3). Let s be ((-2)/7)/(2/c). Factor 4/3 - s*o + 2/3*o**2.
2*(o - 2)*(o - 1)/3
Suppose 8*d = 7*d + 3. Factor 6*a - 12*a**3 - d*a**4 + 5*a**4 - 3*a**3 + 4*a**4 + 3*a**2.
3*a*(a - 2)*(a - 1)*(2*a + 1)
Let i(c) = c**2 + c - 1. Let l(s) = s**2 + 3*s. Suppose 3*r - a = 2*r - 5, -2*r + 4*a = 16. Let j(y) = r*i(y) + l(y). Let j(o) = 0. What is o?
-1, 2
Let u be (-8)/(-6)*42/28. Suppose -u - 28/3*z - 98/9*z**2 = 0. Calculate z.
-3/7
Let j(q) be the first derivative of -q**4/24 - q**3/18 + q**2/12 + q/6 + 4. Factor j(h).
-(h - 1)*(h + 1)**2/6
Let w(x) = 5*x**2 + 6*x. Let g(b) = 2*b**2 + b + 1. Let i(k) = -k**2 - 1. Let a(o) = g(o) + i(o). Let u(t) = -4*a(t) + w(t). Factor u(q).
q*(q + 2)
Let -3*x**4 - 87/4*x**2 + 15*x**3 + 12*x - 9/4 = 0. What is x?
1/2, 1, 3
Suppose 39 = 4*a - 21. Suppose -5*f - a = -10*f. Factor 0 + 1/2*l**2 - 1/2*l**f + 0*l.
-l**2*(l - 1)/2
Let v(u) be the first derivative of u**3/3 + 3*u**2/2 - u + 3. Let r be v(-4). Factor 5*d**2 + 0*d + d**4 - 2*d**2 - d - r*d**3.
d*(d - 1)**3
Let h = 25 + -9. Let -p**2 + 0*p**2 + 4*p**2 + 8*p + 48 + h*p = 0. What is p?
-4
Factor 3*r**2 - 12*r + 0 + 15*r + 0.
3*r*(r + 1)
Let h = -51 + 256/5. Let l = -209/5 - -42. Let h*v**2 - 2/5 + l*v = 0. Calculate v.
-2, 1
Factor 2*c**3 - 2/3*c**4 + 0 + 0*c - 4/3*c**2.
-2*c**2*(c - 2)*(c - 1)/3
Let g(k) be the first derivative of k**6/45 - k**4/18 - k - 4. Let j(b) be the first derivative of g(b). Let j(d) = 0. Calculate d.
-1, 0, 1
Factor -12*l - 9 + 5 + 13 + 3*l**2.
3*(l - 3)*(l - 1)
Let s = -2 - -2. Let f(y) be the second derivative of y**4 - y + s - 1/2*y**2 - 2/3*y**3 + 8/5*y**5 - 32/15*y**6. Factor f(g).
-(2*g - 1)**2*(4*g + 1)**2
Let q = 1907/1190 + -27/17. Let t(y) be the third derivative of 0*y**3 + 0 + 1/8*y**4 + 4*y**2 + 3/40*y**6 + q*y**7 + 0*y + 3/20*y**5. Solve t(m) = 0 for m.
-1, 0
Let k(g) be the second derivative of -g**6/30 + g**5/20 + g**4/12 - g**3/6 - 27*g. Factor k(o).
-o*(o - 1)**2*(o + 1)
Let m(y) be the second derivative of y**7/35 - 7*y**6/60 + 8*y**5/45 - y**4/9 + y**2/2 + 7*y. Let x(n) be the first derivative of m(n). Factor x(a).
2*a*(a - 1)*(3*a - 2)**2/3
Let s(q) = q**3 + 5*q**2 - 6*q + 4. Let d be s(-6). Suppose 2 = -x, -2*k - 3*x - d = x. 