 + 209. Find s, given that 39/7*s**x + 36/7*s + 18/7*s**3 + 12/7 + 3/7*s**4 = 0.
-2, -1
Let a(r) be the second derivative of 1/126*r**7 + 1/45*r**6 - 1/18*r**4 + 0*r**2 - 1/18*r**3 + 0 + 0*r**5 - 3*r. Factor a(h).
h*(h - 1)*(h + 1)**3/3
Let f(a) be the third derivative of -a**6/24 + a**5/3 - 5*a**4/6 + 18*a**2. Factor f(z).
-5*z*(z - 2)**2
Suppose -u - 11 = -27. Let 8 - 18*i**2 + 0*i**4 - u*i**3 + 4*i + 12*i + 10*i**4 = 0. What is i?
-1, -2/5, 1, 2
Let h(c) be the third derivative of -1/40*c**6 + 0*c**3 + 5*c**2 + 1/140*c**7 + 0 + 0*c + 1/8*c**4 - 1/40*c**5. Factor h(r).
3*r*(r - 2)*(r - 1)*(r + 1)/2
Let h(u) be the third derivative of 0 - 1/945*u**7 - u**2 + 0*u**5 + 0*u**3 + 0*u**4 + 0*u**6 + 0*u. Factor h(s).
-2*s**4/9
Let f be 1/(-4) + 18/(-24). Let c be (-209)/(-220) - f/(-5). Factor 0*w + c*w**5 - 1/4*w**3 + 0 + w**4 - 1/2*w**2.
w**2*(w + 1)**2*(3*w - 2)/4
Factor -o**2 - 9*o + 3*o - 2 + 3*o + 0.
-(o + 1)*(o + 2)
Let a(q) be the first derivative of -3*q**4/8 - q**3/2 + 2. Factor a(k).
-3*k**2*(k + 1)/2
Solve 1/2*r - 1/4*r**2 + 3/4 = 0.
-1, 3
Find k, given that 9*k**2 + 12*k**2 + 8*k + 46*k**3 + 15*k**4 + 18*k**2 - 3*k**2 = 0.
-2, -2/3, -2/5, 0
Let p = 121 - 116. Let u(b) be the third derivative of -2*b**2 + 1/300*b**p + 0*b + 0 - 1/30*b**3 + 0*b**4. Factor u(f).
(f - 1)*(f + 1)/5
Let r(o) = o**2 + o - 1. Let j(t) = 8*t**2 + 14*t - 12. Let y(s) = -j(s) + 10*r(s). Factor y(u).
2*(u - 1)**2
Let n(g) be the first derivative of -g**2 + 0*g + 0*g**3 + 2 + 1/30*g**5 + 1/12*g**4. Let d(m) be the second derivative of n(m). Factor d(a).
2*a*(a + 1)
Let g be (1 - -1) + (-13)/(520/48). Factor -g*y + 2*y**3 - 6/5*y**2 + 0.
2*y*(y - 1)*(5*y + 2)/5
Suppose t = -0*t - t. Let 0*o + t*o**2 - 4/9*o**4 + 0 + 0*o**3 - 2/9*o**5 = 0. What is o?
-2, 0
Suppose 7*p - 18*p + 33 = 0. Let s(o) be the third derivative of 0 + 0*o + o**2 + 0*o**p + 1/60*o**6 + 0*o**5 - 1/12*o**4. Factor s(g).
2*g*(g - 1)*(g + 1)
Suppose -3*d - 213 + 219 = 0. Suppose 2/3*c**d - 2/3*c**3 + 0 + 0*c = 0. Calculate c.
0, 1
Let q(j) be the first derivative of j**6/30 - j**5/10 + j**4/12 + 10*j + 4. Let r(f) be the first derivative of q(f). Let r(d) = 0. Calculate d.
0, 1
Suppose 2*w + 2*h - 10 = 0, -5*w + 3*h + 6 = -w. Let q(b) be the first derivative of 0*b**2 - 1/15*b**6 + 0*b + 2/25*b**5 - 1 + 0*b**w + 0*b**4. Factor q(l).
-2*l**4*(l - 1)/5
Solve 0 + 10/3*r**2 - 8/3*r**3 + 2/3*r**4 - 4/3*r = 0 for r.
0, 1, 2
Let r(n) be the first derivative of 0*n**2 + 0*n + 4*n**3 - 7/2*n**4 + 3 - 6/5*n**5. Find q, given that r(q) = 0.
-3, 0, 2/3
Suppose 0*f + 1/2*f**2 + 1/2*f**3 + 0 = 0. What is f?
-1, 0
Let f(t) be the second derivative of 2/3*t**3 + 1/12*t**4 + 3*t + 3/2*t**2 + 0. Factor f(q).
(q + 1)*(q + 3)
Let n = -127/36 - -15/4. What is m in 2/9*m + 0 + n*m**2 = 0?
-1, 0
Let b be (-2)/(-55)*(-75)/(-15). Factor 0 + b*k**4 + 2/11*k - 2/11*k**3 - 2/11*k**2.
2*k*(k - 1)**2*(k + 1)/11
Factor 0*b + 0 + 3/7*b**2.
3*b**2/7
Suppose 0 = 2*d, -4*d + 10 = 4*a + 2. Let r(s) be the first derivative of -1/3*s**a - 3 + 0*s - 1/9*s**3. Solve r(y) = 0.
-2, 0
Let x = -45 + 47. Suppose 5*y = -f + 15, 2*f = 3*y + 4*f - 2. Factor 5*q**x - 9/4*q**5 + 15/2*q**y - q - 37/4*q**3 + 0.
-q*(q - 1)**2*(3*q - 2)**2/4
Let g(f) be the second derivative of -f**6/480 + f**5/240 - f**2/2 + 3*f. Let h(o) be the first derivative of g(o). Let h(j) = 0. Calculate j.
0, 1
Let j(l) be the third derivative of -l**5/120 + 5*l**4/96 + l**3/8 + 4*l**2. Determine h so that j(h) = 0.
-1/2, 3
Factor 0*p**2 - 1/4*p**4 - 1/2*p**3 + 0*p + 0.
-p**3*(p + 2)/4
Let r(v) = v**2 - 8*v + 3. Let n be r(8). Find w, given that -w**3 - w**3 + n*w - w**3 = 0.
-1, 0, 1
Let d(p) be the third derivative of -p**8/1512 - 2*p**7/945 + p**5/135 + p**4/108 + 21*p**2. Factor d(k).
-2*k*(k - 1)*(k + 1)**3/9
Suppose 6*v + 403 = 415. Factor 1/9*t**v - 4/9 + 0*t.
(t - 2)*(t + 2)/9
Let s = 11 - 11. Let j(o) be the second derivative of s*o**4 + 1/90*o**5 + 0*o**2 - o + 0*o**3 + 0. Factor j(a).
2*a**3/9
Find k, given that -128*k**2 + 162/5*k**4 - 288/5*k + 72/5*k**3 - 32/5 = 0.
-2, -2/9, 2
Let m = 10 - 10. Suppose 0 = 4*u + q - 18, m = -3*u - 3*q + 6 + 12. Suppose 6/7*p + 2/7 - 6/7*p**u - 4/7*p**3 - 2/7*p**5 + 4/7*p**2 = 0. What is p?
-1, 1
Let m(p) = -p + 11. Let y be m(-8). Suppose -4*l + 1 = -y. Suppose 2/3 - 4/3*o**3 + 4/3*o**l + 0*o - 8/3*o**2 + 2*o**4 = 0. Calculate o.
-1, 1/2, 1
Let s = -103 + 105. Suppose 1/2*n + 1/2*n**3 + 0 + n**s = 0. What is n?
-1, 0
Determine n so that 2/7 - 4/7*n + 2/7*n**2 = 0.
1
Let h(g) = -2*g - 6*g**2 + 5*g + 3*g**5 + 1 - 9*g**3 + 2 + 6*g**4. Let d(p) = -p**4 + p**3. Let i(n) = -3*d(n) - h(n). Determine s so that i(s) = 0.
-1, 1
Let q(b) be the first derivative of 4*b**5/5 - b**4 - 4*b**3/3 + 2*b**2 + 19. Find z such that q(z) = 0.
-1, 0, 1
Let d be -6*1*(-3)/(-6). Let f be (-11)/(-3) + 2/d. Suppose 3*l + l + l**2 - f*l = 0. Calculate l.
-1, 0
Factor 2*v - 2*v**3 + 1/3*v**4 - 3 + 8/3*v**2.
(v - 3)**2*(v - 1)*(v + 1)/3
Let i be 10/(-15)*(-5)/((-105)/(-18)). Factor 2/7*j**2 - 6/7*j + i.
2*(j - 2)*(j - 1)/7
Let j = -2522/5 - -506. Let c be (-48)/(-70) + (-2)/7. Factor c*y**2 - 8/5*y + j.
2*(y - 2)**2/5
Let o(t) = 3*t**3 + 4*t**2 - t - 6. Let g(v) be the first derivative of -9*v**4/4 - 4*v**3 + 2*v**2 + 17*v - 4. Let h(z) = 4*g(z) + 11*o(z). Factor h(b).
-(b - 1)*(b + 2)*(3*b + 1)
Factor 0 + 1/4*l**3 - 1/2*l**2 + 1/4*l.
l*(l - 1)**2/4
Let a be -3 - -2 - (-13)/5*1. Find x such that -2/5 + a*x**2 - 6/5*x = 0.
-1/4, 1
Factor 0 + 4/3*s - 1/3*s**2.
-s*(s - 4)/3
Determine f, given that 16/3*f - 25/3*f**2 + 1/3*f**5 - 4/3 + 19/3*f**3 - 7/3*f**4 = 0.
1, 2
Suppose 5*f = 4*g - 4, 5*f - 7 = g + 7. Let a be g/9 - (-20)/(-48). Determine h so that 0 - a*h**2 + 1/2*h = 0.
0, 2
Let o(y) be the third derivative of 1/3*y**3 + 1/30*y**6 + 0*y**5 - 3*y**2 - 1/6*y**4 - 1/105*y**7 + 0 + 0*y. Factor o(c).
-2*(c - 1)**3*(c + 1)
Let h(o) = -o**3 + 8*o**2 + 19*o + 16. Let m(p) = 4*p**3 - 24*p**2 - 56*p - 47. Let t(b) = -7*h(b) - 2*m(b). Solve t(u) = 0.
-3, -2
Let r(a) be the first derivative of -a**7/1050 + a**6/150 - a**5/60 + a**4/60 - a**2 + 2. Let x(s) be the second derivative of r(s). Find u such that x(u) = 0.
0, 1, 2
Let z(w) be the first derivative of w**3/3 - 5*w**2 - 11*w + 18. Factor z(a).
(a - 11)*(a + 1)
Let o = 2 - 3. Let j(z) = -4*z - 1. Let p be j(o). Factor -3*c + 2 + 18*c**3 - 4 - 17*c**p.
(c - 2)*(c + 1)**2
Let h be (4/3)/((-4)/(-12)). Determine g, given that -15*g**3 + 16*g**3 - g + 0*g**2 + 3*g**2 - g**h - 2 = 0.
-1, 1, 2
Let z = -1/47 + 101/329. Determine k so that -8/7*k - z*k**3 + 8/7*k**2 + 0 = 0.
0, 2
Let r(t) be the first derivative of -5*t**4/4 + 15*t**3 - 75*t**2/2 + 35*t - 26. Factor r(q).
-5*(q - 7)*(q - 1)**2
Let y(a) = -5*a + 63. Let t be y(12). Determine l so that -4/3*l + 0 + 2/3*l**2 + 4/3*l**t - 2/3*l**4 = 0.
-1, 0, 1, 2
Let v be ((-1)/(-10))/((-14)/455). Let r = -11/4 - v. Determine t, given that 0*t - 1/2*t**4 + t**2 - r + 0*t**3 = 0.
-1, 1
Let j(z) be the first derivative of -4*z**5/25 - 3*z**4/10 - 2*z**3/15 + 2. Factor j(d).
-2*d**2*(d + 1)*(2*d + 1)/5
Let n(a) = -4*a**2 + 0*a**2 + 5*a**2 + 1. Let u be n(-1). Factor 4*t**3 + u*t + 0*t**2 - 6*t**3 + 0*t**2.
-2*t*(t - 1)*(t + 1)
Let p be 4 - (0 + 5) - -3. Let r(c) be the second derivative of 0*c**5 + 0 + 0*c**3 + 0*c**p - 1/60*c**6 + 0*c**4 - c. Determine x so that r(x) = 0.
0
Suppose -10*v + 8*v = 0. Suppose v = -2*i - 18 + 22. Factor 0*s**i + 2/7*s**3 - 2/7*s + 0.
2*s*(s - 1)*(s + 1)/7
Let f(i) = -i**2 - 11*i. Let t be f(-11). Let k(u) be the third derivative of t*u**3 - 2*u**2 - 1/180*u**5 + 0*u + 0 + 1/72*u**4. Factor k(z).
-z*(z - 1)/3
Let k be (-1 + 4 - 4)/((-1)/2). Factor 0*s - 2/11*s**k + 2/11.
-2*(s - 1)*(s + 1)/11
Let r(c) = c**2 + c - 2. Let o be r(-2). Suppose 0 = 4*i - 0*i. Find l such that i + o*l + 3/4*l**2 = 0.
0
Let s(i) be the first derivative of 27*i**5/10 - 9*i**4/8 - 5*i**3/2 - 3*i**2/4 + 3. Factor s(q).
3*q*(q - 1)*(3*q + 1)**2/2
Let u(c) be the third derivative of 1/735*c**7 + 2*c**2 + 0*c - 1/84*c**6 + 0 + 1/392*c**8 + 0*c**3 + 1/42*c**4 - 1/210*c**5. What is n in u(n) = 0?
-1, 0, 2/3, 1
Let z(i) be the first derivative of -4*i**3/21 + 4*i**2/7 + 12*i/7 - 8. Factor z(l).
-4*(l - 3)*(l + 1)/7
Let a(p) be the second derivative of p**5/110 + p**4/22 + p**3