 = 3*z**2 + 4*z - 5. Let q(w) = -5*w**2 - 6*w + 8. Let r(s) = o*h(s) + 5*q(s). Factor r(n).
-n*(n - 2)
Let u = -503 - -527. Factor 32*s**5 + 1/2 - 6*s + 47/2*s**2 - u*s**4 - 26*s**3.
(s - 1)*(s + 1)*(4*s - 1)**3/2
Suppose 2*x = -l + 11, -3*x + 3*l + 3 = -18. Find g such that 18*g**2 - x*g - 12*g**3 + 4 + 1 - 6*g - 2 + 3*g**4 = 0.
1
Factor -7*y + 22*y - 20*y**3 + 10 + 15*y**3.
-5*(y - 2)*(y + 1)**2
Let c(b) = -4*b**2 - 5*b + 1. Let o(d) = -12*d**2 - 15*d + 4. Let v(t) = -21*c(t) + 6*o(t). Solve v(u) = 0.
-1, -1/4
Let f be 1/(-2) + 7 + -6. Factor -f*q - 1/6*q**2 - 1/3.
-(q + 1)*(q + 2)/6
Let a(i) be the first derivative of 2*i**5/25 - i**4/20 - i**3/5 + i**2/10 + i/5 + 1. Find n, given that a(n) = 0.
-1, -1/2, 1
Let r(a) be the second derivative of a**6/6 - 4*a**5 + 40*a**4 - 640*a**3/3 + 640*a**2 - 8*a. Factor r(v).
5*(v - 4)**4
Let c = -709 + 42541/60. Let b(o) be the third derivative of 1/36*o**4 + 1/315*o**7 + 1/30*o**5 + 0 + 0*o + o**2 + 0*o**3 + c*o**6. Let b(f) = 0. What is f?
-1, 0
Let v(y) be the third derivative of -5*y**8/336 + y**7/21 - y**5/6 + 5*y**4/24 + 7*y**2. Determine c so that v(c) = 0.
-1, 0, 1
Let i(c) be the second derivative of -c**4/30 + 8*c**3/15 - 16*c**2/5 + 14*c. Let i(a) = 0. What is a?
4
Let w(h) be the first derivative of -3*h**4/28 + 9*h**2/14 - 6*h/7 - 8. Factor w(d).
-3*(d - 1)**2*(d + 2)/7
Let n(x) be the third derivative of x**6/420 + x**5/42 + x**4/21 - 14*x**2. Determine h, given that n(h) = 0.
-4, -1, 0
Let l(x) be the third derivative of x**6/90 + x**5/90 - x**4/36 + x**2 - 2. Factor l(f).
2*f*(f + 1)*(2*f - 1)/3
Let p(i) = 2*i**4 - 2*i**3 + 4*i**2 + 4*i. Let u(r) = -r**2 - r. Let c(x) = p(x) + 4*u(x). Determine f so that c(f) = 0.
0, 1
Let m(i) be the second derivative of -i**6/120 + i**5/100 + i**4/60 + i**2 - 2*i. Let o(l) be the first derivative of m(l). What is n in o(n) = 0?
-2/5, 0, 1
Let d(f) be the third derivative of f**7/70 - f**5/10 + f**3/2 + 2*f**2. Factor d(z).
3*(z - 1)**2*(z + 1)**2
Let m = 27 + -25. Factor 7/4*o + 1/2 + 5/4*o**m.
(o + 1)*(5*o + 2)/4
Factor -3/5 - 1/5*d**2 - 4/5*d.
-(d + 1)*(d + 3)/5
Suppose 4*h - 12 = -4*i + 16, 3*i = -5*h + 23. Determine p, given that -p**3 - 2*p**2 + 0*p + 3*p**3 - 4*p**2 - 4*p + 2*p**5 + i*p**4 = 0.
-2, -1, 0, 1
Let y(i) be the third derivative of 0*i**5 + 0*i**3 + 0*i - 1/24*i**4 + 9*i**2 + 0 + 1/120*i**6. Factor y(o).
o*(o - 1)*(o + 1)
Let r(k) be the first derivative of -k**7/105 + k**5/15 - k**3/3 - 3*k**2 + 2. Let g(h) be the second derivative of r(h). Suppose g(u) = 0. Calculate u.
-1, 1
Let o(d) = -2*d - 4. Let z be o(-4). Suppose -z*h = h - 15. Factor -b - b + 1 - 12*b**2 + h*b.
-(3*b - 1)*(4*b + 1)
Let h be ((-6)/4)/((-5)/10). Factor s**2 + h*s - s - 5*s + 4*s.
s*(s + 1)
Let z = 1 + 2. Suppose 3*u + z = 9. Factor 1/4*x + 0 - 1/4*x**u.
-x*(x - 1)/4
Let k(l) be the second derivative of 3*l**3 - 9/4*l**4 - 3/2*l**2 + 6*l + 0. Determine x so that k(x) = 0.
1/3
Let q = -8 - -11. Let f(p) be the first derivative of 1/2*p**2 + 1/2*p + 1/6*p**q + 2. Factor f(r).
(r + 1)**2/2
Let f be ((-10)/(-5))/((-2)/(-4)). What is j in -5*j**5 - 3*j**4 + 0*j**2 + 2*j + 16*j**f - 9*j**3 - j**2 = 0?
-2/5, 0, 1
Let b(v) = -27*v**2 + v + 4. Let f be b(-2). Let z = 322/3 + f. Solve -2/3*c**2 + 0 - z*c = 0 for c.
-2, 0
Let b(v) be the second derivative of v**6/10 + v**5/10 - v**4/4 + 6*v. Let o(l) = 7*l**4 + 5*l**3 - 6*l**2 - l. Let m(h) = -15*b(h) + 6*o(h). Factor m(f).
-3*f*(f - 1)**2*(f + 2)
Suppose 0*d + 2*d - 4 = 0. Factor 0 - 3*k**d - 2 + 3*k + 0 + k**3 + 1.
(k - 1)**3
Factor 0 - 3/7*p**5 + 0*p - 3/7*p**4 + 3/7*p**3 + 3/7*p**2.
-3*p**2*(p - 1)*(p + 1)**2/7
Let l(m) = -4*m + 17. Let q be l(4). Let s(o) be the first derivative of 54/25*o**5 + 42/5*o**3 - q + 19/5*o**2 + 81/10*o**4 + 4/5*o. Factor s(h).
2*(h + 2)*(3*h + 1)**3/5
Let o(c) be the second derivative of -2*c + 0 + 1/3*c**2 + 1/6*c**4 + 1/30*c**5 + 1/3*c**3. Factor o(g).
2*(g + 1)**3/3
Solve -g**2 - 5/2*g + 1/2*g**3 + 3 = 0 for g.
-2, 1, 3
Let o = -2 - -5. Suppose 4*z - 20 = 0, b - 2*b = -z + o. Factor -1/2*f**3 - 1/4*f**b + 1/2*f + 1/4.
-(f - 1)*(f + 1)*(2*f + 1)/4
Find a such that 0 + 8/11*a**2 + 8/11*a - 6/11*a**3 + 2/11*a**5 - 4/11*a**4 = 0.
-1, 0, 2
Let u(g) be the second derivative of -g**6/150 + g**5/25 - g**4/10 + 2*g**3/15 - g**2/10 + 12*g. Find k, given that u(k) = 0.
1
Let d(y) = 10*y - 10. Let g be d(7). Let q be 2/(-8) - (-55)/g. Suppose -2/3*r + q*r**2 - 2/3 + 2/3*r**3 = 0. Calculate r.
-1, 1
Let q be (-6)/9 + 28/6. Let z(k) = k - 2. Let w be z(4). Solve 0*i**2 - 5 + q + i**w = 0 for i.
-1, 1
Determine z, given that -4 - 4*z**2 - 9*z + 27*z + 5 + 9 = 0.
-1/2, 5
Suppose -3*a - 5*j = -21 + 1, 12 = -4*a + 3*j. Factor -2/3*q**4 + 0*q**3 + a + 2/3*q**2 + 0*q.
-2*q**2*(q - 1)*(q + 1)/3
Let d(f) be the third derivative of -7*f**8/480 - f**7/45 - f**6/90 + f**4/12 + 3*f**2. Let i(w) be the second derivative of d(w). Factor i(q).
-2*q*(7*q + 2)**2
Suppose -2*x**2 - x + 4*x - 9*x**3 + 8*x**3 = 0. Calculate x.
-3, 0, 1
Let g(y) be the first derivative of y**4/20 - 2*y**3/15 - y**2/10 + 2*y/5 + 5. Find p, given that g(p) = 0.
-1, 1, 2
Let u(p) = -p**3 + 2*p**2 + p - 2. Let z(w) = 4*w**3 - 6*w**2 - 3*w + 7. Let y = 30 - 16. Let t(n) = y*u(n) + 4*z(n). Find j, given that t(j) = 0.
-1, 0
Let r be (-90)/(-40)*(-3)/9*-2. What is y in 3/2*y**3 + 0 - 3/2*y + 3/2*y**2 - r*y**4 = 0?
-1, 0, 1
Let u(i) = -i**2 - i + 4. Let s be u(5). Let a = s + 79/3. What is f in 2/3*f + 1/3*f**4 + 0*f**2 - a - 2/3*f**3 = 0?
-1, 1
Let a(n) be the first derivative of -3*n**4/20 + 9*n**3/5 - 81*n**2/10 + 81*n/5 - 2. Factor a(i).
-3*(i - 3)**3/5
Let z(c) be the first derivative of c**9/10584 + c**8/1960 - c**6/315 - 5*c**3/3 + 1. Let y(v) be the third derivative of z(v). Find n, given that y(n) = 0.
-2, 0, 1
Let f(v) = -v**2 + 2*v + 2. Let u be f(-3). Let r = -8 - u. Determine h so that -5 - 21*h**2 + 1 - 16*h - 4*h**3 - r*h**3 = 0.
-1, -2/3
Find p such that -49/3 + 13/3*p**2 - 35/3*p - 1/3*p**3 = 0.
-1, 7
Let d(i) be the first derivative of -i**4/12 + 14*i**3/9 - 10*i**2 + 24*i - 38. Let d(m) = 0. Calculate m.
2, 6
Let w(l) be the third derivative of -l**5/60 - l**4/4 - 6*l**2 + l. Factor w(k).
-k*(k + 6)
Factor 6/13*m**2 - 2/13 + 2/13*m - 10/13*m**3 + 4/13*m**4.
2*(m - 1)**3*(2*m + 1)/13
Let v(c) = -c**2 + 5*c - 1. Let w(b) = b**3 + 10*b**2 - 12*b - 7. Let a be w(-11). Let r be v(a). Factor 0*x + 1/2*x**5 + 0 + 1/2*x**r + 0*x**2 + x**4.
x**3*(x + 1)**2/2
Let z(f) = f**3 + 6*f**2 - 2*f + 10. Let g be z(-7). Let t = g - -27. Let 0 + 4/3*n + 2/3*n**t = 0. What is n?
-2, 0
Suppose -69 = -m - 67. Suppose 4*h - 5*h + 4*i = -38, 5*h - 65 = -5*i. Determine y so that 0 - 15/2*y**4 - h*y**3 - 27/2*y**m - 3*y = 0.
-1, -2/5, 0
Factor -3/2 - 9/2*v + 6*v**2.
3*(v - 1)*(4*v + 1)/2
Let g(m) be the second derivative of -3/8*m**5 + 17/8*m**4 - 4*m**3 + 3*m**2 + 3*m + 0. Factor g(p).
-3*(p - 2)*(p - 1)*(5*p - 2)/2
Factor -3*u**4 + 9*u**4 - 2*u**4 - 202*u**5 + 206*u**5.
4*u**4*(u + 1)
Let c(a) be the second derivative of 0*a**4 - 1/2*a**3 + 0*a**2 + 0 + 3/20*a**5 + 2*a. Find j such that c(j) = 0.
-1, 0, 1
Let h(l) be the first derivative of -2*l**5/5 + 3*l**4/2 - 2*l**3 + l**2 + 10. Determine p, given that h(p) = 0.
0, 1
Let o(q) = -6*q**2 + 6*q. Let l(c) = 17*c**2 - 17*c. Let m(b) = -3*l(b) - 8*o(b). Determine r, given that m(r) = 0.
0, 1
Let w(k) = k**3 - 3*k**2 + k - 3. Let q be w(3). Factor -2*t**2 - 4*t**4 + q*t**2 + 2*t**4 - 4*t**3.
-2*t**2*(t + 1)**2
Let y(d) be the third derivative of d**6/360 - d**4/24 + d**3/9 - 8*d**2. Determine f so that y(f) = 0.
-2, 1
Let n(w) = -w + 1. Let b be n(1). Suppose b = 3*a - 0*a. Suppose -2/9*y**3 + a - 4/9*y**2 - 2/9*y = 0. What is y?
-1, 0
Let a(d) = -2*d**4 + d**2 - 1. Let f(o) = 5*o**4 - 16*o**3 + 76*o**2 - 112*o + 51. Let t(j) = -2*a(j) - f(j). Factor t(u).
-(u - 7)**2*(u - 1)**2
Suppose -5 = -3*h - 29. Let x = -5 - h. Factor 2*c**4 - 3*c + 2*c**5 + x*c.
2*c**4*(c + 1)
Let t(q) be the third derivative of -q**2 - 1/6*q**4 + 0*q + 0 + 1/3*q**3 + 1/30*q**5. Factor t(f).
2*(f - 1)**2
Let o be (-6)/9 + (-4)/(-6). Let i(u) = -u**3. Let l be i(o). Factor 1/2*w + l + 0*w**2 - 1/2*w**3.
-w*(w - 1)*(w + 1)/2
Suppose d + 3*o = 9 + 5, -32 = -4*d - 4*o. Suppose 0 = -c + d*c - 12. Factor 7*g**4 - 9*g**4 + g**c + g*