 1. Let d(s) = 2*s**3 + 7*s**2 + 3. Let j(g) = d(g) - 3*n(g). Let w be j(7). Factor w*p**2 - 2 + 2 + 2 + 6*p + 2*p**3.
2*(p + 1)**3
Let t(q) be the first derivative of q**5/80 - q**4/24 - q**3/24 + q**2/4 + q + 2. Let y(x) be the first derivative of t(x). Suppose y(m) = 0. What is m?
-1, 1, 2
Let i(b) = b**3 - b**2 - b + 5. Let h be i(0). Factor 3*t**2 - 2*t**4 - t**3 + 2*t**5 - h*t**2 - t**5 + 4*t**4.
t**2*(t - 1)*(t + 1)*(t + 2)
Let c(v) be the first derivative of v**5/10 - v**4/2 + 5*v**3/6 - v**2/2 + 13. Solve c(u) = 0.
0, 1, 2
Factor -3*g**2 - 32*g + 44 + 46*g - 14 - 23*g.
-3*(g - 2)*(g + 5)
Let h = -3/4 - -19/20. What is t in -h*t + 0 + 1/5*t**2 = 0?
0, 1
Let p(s) be the third derivative of -7/75*s**7 + 0 + 2*s**2 + 1/15*s**4 + 0*s + 77/300*s**6 - 16/75*s**5 + 0*s**3. Factor p(c).
-2*c*(c - 1)*(7*c - 2)**2/5
Let u be 2/(-4) + 50/20. Factor 2/7 - 2/7*z**3 + 6/7*z**u - 6/7*z.
-2*(z - 1)**3/7
Let u(n) be the first derivative of 9*n**5/5 - 15*n**4/2 + 4*n**3 + 12*n**2 - 43. Let u(j) = 0. Calculate j.
-2/3, 0, 2
Factor -8/7*p + 4/7*p**2 + 0.
4*p*(p - 2)/7
Let f be ((-6)/4)/(12/16). Let z be 1/f*(-6)/12. Determine d so that z*d - 1/4*d**3 - 1/4*d**2 + 1/4 = 0.
-1, 1
Let o(s) = 0*s**2 - 6*s + 2*s - 4*s**2. Let k(i) = 2*i**2 + 2*i. Let v(c) = 11*k(c) + 6*o(c). Factor v(n).
-2*n*(n + 1)
Suppose 0*k + 0 + 0*k**2 + 2/5*k**5 + 2/5*k**4 + 0*k**3 = 0. Calculate k.
-1, 0
Let d(k) be the first derivative of k**3 + 9*k**2 + 27*k - 9. Factor d(x).
3*(x + 3)**2
Factor 0*q - 12/7*q**4 + 0 - 4/7*q**2 - 16/7*q**3.
-4*q**2*(q + 1)*(3*q + 1)/7
Let j = 21 + -21. Let x(z) be the second derivative of z + 0*z**4 + 1/6*z**3 + 0 + j*z**2 - 1/20*z**5. Factor x(w).
-w*(w - 1)*(w + 1)
Suppose -7*g - 3*g + 30 = 0. Factor 10/3*t - 2*t**2 - 2/3*t**g - 4/3 + 2/3*t**4.
2*(t - 1)**3*(t + 2)/3
Factor -2/7*f + 0 - 6/7*f**2.
-2*f*(3*f + 1)/7
Let o(b) = -2*b**2 + b + 2. Let x(r) = -2*r**2 + 2. Let l(s) = -3*o(s) + 2*x(s). Factor l(z).
(z - 2)*(2*z + 1)
What is l in 8/5 - 2/5*l**2 + 6/5*l = 0?
-1, 4
Let l(o) be the third derivative of 4*o**2 + 1/60*o**6 - 1/75*o**5 + 0*o + 1/75*o**7 + 0 + 0*o**4 + 0*o**3. Solve l(q) = 0 for q.
-1, 0, 2/7
Let q = -40/27 + 1129/756. Let k(y) be the third derivative of 0*y + 0 + y**2 - q*y**4 + 0*y**3 + 1/210*y**5. Factor k(b).
2*b*(b - 1)/7
Let n(g) be the first derivative of -3*g**4/8 - g**3/3 - 2. Let n(t) = 0. What is t?
-2/3, 0
Let n(a) = -a**3 - 16*a**2 + 18*a + 17. Let h be n(-17). Factor -1/4*f**2 - 1/4*f + h + 1/4*f**3 + 1/4*f**4.
f*(f - 1)*(f + 1)**2/4
Let u(a) = -3*a**2 - 2*a + 7. Let l(b) = -5*b**2 - 5*b + 15. Let r(v) = -2*l(v) + 5*u(v). What is c in r(c) = 0?
-1, 1
Let t(w) = -w - 4. Let q be t(-7). Determine p so that 2/3 - 26/3*p**q - p**5 + 8*p**2 - 11/3*p + 14/3*p**4 = 0.
2/3, 1
Let s = -2/1135 - -9086/3405. Find l such that -s*l**3 + 0*l - 2*l**2 + 0 - 2/3*l**4 = 0.
-3, -1, 0
Let r(z) be the second derivative of z**7/84 - z**5/20 + z**3/12 + 2*z. Find m, given that r(m) = 0.
-1, 0, 1
Factor -11/5*s**5 + 0*s**2 + 0*s - 2/5*s**3 + 0 - 13/5*s**4.
-s**3*(s + 1)*(11*s + 2)/5
Factor -10*y - 24*y**3 - 5 + 8*y**2 + 22*y**3 + 9.
-2*(y - 2)*(y - 1)**2
Factor 0 - 4/3*o**2 - 2/3*o**3 - 2/3*o.
-2*o*(o + 1)**2/3
Let h(v) = -v**3 + 7*v**2 - 4*v - 7. Suppose 5*r = 15, -2*r = -3*m + 5*m - 18. Let i be h(m). Factor 1/2*k**i - 1/2*k**3 - 1/2*k**4 + 0 + 0*k + 1/2*k**2.
k**2*(k - 1)**2*(k + 1)/2
Let t(z) be the first derivative of -2*z**4 - 4*z**3 + 4*z**2 + 12*z - 55. Let t(u) = 0. Calculate u.
-3/2, -1, 1
Let k be 2/((-10)/(-5)) - 0. Let y(z) be the first derivative of -4/7*z + 2/21*z**3 - 1/7*z**2 + k. What is q in y(q) = 0?
-1, 2
Let y be (2 + -1)*(-4)/1. Let f = -15/4 - y. Suppose 0*o + 0 - f*o**2 - 1/4*o**3 = 0. Calculate o.
-1, 0
Let d be (-15)/(-2450)*4/18. Let m(s) be the third derivative of -1/105*s**5 + 1/21*s**3 + d*s**7 + 0*s**4 + s**2 + 0 + 0*s + 0*s**6. Solve m(q) = 0 for q.
-1, 1
Let o(u) = -2*u + 2*u - u**2 - 2. Let j(a) = 6*a**2 + 11. Let x = -60 + 26. Let c(v) = x*o(v) - 6*j(v). Factor c(g).
-2*(g - 1)*(g + 1)
Let i(d) be the second derivative of 0*d**2 + 2/9*d**3 + 0 - 1/18*d**4 + 4*d. Factor i(z).
-2*z*(z - 2)/3
Let i(l) be the third derivative of l**8/672 + l**7/140 + l**6/80 + l**5/120 + 5*l**2. Suppose i(q) = 0. What is q?
-1, 0
Let s(c) = -c**5 + c**3 - c**2 + 1. Let h(w) = -w**5 - w**4 + w + 1. Let t(i) = 3*h(i) - 6*s(i). Factor t(g).
3*(g - 1)**3*(g + 1)**2
Factor 4*i - i**2 - 2*i + 921 + 2*i - 916.
-(i - 5)*(i + 1)
Let x(c) be the first derivative of c**4/24 - c**3/18 - c**2/12 + c/6 + 4. Determine s so that x(s) = 0.
-1, 1
Let c be 0 - 4/(-1) - 6. Let j(r) = -4*r - 4. Let h be j(c). Determine b, given that -2/5*b**h + 0*b + 0*b**3 + 4/5*b**2 - 2/5 = 0.
-1, 1
Let c(l) be the second derivative of 7*l**5/120 - 25*l**4/24 - 53*l**3/18 - 2*l**2 - 5*l. Factor c(b).
(b - 12)*(b + 1)*(7*b + 2)/6
Let x(r) be the second derivative of -5*r**4/24 - 5*r**3/3 + 25*r**2/4 - 32*r. Solve x(u) = 0.
-5, 1
Let h(y) = -y + 1. Let m(t) = t**2 + 5*t. Let d = -6 - -4. Let u(a) = d*m(a) - 4*h(a). Solve u(s) = 0.
-2, -1
Let b(t) be the third derivative of 0 - 1/45*t**5 + 0*t + 1/180*t**6 + 2/9*t**3 - 1/36*t**4 - 7*t**2. Factor b(u).
2*(u - 2)*(u - 1)*(u + 1)/3
Factor 0*t + 2/3 - 2/3*t**2.
-2*(t - 1)*(t + 1)/3
Let l(w) be the third derivative of -w**8/1512 - 2*w**7/945 - w**6/540 + 11*w**2. Solve l(u) = 0.
-1, 0
Determine z so that 1/4*z**2 + 3/4 - z = 0.
1, 3
Determine t, given that -4/7 + 36/7*t - 81/7*t**2 = 0.
2/9
Let i = 10 - 18. Let q = 23 + i. Factor 4*v**4 - 13*v**3 + q*v**3 - 6*v**4.
-2*v**3*(v - 1)
Let y(k) = -3*k**2 + 47*k + 70. Let x be y(17). Find j such that -3/5*j**x - 24/5*j - 48/5 = 0.
-4
Factor 0*b**2 - 9/5*b + 3/5*b**3 - 6/5.
3*(b - 2)*(b + 1)**2/5
Let z(r) be the first derivative of -r**6/180 + r**5/15 - r**4/3 - 2*r**3/3 - 1. Let a(p) be the third derivative of z(p). Factor a(f).
-2*(f - 2)**2
Let j(f) = 2*f - 8*f - 4*f**2 - 2*f**3 + 4*f**5 + 5*f**4 - 2*f**3 - f**2. Let g(w) = w**4 - w**2 - w. Let r(m) = 6*g(m) - j(m). Let r(o) = 0. Calculate o.
-1, 0, 1/4, 1
Suppose 6*o - 48 = 2*o. Let g be (16/o)/(4/6). Let 5/3*v**g - 8/3*v - 4/3 = 0. What is v?
-2/5, 2
Let r(n) = n**2 - 15*n + 16. Let u be r(14). Factor 0*x**u - 1/4*x + 1/4*x**3 + 0.
x*(x - 1)*(x + 1)/4
Let x(d) = 6*d**2 - 54*d + 53. Let h(n) = 3*n**2 - 27*n + 26. Let i(j) = 5*h(j) - 2*x(j). Factor i(a).
3*(a - 8)*(a - 1)
Suppose 0 = 4*r + 2 + 2. Let f be (-24)/(-9) - 3 - r. Find t such that 4/3*t - 4/3*t**3 - 2/3*t**4 + f + 0*t**2 = 0.
-1, 1
Suppose 0 - 2/3*i**5 + 14/3*i**3 + 4*i + 2/3*i**4 - 26/3*i**2 = 0. Calculate i.
-3, 0, 1, 2
Factor -4*a + 502*a**2 - 4*a - 4 - 506*a**2.
-4*(a + 1)**2
Let t(n) = -n**2 + n - 1. Let u(r) = 2*r - 7. Let s be u(5). Let l(f) = 7*f**2 + 5*f + 3. Let m(x) = s*t(x) + l(x). Suppose m(a) = 0. What is a?
-2, 0
Let q(n) be the third derivative of n**7/105 + n**6/60 - n**5/30 - n**4/12 - 7*n**2. Factor q(r).
2*r*(r - 1)*(r + 1)**2
Let a = 4441/30 + -148. Let l(v) be the second derivative of a*v**4 - 1/5*v**2 + 0 + 1/15*v**3 + 2*v - 1/50*v**5. Find k, given that l(k) = 0.
-1, 1
Suppose 5*l + 0 = 4*d + 1, -6 = -5*d - l. Let a be 0 + d + (3 - 2). Find n such that n + 3*n + n - 2 - n - a*n**2 = 0.
1
Suppose 4 = 2*z + 2*u, 9 = 5*z + 2*u - 1. Factor 3*y - 2 - z*y - 2*y + 2*y + y**2.
(y - 1)*(y + 2)
Let o = -2 - -2. Let s(w) be the first derivative of 0*w + 0*w**4 + 1/9*w**6 - 2 + 0*w**2 + 2/15*w**5 + o*w**3. Factor s(z).
2*z**4*(z + 1)/3
Let c(b) = 3*b**3 - 4*b**2 - 10*b - 10. Let y(d) = d**3 + 5*d - 2*d**3 - d**2 + 3 + 2*d**2 - 2*d. Let m(w) = 2*c(w) + 7*y(w). Factor m(g).
-(g - 1)*(g + 1)**2
Suppose 0 = 2*z - 7*z + 10. Let r(n) be the first derivative of 11/10*n**5 + 0*n - z + 3/2*n**3 - 1/2*n**2 - 15/8*n**4 - 1/4*n**6. Solve r(m) = 0.
0, 2/3, 1
Let a(g) = 7*g**2 + 3. Let y(f) = f**2 + 1. Suppose -3*z + 35 = -4*j, -9 = -z + 2*j + 6. Let n(x) = z*y(x) - a(x). Factor n(o).
-2*(o - 1)*(o + 1)
Let g(f) = 2*f + 1. Let t be g(1). Solve -t*k**2 - 7*k - 8 - k + k**2 = 0.
-2
Factor 4/5*d + 4/5*d**2 + 0.
4*d*(d + 1)/5
Let x(k) be the first derivative of -k**4/34 - 10*k**3/51 - 8*k**2/17 - 8*k/17 + 13. Find b, given that x(b) = 0.
-2, -1
Let v(x) = 9*x**3 - 3*x**2 + 6. Let d(t) = t**3 + t**2 - t + 1. Let b(a) = 6*d(a) - v(a). Find q such that b(q) = 0.
0, 1, 2