7*b + 2)
Let t(a) be the first derivative of -a**4/6 - 8*a**3/9 - 5*a**2/3 - 4*a/3 - 200. Factor t(s).
-2*(s + 1)**2*(s + 2)/3
Let h = 1565/12 + -519/4. Find l, given that h*l**2 - 2/3*l**3 + 2 + 10/3*l = 0.
-1, 3
Let c(p) be the third derivative of 0*p**4 + 6*p**2 + 0*p**3 + 0 + 0*p - 1/90*p**5 + 1/180*p**6. Factor c(n).
2*n**2*(n - 1)/3
Find p such that 0*p**2 + 1/6*p**5 + 0 + 0*p**4 - 1/6*p**3 + 0*p = 0.
-1, 0, 1
Let l(f) = -f**3 + 6*f**2 - 6*f + 5. Let i be l(5). Let s be -1*(-3 - 3/3). Suppose i*j + 1/4*j**s + 0 + 0*j**3 + 0*j**2 = 0. What is j?
0
Let c(n) = -5*n**2 - 25*n - 11. Let x(b) be the second derivative of b**4/12 + 5*b**3/6 + b**2 - 14*b. Let j(f) = 2*c(f) + 11*x(f). Solve j(v) = 0 for v.
-5, 0
Let o(i) = 8*i**3 + 8*i**2 - 4*i + 4. Let z(c) = -9*c**3 - 10*c**2 + 4*c - 5. Let k(y) = -5*o(y) - 4*z(y). Factor k(p).
-4*p*(p - 1)*(p + 1)
Let -7/2*k**4 + 15*k - 1/2*k**2 - 15*k**3 + 4 = 0. What is k?
-4, -1, -2/7, 1
Let t(b) = -3*b**5 - 13*b**4 - 4*b**3 - 3*b - 3. Let k(r) = 4*r**5 + 12*r**4 + 4*r**3 + 2*r + 2. Let y(d) = -3*k(d) - 2*t(d). Suppose y(v) = 0. What is v?
-1, -2/3, 0
Let r(n) be the second derivative of n**4/6 - 11*n**3/6 + 6*n**2 - 49*n. Let k be r(4). Suppose -1/8*f**2 + 0 + k*f = 0. What is f?
0
Let x(y) be the first derivative of 9*y**6/2 - 141*y**5/5 + 273*y**4/4 - 81*y**3 + 48*y**2 - 12*y + 104. Solve x(p) = 0 for p.
2/9, 1, 2
Let h be ((-4)/3)/(12274/(-3249)). Factor -2/17*x**4 + h*x**3 + 8/17*x**2 + 0 + 0*x.
-2*x**2*(x - 4)*(x + 1)/17
Let l(z) be the third derivative of -5*z**6/32 - 3*z**5/2 - 21*z**4/8 - 2*z**3 - 78*z**2. What is v in l(v) = 0?
-4, -2/5
Let u be (9/225)/(-1 + 2). Let f(i) be the third derivative of 0*i + 0 + 1/75*i**6 - u*i**5 - 1/525*i**7 + 3*i**2 - 1/15*i**3 + 1/15*i**4. Factor f(d).
-2*(d - 1)**4/5
Let g = 90/11 - 8348/1023. Let f = 29/93 + g. Suppose 0 - f*m - 1/3*m**2 = 0. Calculate m.
-1, 0
Let c(a) be the first derivative of 9*a - 5 + 3*a**2 + 1/3*a**3. Factor c(p).
(p + 3)**2
Suppose 0 = 3*s - v - 14, -5*v + 15 + 10 = 4*s. Suppose 5*d + 5*h + s = 0, -29 = 3*d - 6*d + 5*h. Factor 0*r**2 - 9 + 4 + r**2 + 4 - r**d + r.
-(r - 1)**2*(r + 1)
Let x(y) be the first derivative of y**4/6 + 58*y**3/27 + 65*y**2/9 - 50*y/9 - 264. What is z in x(z) = 0?
-5, 1/3
Let f(u) be the first derivative of -u**4/24 - 17*u**3/6 - 60*u**2 - 288*u + 341. Solve f(i) = 0 for i.
-24, -3
Let l(z) be the first derivative of 1/9*z**3 - 6*z - 1/18*z**4 + 1/45*z**6 + 0*z**2 - 4 - 1/30*z**5. Let t(s) be the first derivative of l(s). Factor t(f).
2*f*(f - 1)**2*(f + 1)/3
Let h(r) be the third derivative of r**8/3360 - r**7/315 - 17*r**4/24 + 17*r**2. Let v(f) be the second derivative of h(f). Determine s, given that v(s) = 0.
0, 4
Let o(v) be the third derivative of -v**7/840 + v**6/20 - 3*v**5/16 + 11*v**4/48 - 54*v**2 - 2*v. Factor o(t).
-t*(t - 22)*(t - 1)**2/4
Solve 0 + 6*y - 6*y**3 - 1/2*y**4 + 1/2*y**2 = 0 for y.
-12, -1, 0, 1
Let y(p) be the first derivative of 6*p**3 + 3*p - 33 - 6*p**2 - 3*p**4 + 3/5*p**5. Factor y(m).
3*(m - 1)**4
Let f be (3 - (-2 + 5))*(-3)/(-6). Let z(q) be the second derivative of 0*q**3 + 5*q - 1/16*q**4 + f*q**2 - 3/80*q**5 + 0. Factor z(g).
-3*g**2*(g + 1)/4
Let f = -23 + 26. Suppose 8*h**2 + f*h - 9*h**2 - 3*h + h**4 = 0. Calculate h.
-1, 0, 1
Let f(b) be the third derivative of b**6/180 - b**5/30 + 30*b**2. Factor f(l).
2*l**2*(l - 3)/3
Let x(s) be the third derivative of -s**5/300 - s**4/10 + 32*s**3/15 + 400*s**2. Factor x(a).
-(a - 4)*(a + 16)/5
Let p be (4/5)/((-2)/5) + 7. Determine z, given that 5*z**2 - 9*z**3 - 3*z**5 - 2*z**4 + 2*z + 10*z**p - 3*z**4 + 0*z**4 = 0.
-1, -2/7, 0, 1
Let l be 3 - -2 - (-780)/24. Factor l - 15*p + 3/2*p**2.
3*(p - 5)**2/2
Suppose 641*w - 24*w - 3*w**2 + 745*w - 372*w - 49005 - 2*w**2 = 0. What is w?
99
Let q(f) be the third derivative of f**6/30 - f**5 - 11*f**4/2 - 34*f**3/3 + f**2 - 124. Factor q(l).
4*(l - 17)*(l + 1)**2
Let m(g) = -g - 1. Let k(q) = -q. Let s(x) = -10*k(x) + 5*m(x). Let r be s(4). Factor -16*l**3 + 4*l**3 + 4*l - r*l**2 + 7*l**2.
-4*l*(l + 1)*(3*l - 1)
Let s be ((-42)/20)/1*132/(-231). Solve s*z + 0 + 2/5*z**2 = 0 for z.
-3, 0
Let c = 13628 - 40870/3. Suppose -2/9*x**3 - 686/9 - 98/3*x - c*x**2 = 0. Calculate x.
-7
Let o be (0 + 0)/(7 + (-64)/8). Let r = -5 - -8. Factor 6/5*c**4 + 9/5*c**r + 0*c - 3/5*c**5 + o + 0*c**2.
-3*c**3*(c - 3)*(c + 1)/5
Let c(o) = o**2 - 6*o - 1. Let d(z) = z**2 + 1. Suppose 0 = -21*s + 25*s + 24. Let y(w) = s*d(w) + 2*c(w). Factor y(i).
-4*(i + 1)*(i + 2)
Let t = -39 + 41. Solve -28*p**t + 16 - 3*p**5 + 34*p**2 + 9*p**3 - 16 = 0 for p.
-1, 0, 2
Let w = -123 + 1601/13. Let b be (360/(-42) - -9) + 18/7. Suppose 4/13*n**2 + w*n + 2/13*n**b + 0 = 0. What is n?
-1, 0
Let g = -268 - -270. Let j(o) be the third derivative of 0*o - 1/210*o**7 + 0*o**3 - 1/24*o**4 - 1/40*o**6 + 3*o**g + 0 - 1/20*o**5. Let j(z) = 0. Calculate z.
-1, 0
Let n(d) be the first derivative of d**6/1080 - d**5/180 + d**4/72 - d**3/3 + 13. Let v(z) be the third derivative of n(z). What is t in v(t) = 0?
1
Solve -20/7*i**3 - 18/7*i**2 + 0 + 0*i - 2/7*i**4 = 0 for i.
-9, -1, 0
Let i(u) be the third derivative of -u**7/945 - u**6/54 - 4*u**5/45 - 11*u**4/54 - 7*u**3/27 + u**2 - 7*u. Factor i(h).
-2*(h + 1)**3*(h + 7)/9
Let p(v) be the third derivative of v**6/120 + v**5/60 + v**4/24 + v**3/6 - 18*v**2. Let m(z) = 8*z**3 - 6*z**2 + 14. Let s(x) = 2*m(x) - 36*p(x). Factor s(n).
-4*(n + 1)**2*(5*n + 2)
Let b(t) be the second derivative of t**4/6 + 20*t**3/3 + 19*t**2 + 4*t - 17. Find q, given that b(q) = 0.
-19, -1
Suppose -13*y - 1506 = -3664. Suppose 0 = -164*k + y*k. What is a in k*a - 2/5*a**5 + 0 + 0*a**2 - 2/5*a**3 - 4/5*a**4 = 0?
-1, 0
Let f(n) = 10*n**5 - 225*n**4 + 360*n**3 - 180*n**2. Let i(r) = r**5 - 25*r**4 + 40*r**3 - 20*r**2. Let j(z) = -4*f(z) + 35*i(z). Solve j(v) = 0 for v.
0, 1, 2
Suppose -20*m**2 - 19*m**2 + 2*m - 2*m**3 - 2*m**4 + 61*m**2 - 20*m**2 = 0. Calculate m.
-1, 0, 1
Factor -21/2 + 21/8*u**2 + 36*u.
3*(u + 14)*(7*u - 2)/8
Let j(s) be the first derivative of s**5/15 + s**4/12 - 4*s**3/3 - 14*s**2/3 - 16*s/3 + 21. Factor j(x).
(x - 4)*(x + 1)*(x + 2)**2/3
Let r(c) be the third derivative of -c**6/220 + 4*c**5/11 - 437*c**4/44 + 722*c**3/11 + 197*c**2 + 1. Factor r(n).
-6*(n - 19)**2*(n - 2)/11
Let v(m) be the second derivative of 3*m**5/28 - 11*m**4/4 - 25*m**3/7 + 48*m**2/7 + 62*m. Factor v(k).
3*(k - 16)*(k + 1)*(5*k - 2)/7
Let v(u) be the second derivative of -15*u**2 + 145/6*u**3 + 20*u - 35/4*u**4 + 0 + u**5. Solve v(r) = 0 for r.
1/4, 2, 3
Let y(n) = 1114*n + 5572. Let a be y(-5). Factor -7 - 3/2*h**a + 23/2*h.
-(h - 7)*(3*h - 2)/2
Let l(n) = -4*n. Let d be l(-11). Suppose 3*z = -4*k - 2*z + 65, 0 = -3*k + z + d. Solve -27*j**2 + 0*j**2 - j - 5*j - 36*j**3 - k*j**4 = 0 for j.
-1, -2/5, 0
Suppose 0 = 29*b + 55*b - 205 + 37. Solve 3/4 + 1/4*u**4 - 1/2*u**3 - u**b + 1/2*u = 0 for u.
-1, 1, 3
Let w(c) = 3*c**4 + 24*c**3 + 139*c**2 - 366*c + 196. Let y(q) = -q**4 + q**3 + q**2 + q. Let x(i) = 3*w(i) + 6*y(i). Factor x(t).
3*(t - 1)**2*(t + 14)**2
Suppose 2641*o - 2630*o = 44. Solve -8/7 + 2/7*w**o - 2/7*w**3 - 18/7*w**2 - 22/7*w = 0 for w.
-1, 4
Let s(z) be the second derivative of z**6/180 - 11*z**5/30 + 121*z**4/12 - 1331*z**3/9 + 14641*z**2/12 + 65*z - 1. Factor s(h).
(h - 11)**4/6
Let q(k) be the first derivative of k**7/15 - 19*k**6/60 + 4*k**5/15 + k**4/3 + 11*k**2/2 + 12. Let b(o) be the second derivative of q(o). Factor b(c).
2*c*(c - 2)*(c - 1)*(7*c + 2)
Let r(c) be the third derivative of 1 - 1/27*c**4 + 0*c + c**2 - 1/9*c**3 - 1/270*c**5. Suppose r(k) = 0. What is k?
-3, -1
Suppose -3*c + 63 = 3*a, -c + 4*a = -6*c + 100. Let u = -11 + c. Factor u - 5 + q + 5*q**3 - 6*q**3.
-q*(q - 1)*(q + 1)
Let c(n) be the second derivative of 0 - 8*n**2 + 7/3*n**4 - 16/3*n**3 - 8*n + n**5. Factor c(d).
4*(d - 1)*(d + 2)*(5*d + 2)
Let f(h) be the third derivative of 6*h**2 + 0*h + 0*h**3 + 1/30*h**6 + 0*h**4 - 1/30*h**5 - 1/105*h**7 + 0. Let f(p) = 0. Calculate p.
0, 1
Factor 0 + 46/7*d**2 + 2/7*d**3 - 48/7*d.
2*d*(d - 1)*(d + 24)/7
Let p = 96 + -65. Determine i, given that -p - 5*i + 1 - 36*i**2 + 41*i**2 = 0.
-2, 3
Let p(k) = 3*k**2 + k - 1. Let i(h) = 46*h**2 + 59*h + 469. Let r(w) = -4*i(w) + 60*p(w). Factor r(s).
-