).
(n + 2)**2/2
Let q(z) = -75*z - 671. Let t be q(-9). Factor -1/5*d**3 + 4/5*d**t + 0 - 4/5*d**2 + 1/5*d.
d*(d - 1)*(d + 1)*(4*d - 1)/5
Let j(l) be the first derivative of l**5/45 - l**4/6 - 5*l**3/9 - 4*l**2/9 + 75. What is x in j(x) = 0?
-1, 0, 8
Let l(b) be the first derivative of -2*b**3/5 + 9*b**2/5 + 12*b + 767. What is f in l(f) = 0?
-2, 5
Let o = -2315 - -2317. Let -2/13 - 2/13*g**3 - 6/13*g - 6/13*g**o = 0. What is g?
-1
Let c(h) be the first derivative of -h**6/4 - 9*h**5/10 + 2*h**3 - 54. Determine y so that c(y) = 0.
-2, 0, 1
Let s(u) = -u**3 - 14*u**2 + 12*u - 45. Let o be s(-15). Factor -7/9*v**3 - v**2 - 2/9*v + o.
-v*(v + 1)*(7*v + 2)/9
Let n(d) = 325*d. Let y(o) = o**2 + 487*o. Let q(i) = -8*n(i) + 5*y(i). Factor q(m).
5*m*(m - 33)
Let m(a) = 3*a**3 - 72*a**2 + 420*a - 594. Let p(g) = -3*g**3 + 71*g**2 - 420*g + 595. Let v(f) = -5*m(f) - 6*p(f). Factor v(r).
3*(r - 10)**2*(r - 2)
Let v = 17 - 16. Let n be v/(-2 + 20/8). Determine q, given that q + 4*q - 5*q + 14*q**3 - 2*q + 4*q**n + 8*q**4 = 0.
-1, 0, 1/4
Let k be ((-2)/10)/(5 - (-106)/(-20)). Let g(z) be the first derivative of 2 - 2*z + 0*z**2 + k*z**3. Let g(w) = 0. What is w?
-1, 1
Find y, given that -3/5*y**3 + 27/5*y**2 + 0 - 42/5*y = 0.
0, 2, 7
Let n = -763/3 - -255. Let f(k) be the third derivative of 1/168*k**8 - 1/30*k**6 + 3*k**2 + 0 + 0*k + n*k**3 - 7/12*k**4 - 2/105*k**7 + 4/15*k**5. Factor f(r).
2*(r - 1)**4*(r + 2)
Suppose 0 = -4*u - 8 + 16. Let l(d) = -4*d**4 - d**2 - 3*d - 1. Let q(t) = 3*t**4 + 2*t + 1. Let j(f) = u*l(f) + 3*q(f). Solve j(n) = 0 for n.
-1, 1
Let y(i) = -9*i**2 - 2*i. Let x(p) = p**3 + 18*p**2 + 5*p. Let a = 26 + -17. Let o(r) = a*y(r) + 4*x(r). Suppose o(w) = 0. Calculate w.
0, 1/4, 2
Let p(l) be the third derivative of l**8/336 - l**7/105 - l**6/40 - 16*l**2 + 2*l. Let p(f) = 0. What is f?
-1, 0, 3
Determine v so that -4/9*v**2 - 64 - 32/3*v = 0.
-12
Factor -8/5 + 4*r + 12/5*r**2.
4*(r + 2)*(3*r - 1)/5
Let f(t) be the first derivative of t**3/4 + 129*t**2/4 + 745. Factor f(p).
3*p*(p + 86)/4
Let t(a) be the second derivative of -a**5/30 - 4*a**4/3 + a + 18. Factor t(k).
-2*k**2*(k + 24)/3
Let p(y) = y**3 + 3*y**2 + 4*y + 7. Let l = -26 - -24. Let s be p(l). Let -5/7*g - 1/7*g**4 + 3/7*g**2 + 2/7 + 1/7*g**s = 0. What is g?
-2, 1
Let t = -35 + 38. Solve -2*i**2 + i**2 - 3*i - 2*i - 2 + 5*i**3 + t*i**2 = 0.
-1, -2/5, 1
Let y(w) be the first derivative of w**3/3 + 9*w**2/2 + 155. Factor y(r).
r*(r + 9)
Suppose -q + 4*j = -2*q + 13, -24 = -4*q - 2*j. Let g be 5 - q/(15/6). What is t in -t**2 + 5*t**2 - 15*t**5 - 11*t**4 + 0*t**4 + 8*t**g = 0?
-1, -2/5, 0, 2/3
Let r be (-363)/484 - -1*1. Factor -r - 3/4*w**2 - 1/4*w**3 - 3/4*w.
-(w + 1)**3/4
Let d be 2/(-5) - (-6)/(300/1045). Suppose d*h**2 - 1/2*h**3 + 25/2*h**5 + 2 - 12*h - 45/2*h**4 = 0. Calculate h.
-1, 2/5, 1
Let g(c) be the second derivative of -2*c + 5 + 1/42*c**4 + 0*c**2 + 1/70*c**5 - 2/21*c**3. Factor g(y).
2*y*(y - 1)*(y + 2)/7
Let j(m) = -2*m**2 + 12*m + 2. Let t(c) = -c**2 + 14*c + 34. Let k be t(16). Let u(z) = -5*z**2 + 36*z + 7. Let n(v) = k*u(v) - 7*j(v). What is b in n(b) = 0?
0, 3
Factor 4/3*z**2 + 22/3*z**3 + 10/3*z**4 + 0*z + 0.
2*z**2*(z + 2)*(5*z + 1)/3
Let d(y) = -y**2 + 14*y - 51. Let t be d(8). Let q be ((0/t)/(-2))/(-1). Factor 2/11*g**2 + 2/11*g**5 - 2/11*g**4 - 2/11*g**3 + 0 + q*g.
2*g**2*(g - 1)**2*(g + 1)/11
Determine b, given that -12*b**2 + 15/8*b**3 + 111/8*b - 15/4 = 0.
2/5, 1, 5
Let p(q) be the third derivative of -1/75*q**6 + 0 + 4*q**2 + 1/20*q**4 - 1/75*q**5 + 1/840*q**8 + 0*q**7 + 0*q + 2/15*q**3. Suppose p(m) = 0. What is m?
-1, 1, 2
Let v(n) be the third derivative of n**5/15 - n**4/12 + 5*n**2. Let w(o) = -5*o**2 + 2*o. Let l(j) = 6*v(j) + 5*w(j). What is y in l(y) = 0?
-2, 0
Let p = 75/14 + -34/7. Let f(y) be the second derivative of 5*y + p*y**3 - 1/4*y**4 + 3/80*y**5 + 0*y**2 + 0. Solve f(d) = 0 for d.
0, 2
Let y(k) be the second derivative of k**6/70 - 3*k**5/28 - k**4/28 + 5*k**3/14 + 152*k. Factor y(o).
3*o*(o - 5)*(o - 1)*(o + 1)/7
Suppose -3*d + 20 = -106. Let w be (6/(-7))/((-12)/d). Find i such that 7/6*i**w - 1/6*i**2 - 4/3*i + 1/6*i**5 - 2/3 + 5/6*i**4 = 0.
-2, -1, 1
Let v = -2 - -4. Let j(w) be the first derivative of -w**3 - 3*w**v + 3*w**2 + 2*w**3 + 2. Let j(m) = 0. Calculate m.
0
Let t(n) be the second derivative of n**8/3360 - n**7/630 + n**6/360 - n**4/2 + 14*n. Let j(z) be the third derivative of t(z). Factor j(s).
2*s*(s - 1)**2
Let m(f) be the first derivative of -50*f**3/21 + 370*f**2/7 - 2738*f/7 + 186. What is g in m(g) = 0?
37/5
Let d = 16 - 12. Suppose -14 = -d*i + 10. Factor 3*p - 4*p**3 - 6 - 11*p**2 + i.
-p*(p + 3)*(4*p - 1)
Let a(n) be the first derivative of -9 + 1/10*n**4 + 2/5*n - 1/5*n**2 - 2/15*n**3. Let a(s) = 0. What is s?
-1, 1
Let m(s) be the first derivative of -s**5 + 45*s**4/2 - 85*s**3/3 - 185. Factor m(b).
-5*b**2*(b - 17)*(b - 1)
Let r(q) = -2*q**3 - q**2 + q. Let p(d) = -3*d**3 + 20*d**2 + 43*d + 20. Let j(s) = 5*p(s) - 10*r(s). What is v in j(v) = 0?
-20, -1
Let x be 0*(5/6)/((-20)/(-4)). Find b, given that 3/7*b**2 + 6/7*b - 3/7*b**3 + x = 0.
-1, 0, 2
Let i(d) = -d**2 + 4*d + 34. Let k be i(8). Let r(p) be the first derivative of 3/4*p**4 + 1/6*p**6 + 0*p + 4/5*p**5 - 2*p**k - 4 - 4/3*p**3. Factor r(b).
b*(b - 1)*(b + 1)*(b + 2)**2
Let l(s) = 3*s**3 + 6*s**2 - 6*s + 3. Let r(v) = 9*v**3 + 16*v**2 - 17*v + 8. Let i(d) = 8*l(d) - 3*r(d). Factor i(p).
-3*p*(p - 1)*(p + 1)
Let w(o) be the first derivative of o**5/5 - o**4/4 - o**3 + o**2/2 + 2*o - 58. Factor w(d).
(d - 2)*(d - 1)*(d + 1)**2
Let s(n) be the third derivative of -n**6/420 - 2*n**5/35 + 15*n**2. Factor s(g).
-2*g**2*(g + 12)/7
Let r(m) be the first derivative of 2*m**3/33 + 28*m**2/11 + 54*m/11 - 300. Let r(c) = 0. Calculate c.
-27, -1
Let m(c) = 4*c**3 + 19*c**2 + c + 14. Let g(v) = -4*v**3 - 18*v**2 - 2*v - 12. Let y(l) = -7*g(l) - 6*m(l). Solve y(d) = 0 for d.
-2, -1, 0
Let z(v) = -v**5 + 2*v**4 + v**3 - v**2 + v - 1. Let g(f) = -4*f**5 + 4*f**4 + 39*f**3 - 89*f**2 + 80*f - 27. Let b(n) = -4*g(n) + 12*z(n). Factor b(a).
4*(a - 3)*(a - 1)**3*(a + 8)
Let z(p) be the second derivative of -p**7/7 - 159*p**6/10 - 12873*p**5/20 - 20657*p**4/2 - 27378*p**3 - 26364*p**2 + p - 403. Suppose z(f) = 0. Calculate f.
-26, -1, -1/2
Let q(d) be the first derivative of 3/8*d**3 - 7 + 0*d + 1/20*d**5 + 3/2*d**2 - 13/32*d**4. Let t(p) be the second derivative of q(p). Factor t(k).
3*(k - 3)*(4*k - 1)/4
Let x(t) be the third derivative of t**8/1176 + t**7/147 + t**6/140 - 17*t**5/210 - t**4/3 - 4*t**3/7 + 65*t**2. What is z in x(z) = 0?
-3, -2, -1, 2
Let i = 292 + -142. Let o = -150 + i. Factor -2*s**4 + 0 - 1/2*s**3 + o*s + 0*s**2.
-s**3*(4*s + 1)/2
Let k be 1/4*(-152)/(-323). Find u, given that -2/17*u + k*u**2 + 0 = 0.
0, 1
Let m(w) be the second derivative of -w**7/105 + 13*w**6/75 - 11*w**5/25 - w**4/15 + 23*w**3/15 - 11*w**2/5 - 10*w - 11. Solve m(v) = 0.
-1, 1, 11
Let a = -42 + 45. Suppose -18*n**4 + 4*n**5 + 48*n**2 + 52*n**a - 9*n**4 + 16*n + 51*n**4 = 0. Calculate n.
-2, -1, 0
Factor 1 - 5*s**2 + 4*s - 8*s**2 + s**2 + 1 + 14*s**2.
2*(s + 1)**2
Let k(q) be the third derivative of -1/270*q**5 + 7*q**2 + 0*q**4 + 0*q**3 + 1/120*q**6 + 0*q + 0. Factor k(x).
x**2*(9*x - 2)/9
Let b(d) be the first derivative of d**3/2 + 69*d**2 + 3174*d + 40. Factor b(g).
3*(g + 46)**2/2
Let y(g) be the first derivative of -3/2*g**2 - 1 + 1/20*g**5 + 1/8*g**4 + 0*g + 0*g**3. Let u(s) be the second derivative of y(s). Solve u(z) = 0 for z.
-1, 0
Suppose 56*i + 1 - 1 = -0. Let a be 11/14 + (-2)/4. Factor a*h**5 + 0*h**2 + 2/7*h**3 - 4/7*h**4 + i + 0*h.
2*h**3*(h - 1)**2/7
Let j(n) be the second derivative of -1/10*n**5 + 0 + 0*n**2 - 12*n - 1/3*n**3 - 1/3*n**4. Suppose j(z) = 0. What is z?
-1, 0
Let -a**2 + 24*a + 16*a**3 - 46*a**2 + 3*a**2 + 0*a**2 + 4*a**4 = 0. Calculate a.
-6, 0, 1
Let n(z) be the third derivative of -20*z**2 + 0*z**3 + 1/80*z**5 + 0 + 1/16*z**4 + 0*z + 1/56*z**7 - 1/20*z**6. Find f such that n(f) = 0.
-2/5, 0, 1
Let d(p) be the second derivative of -55/24*p**4 + 3/4*p**6 + 0*p**2 - 3/2*p**5 + 0 + 7*p - 5/6*p**3. Let d(g) = 0. What is g?
-1/3, 0, 2
Suppose -t - 2 = -2*u + 1, -2*u - 5*t = 15. Factor -7/5*l**4 + u*l - 1/5*l**5 - 3*l**3 - 9/5*l**2 + 0.
-l