y be (8/(-10))/((-198)/(-110))*-24. Factor 14/3*b**3 + 22/3*b + 4/3 + y*b**2.
2*(b + 1)**2*(7*b + 2)/3
Let h(r) be the second derivative of 11*r**7/84 - 3*r**6/20 - 13*r**5/40 + 3*r**4/8 + r**3/6 + 2*r + 72. Suppose h(s) = 0. What is s?
-1, -2/11, 0, 1
Let l(v) be the third derivative of -v**7/840 - v**6/240 + 3*v**5/20 - v**4/8 + 3*v**3/2 + 36*v**2. Let j(o) be the second derivative of l(o). Factor j(y).
-3*(y - 2)*(y + 3)
Let l be 12/(-9) + (6/4)/3. Let c = 7/6 + l. What is b in 0*b**4 + 1/3*b**3 + 0 - c*b**5 + 0*b + 0*b**2 = 0?
-1, 0, 1
Let d(q) be the first derivative of -2*q**3/27 + 22*q**2/3 - 242*q + 489. Factor d(p).
-2*(p - 33)**2/9
Let w be 0/(-2) + 21/3. Suppose -8*f - 6*f**2 + 4 - 3 - w + 4*f**2 = 0. What is f?
-3, -1
Let o(w) be the second derivative of w**7/1260 + w**6/180 - w**4/3 - 10*w. Let l(y) be the third derivative of o(y). Solve l(g) = 0 for g.
-2, 0
Let o = 70 + -62. Factor -8*y**2 + o*y - 4 - 5*y**3 + 2*y + 12*y**3 - 5*y**3.
2*(y - 2)*(y - 1)**2
Suppose 78 = -2*q + 2*k + 28, 4*q = 2*k - 104. Let b be 147/22*(-36)/q. Let -8/11*n - b*n**5 - 252/11*n**4 - 72/11*n**2 + 0 - 218/11*n**3 = 0. Calculate n.
-1, -2/7, 0
Let m(n) be the second derivative of 3*n**6/85 - 2*n**5/17 + 2*n**4/51 + n - 72. Factor m(w).
2*w**2*(w - 2)*(9*w - 2)/17
Let i(t) be the third derivative of t**5/45 - 11*t**4/9 + 3*t**2 + 29. Factor i(a).
4*a*(a - 22)/3
Let l be (182/(-42))/((-7)/3 - -2). Find w, given that 16*w**2 - 34*w - 32*w + 13*w - 2*w**3 + 32 + l*w = 0.
2, 4
Let x(y) be the third derivative of y**7/2940 - y**6/210 + 3*y**5/140 - 9*y**3/2 - 39*y**2. Let p(g) be the first derivative of x(g). Factor p(d).
2*d*(d - 3)**2/7
Let f(a) be the third derivative of -a**8/336 + a**7/70 + a**6/24 - a**5/20 - a**4/6 - 41*a**2. Factor f(q).
-q*(q - 4)*(q - 1)*(q + 1)**2
Let m be -2 + (-24)/84*(3654/8)/(-9). Let -m*u**2 + 5/2*u**3 + 20*u - 10 = 0. Calculate u.
1, 2
Let c(i) = i**3 + 7*i**2 - 56*i + 64. Let n(j) = 3*j**3 + 22*j**2 - 168*j + 191. Let y(o) = 11*c(o) - 4*n(o). Let y(g) = 0. What is g?
-15, 2
Let s = 28351 + -141753/5. Factor -s*i**3 + 0*i + 0 + 8/5*i**2.
-2*i**2*(i - 4)/5
Let b(i) be the second derivative of i**5/10 + 35*i**4/6 - 12*i**3 - 2*i + 63. What is t in b(t) = 0?
-36, 0, 1
Suppose 14*a - 12 = -12. Let n be (-2)/(-4) - (-1)/(-3)*a. Factor -2*x**3 - 1/2 + n*x**2 + 2*x.
-(x - 1)*(x + 1)*(4*x - 1)/2
Let v(l) = 4*l + 61. Let q be v(-15). Let r be (-20)/20 + q/((-12)/(-15)). Solve -1/2*n - r - 1/4*n**2 = 0.
-1
Suppose -s - 4*w - 1 = 0, s + 3*w = -0*s - 2. Let a(x) = x + 5. Let b be a(s). Let b*r - 2/7*r**2 + 0 + 2/7*r**4 + 0*r**3 = 0. What is r?
-1, 0, 1
Let n = 735 + -732. Let i = -1/493 + 7897/4437. Suppose -i*y**2 + 4/9 - 2/9*y - 10/9*y**n = 0. What is y?
-1, 2/5
Let s(b) be the third derivative of 121*b**6/300 + 154*b**5/25 - 29*b**4/5 + 32*b**3/15 + 175*b**2 + 2. Factor s(c).
2*(c + 8)*(11*c - 2)**2/5
Let m(n) be the second derivative of 4*n + 4*n**3 + 36*n**2 + 0 + 1/6*n**4. Factor m(c).
2*(c + 6)**2
Let b = 2/6413 + 6407/19239. Let -1/6*c**2 - 1/6 + b*c = 0. Calculate c.
1
Let g be -3*(-2)/18 - (-1)/3. Solve 6*k**2 + 4/3 - 10/3*k**3 + g*k**4 - 14/3*k = 0 for k.
1, 2
Suppose -11*v = 5 - 38. Suppose -5*j + 16 + 2 = x, v = 5*x - 4*j. Suppose 10/7*n**x + 2*n**4 - 10/7*n + 4/7 - 18/7*n**2 = 0. What is n?
-1, 2/7, 1
Let q = 989 + -989. Let h(g) be the second derivative of 1/48*g**4 + 3*g + 0*g**3 - 1/120*g**6 + 0*g**5 + q*g**2 + 0. Factor h(v).
-v**2*(v - 1)*(v + 1)/4
Let c(y) be the second derivative of -y**5/35 + 4*y**4/7 - 34*y**3/21 - 60*y**2/7 - y - 11. Factor c(g).
-4*(g - 10)*(g - 3)*(g + 1)/7
Suppose -4*x - 40 = -2*m, -3*m - 56 = 3*x - 17. Let w(d) = -5*d**2 - 16*d + 19. Let k(z) = -3*z**2 - 8*z + 10. Let o(c) = x*k(c) + 6*w(c). Factor o(u).
(u - 2)*(3*u - 2)
Let f(u) be the first derivative of u**5/60 + u**4/9 + 5*u**3/18 + u**2/3 + 32*u + 15. Let l(h) be the first derivative of f(h). Factor l(n).
(n + 1)**2*(n + 2)/3
Suppose -5*n - 9*n = 4032. Let x = 291 + n. Solve 8/5 - 6*u**2 + 161/5*u**x + 147/5*u**4 - 36/5*u = 0 for u.
-1, -2/3, 2/7
Let f(v) = -v**2 - 2*v. Let t(s) = 2*s**2 + 4*s. Let a(q) = -3*f(q) - t(q). Let a(d) = 0. Calculate d.
-2, 0
Factor -13*l**2 - 23*l**2 - 16*l + 8 - 9*l**2 - 64*l + 3*l**2.
-2*(l + 2)*(21*l - 2)
Let p(w) be the third derivative of w**7/42 + w**6/24 - w**5/4 - 5*w**4/24 + 5*w**3/3 - 43*w**2. Factor p(q).
5*(q - 1)**2*(q + 1)*(q + 2)
Let k(m) be the second derivative of m**7/14 - m**6/15 - 3*m**5/20 + m**4/6 + 76*m. Determine z, given that k(z) = 0.
-1, 0, 2/3, 1
Let h be (-30)/144 + (-1)/(-4). Let f(l) be the first derivative of -1/8*l**2 + 1/8*l**4 - h*l**6 - 1/4*l + 1/6*l**3 + 4 - 1/20*l**5. Factor f(b).
-(b - 1)**2*(b + 1)**3/4
Let t(l) = 11*l**4 - 390*l**3 + 6133*l**2 + 6539*l + 10. Let u(o) = 5*o**4 - 195*o**3 + 3067*o**2 + 3269*o + 4. Let x(v) = 2*t(v) - 5*u(v). Factor x(n).
-3*n*(n - 33)**2*(n + 1)
Let p = -1296 - -1299. Find w such that -2 + 2/3*w**4 + 10/3*w - 4*w**p + 2/3*w**5 + 4/3*w**2 = 0.
-3, -1, 1
Let p(h) = -2*h**2 - 12*h - 10. Suppose -4 = o - 9. Let w(a) = 4*a**2 + 24*a + 20. Let f(t) = o*p(t) + 3*w(t). Find c such that f(c) = 0.
-5, -1
Factor -a**2 + 4*a - 476 + 7*a + 55*a - 613 + 0*a.
-(a - 33)**2
Let r = 37 - -189. Determine l, given that -10*l**2 - 2*l - 4*l**3 + 115 + 115 - r = 0.
-2, -1, 1/2
Let p(r) be the second derivative of r**3 + 0 + 0*r**2 - 1/2*r**6 + 1/14*r**7 + 27/20*r**5 - 7/4*r**4 - 18*r. Factor p(g).
3*g*(g - 2)*(g - 1)**3
Suppose 6*p - 10 = 4*p. Let d(c) = 15*c - 20. Let w(h) = h**2 - h - 1. Let u(a) = p*w(a) - d(a). Factor u(s).
5*(s - 3)*(s - 1)
Let v(x) be the first derivative of -x**6/10 - 3*x**5/25 + 3*x**4/20 + x**3/5 - 256. Factor v(z).
-3*z**2*(z - 1)*(z + 1)**2/5
Let w = 10311/5 + -2061. Solve w + 48/5*o**2 - 42/5*o**3 - 27/5*o + 18/5*o**4 - 3/5*o**5 = 0.
1, 2
Let k(g) = g**4 - g**2 + g. Let i(t) = 12*t**4 - 3*t**3 - 20*t**2 + 6*t. Let o(f) = -2*i(f) + 22*k(f). Factor o(z).
-2*z*(z - 5)*(z + 1)**2
Let r(x) be the second derivative of -5*x**4/12 + 15*x**3 - 405*x**2/2 + 56*x. Factor r(n).
-5*(n - 9)**2
Let m(v) = -3*v**2 + 5. Let f(i) = -1. Suppose -11 = -t - 4*r + 4, -5 = -3*t - 2*r. Let l(x) = t*m(x) - 2*f(x). Suppose l(a) = 0. What is a?
-1, 1
Let h(o) be the second derivative of o**5/10 - 209*o**4/24 + 689*o**3/3 - 169*o**2 - 143*o. Suppose h(g) = 0. Calculate g.
1/4, 26
Let b(m) = m**3 - 7*m**2 + 6*m + 2. Let p be b(6). Factor -2/7*y + 2/7 + 2/7*y**3 - 2/7*y**p.
2*(y - 1)**2*(y + 1)/7
Let -200/3 + 20/3*p - 1/6*p**2 = 0. Calculate p.
20
Let c(s) = s**3 - 51*s**2 + 96*s + 98. Let x be c(49). Let p(a) be the second derivative of 3/70*a**5 + 0 + 0*a**3 + x*a**2 - 1/21*a**4 + 5*a. Factor p(v).
2*v**2*(3*v - 2)/7
What is x in 2/5*x**5 - 384/5 - 12/5*x**4 - 142/5*x**3 - 72/5*x**2 + 608/5*x = 0?
-4, 1, 12
Factor -10/7*m**2 + 4 - 66/7*m.
-2*(m + 7)*(5*m - 2)/7
Let g = 109 + -110. Let w be 2 + 4/g - 88/(-24). Find k such that -10/3 - w*k + 5/3*k**2 = 0.
-1, 2
Let y(l) be the second derivative of -l**6/15 + l**5/10 + l**4/2 - 5*l**3/3 + 2*l**2 - 2*l - 45. Factor y(t).
-2*(t - 1)**3*(t + 2)
Let x(j) be the first derivative of -4*j**3/3 + 46*j**2 + 200*j - 886. Factor x(m).
-4*(m - 25)*(m + 2)
Let a(s) be the second derivative of 15*s - 1/15*s**4 + 0 + 1/30*s**3 + 0*s**2. Factor a(x).
-x*(4*x - 1)/5
Let r be (-110)/33*(8/(-20) - 0). Suppose -3*w + 0 = -9. Factor -22/3*o**2 - 8/3*o**w - 10/3*o + r.
-2*(o + 1)*(o + 2)*(4*o - 1)/3
Suppose r + 46 = 2*z, r - 2*r = 4*z - 98. Let f = z + -16. Suppose f - w**2 - 2*w + 0*w**2 - 9 = 0. What is w?
-1
Let t = -2 - -2. Suppose -2*h - 6 + 20 = t. Factor -9*u + 9*u**2 - 12*u - h*u**3 + 19*u.
-u*(u - 1)*(7*u - 2)
Let x(k) be the first derivative of k**3/3 + 9*k**2/4 - 5*k/2 - 19. Factor x(q).
(q + 5)*(2*q - 1)/2
Let c = 32409/13510 - -3/2702. Factor 0*d**3 - 4/5*d**2 + 8/5*d**5 + 0 + c*d**4 + 0*d.
4*d**2*(d + 1)**2*(2*d - 1)/5
Let j(q) be the third derivative of -3*q**8/560 - 209*q**7/350 + 499*q**6/200 - 359*q**5/100 + 9*q**4/5 + 4*q**2 - 13. Determine d, given that j(d) = 0.
-72, 0, 1/3, 1
Let t(f) = -151*f - 4830. Let a be t(-32). Factor 0 + 0*s**a - 1/10*s + 1/10*s**3.
s*(s - 1)*(s + 1)/10
What is n in 2/9*n**4 - 4/9*n**2 - 4/9*n**3 + 2/9*n**5 + 2/9*n + 2/9 = 0?
-1, 1
Solve 3*z**3 - 845 - 1549 - 117*z**2 - 2233 + 1521