j**2.
5*(j - 14)*(2*j + 1)
Let s(v) be the first derivative of -1/30*v**5 + 0*v**3 + 1/120*v**6 + 0*v**4 + v**2 + 0*v - 8. Let d(a) be the second derivative of s(a). Factor d(u).
u**2*(u - 2)
Let o(w) be the first derivative of -2/13*w**2 - 2/65*w**5 - 10 - 10/39*w**3 - 2/13*w**4 + 0*w. Suppose o(k) = 0. Calculate k.
-2, -1, 0
Factor 10*a**4 - 3*a**5 + 52*a**2 - 575 + 34*a**3 + 37*a + 4*a**5 + 585.
(a + 1)**3*(a + 2)*(a + 5)
Let g(b) = 2*b**2. Let q be g(1). Suppose 4*y**4 + 4*y**5 + 3*y**5 - q*y - 5*y**5 - 4*y**2 = 0. What is y?
-1, 0, 1
Suppose -31 + 23 = -2*z. Suppose 2*q = -3*x - 12, 7*q - z*q + 8 = -2*x. Suppose -1/4*j**4 + 1/4*j**3 + 1/2*j**2 + 0 + q*j = 0. What is j?
-1, 0, 2
What is k in -10/7*k + 2/7*k**2 - 4 = 0?
-2, 7
Let w(n) be the second derivative of -5/12*n**4 + 0*n**2 - 20*n + 0*n**3 + 0. Factor w(x).
-5*x**2
Let n = 1846/9 - 23980/117. Factor 0*a + n - 2/13*a**2.
-2*(a - 1)*(a + 1)/13
Let d(v) be the third derivative of v**8/1008 - v**7/70 + v**6/45 + 9*v**2 + 4. Find t, given that d(t) = 0.
0, 1, 8
Determine n, given that 73167 + 1802*n**2 + 0*n**4 + 65598*n + 258*n**3 - 1640*n**2 - 7470*n**2 - 3*n**4 = 0.
-1, 29
Suppose -86*r + 21 = -2*o - 81*r, 0 = -2*o - 3*r + 19. Determine n so that 0 + 3/2*n**o - n = 0.
0, 2/3
Factor 480*t - 13*t**3 - 1440 + 23*t**2 + 18*t**3 + 87*t**2.
5*(t - 2)*(t + 12)**2
Let b(m) = m**2 + m + 1. Let n(x) = -3*x**2 - 298*x - 4498. Let v(l) = -2*b(l) + n(l). Factor v(p).
-5*(p + 30)**2
Let h(y) be the second derivative of 9*y + 0 - 1/5*y**3 - 1/30*y**4 + 0*y**2. Factor h(r).
-2*r*(r + 3)/5
Let i be 13/(-2)*(-2 + 0). Let q(c) = 3*c - 1. Let k be q(1). Suppose -3 - 15*o**3 - 13*o**3 - i*o**k - o + 14*o + 1 = 0. What is o?
-1, 1/4, 2/7
Let m = 18 + -18. Suppose -2*t - 3*l - 12 = 0, 5*t = t + 2*l + 8. Solve t + 0*h + m*h**2 + 3/2*h**4 + 3/2*h**3 = 0 for h.
-1, 0
Let q be ((-5)/(10/3))/(9/(-12)). Let 2 - l + 4*l + l**q - 4 - 2*l = 0. Calculate l.
-2, 1
Let a(x) be the third derivative of x**6/780 - x**5/15 + 16*x**4/13 - 96*x**3/13 + 6*x**2 + 28*x. Suppose a(m) = 0. Calculate m.
2, 12
Let r(u) be the third derivative of -1/60*u**5 + 1/420*u**7 + 17*u**2 + 1/240*u**6 + 0 + 0*u**3 + 0*u + 0*u**4. Factor r(g).
g**2*(g - 1)*(g + 2)/2
Let i be 1 + ((-7)/((-140)/(-116)) - -6). What is v in -9/10*v + 2/5*v**3 - 1/5 + 1/2*v**5 + i*v**4 - v**2 = 0?
-1, -2/5, 1
Let w(n) be the third derivative of -n**7/3150 - 11*n**4/24 + 17*n**2. Let r(k) be the second derivative of w(k). Solve r(c) = 0.
0
Let l(y) = 3*y - 2. Let h be l(3). Suppose -3*q - i = q - h, 4*i = -4. Factor 3*z**4 - 2*z**3 - 15*z**2 + 15*z**q.
z**3*(3*z - 2)
Let p(k) be the third derivative of k**10/252000 - k**9/100800 - 11*k**5/60 + 10*k**2. Let g(s) be the third derivative of p(s). What is y in g(y) = 0?
0, 1
Let m(z) be the third derivative of -z**8/168 + z**7/105 + z**6/20 - z**5/30 - z**4/6 - z**2 - 32*z. Suppose m(q) = 0. What is q?
-1, 0, 1, 2
What is z in -28/5 + 116/5*z - 94/5*z**3 + 41/5*z**4 - 4/5*z**5 + z**2 = 0?
-1, 1/4, 2, 7
Let v(k) be the second derivative of 0*k**2 - 1/3*k**4 + 3/20*k**5 - 35*k - 2/9*k**3 + 7/90*k**6 + 0. Factor v(h).
h*(h - 1)*(h + 2)*(7*h + 2)/3
Let u(v) be the first derivative of v**5/20 - 3*v**4/8 + v**3 - 5*v**2/4 + 3*v/4 - 634. Suppose u(m) = 0. What is m?
1, 3
Let q(p) = p + 3. Let x be q(-4). Let h be x/2*0 - 0. Determine r so that -1 - r**4 + 21*r**3 + h*r**4 + 2*r**2 + r**5 + r - 23*r**3 = 0.
-1, 1
Let l(c) be the first derivative of 8/5*c**5 - 3*c**4 - 1/3*c**6 - 22 - c**2 + 0*c + 8/3*c**3. Factor l(k).
-2*k*(k - 1)**4
Let k(y) be the second derivative of 5*y**6/24 - 11*y**5/8 + 25*y**4/12 + 5*y**3/4 - 45*y**2/8 - 84*y. Determine q, given that k(q) = 0.
-3/5, 1, 3
Let b(o) be the first derivative of 1/36*o**4 - 3*o**2 + 0*o - 3 - 1/180*o**5 + 0*o**3. Let l(h) be the second derivative of b(h). Factor l(s).
-s*(s - 2)/3
Suppose 7*q = 8*q. Suppose q = 3*l - 7*l + 12. Let f(i) = 2*i**2 + 3*i + 1. Let c(g) = g**2 + g. Let a(v) = l*c(v) - f(v). Solve a(m) = 0 for m.
-1, 1
Determine s, given that 102/5*s**2 - 96/5*s**3 + 99/5*s - 102/5*s**4 + 0 - 3/5*s**5 = 0.
-33, -1, 0, 1
Solve 18*t**3 - 7*t**3 + 36*t - 14*t**3 - 6*t**3 + 14*t**2 + 8 - 4*t**4 = 0 for t.
-2, -1/4, 2
Suppose 3*m = 3*t, 3*m + t = -m + 10. Let o be 1 + (-13)/18 + m/9. Solve -o - 3/4*u**2 + 7/4*u**3 + 5/4*u**4 - 7/4*u = 0.
-1, -2/5, 1
Let i(l) be the third derivative of -l**6/50 + 16*l**5/75 - 2*l**4/5 - 32*l**3/15 - 5*l**2 - 7. What is a in i(a) = 0?
-2/3, 2, 4
Factor 20 - 5 + 6*x**2 - 8 - 2*x**4 - 11 + 2*x - 2*x**3.
-2*(x - 1)**2*(x + 1)*(x + 2)
Factor -3/8*i**3 - 183/8*i**2 + 0 + 93/4*i.
-3*i*(i - 1)*(i + 62)/8
Suppose 33 = -2*i - 45. Let y(r) = 3*r**3 - 2*r**2 + 2*r - 2. Let a(h) = h**2 - 2 + 17 - 2 - 13*h - 19*h**3 + 12*h**2. Let w(n) = i*y(n) - 6*a(n). Factor w(t).
-3*t**3
Factor 19/2*i**2 + 9/2*i + 1/2*i**4 + 11/2*i**3 + 0.
i*(i + 1)**2*(i + 9)/2
Let t(u) = -u**2 + 3. Let x be t(4). Let o(z) = 2*z + 31. Let m be o(x). Determine g so that 18*g**2 - m*g**3 + 2*g**3 - 9*g**2 - 12 = 0.
-1, 2
Suppose 97 + 84 + 93 + 195*a - 74 - 5*a**2 = 0. Calculate a.
-1, 40
Let r(t) be the first derivative of 2*t**6/27 + 2*t**5/45 - 4*t**4/9 - 2*t**3/27 + 2*t**2/3 - 136. Let r(c) = 0. Calculate c.
-2, -1, 0, 1, 3/2
Let y = -37 - -39. Factor s**2 - 4*s + s - s**y - 3*s**2.
-3*s*(s + 1)
Let 5/4 + 5/4*y - 5/4*y**2 - 5/4*y**3 = 0. What is y?
-1, 1
Let p(q) = 1. Let z(l) be the first derivative of -2*l**3/3 - 1. Let a(b) = 2*p(b) + z(b). Let a(i) = 0. Calculate i.
-1, 1
Let w(g) = -34*g**3 + 640*g**2 - 5120*g - 28. Let j(h) = 7*h**3 - 128*h**2 + 1024*h + 6. Let t(z) = 14*j(z) + 3*w(z). Determine d so that t(d) = 0.
0, 16
Let m(k) be the second derivative of -1/4*k**5 + 25/6*k**4 + 0*k**2 + 0 + 0*k**3 + 45*k. Factor m(d).
-5*d**2*(d - 10)
Let h(q) be the second derivative of q**4/18 - 202*q**3/9 + 10201*q**2/3 + 543*q. Factor h(y).
2*(y - 101)**2/3
Suppose -2*q - 4*a - 1 = 5, -2*a + 22 = -4*q. Let t be (-140)/((-35)/q)*1/(-3). What is u in 4/3 + 0*u + 7*u**4 - t*u**3 - 15*u**2 = 0?
-1, -1/3, 2/7, 2
Let v(x) be the first derivative of x**3/3 - 40*x**2 + 1600*x - 15. Factor v(n).
(n - 40)**2
Let s = 319 + -219. Factor 11*u**2 - s*u**3 + 8 + 14*u**2 + 8 + 64*u - 5*u**2.
-4*(u - 1)*(5*u + 2)**2
Let p be 1262/(-72) - (-2)/(-9). Let q = 18 + p. Factor 1/2*x**3 + 1/4*x**4 - q*x - 1/4*x**5 + 1/4 - 1/2*x**2.
-(x - 1)**3*(x + 1)**2/4
Let a = -31 - -25. Let r(p) = p**2 + 8*p + 14. Let v be r(a). Factor -15/7*b**v + 3/7 + 3/7*b + 9/7*b**3.
3*(b - 1)**2*(3*b + 1)/7
Let k(z) = 19*z - 28. Let y be k(7). Factor -49*g**2 + 2160*g - y*g**2 - 9255 + 5*g**3 - 26*g**2 + 615.
5*(g - 12)**3
Factor -j + 6/7 + 1/7*j**2.
(j - 6)*(j - 1)/7
Find t such that 3/2*t**2 - 15/2*t**3 - 27 + 3/2*t**4 + 63/2*t = 0.
-2, 1, 3
Factor -2*g**2 + 15 + g**3 + 3*g**2 - 4616*g + 4599*g.
(g - 3)*(g - 1)*(g + 5)
What is c in -20/3*c**3 - 140*c - 142/3*c**2 - 1/3*c**4 - 147 = 0?
-7, -3
Suppose 3*u + 9 = 18. Let p(x) = -2*x**3 - 5*x**2 + 24*x - 15. Let m(j) = 3*j**3 + 4*j**2 - 25*j + 14. Let k(s) = u*m(s) + 4*p(s). Factor k(h).
(h - 3)**2*(h - 2)
Let g(a) be the third derivative of a**8/224 + a**7/21 + a**6/5 + 9*a**5/20 + 29*a**4/48 + a**3/2 + a**2 + 4. Factor g(l).
(l + 1)**3*(l + 3)*(3*l + 2)/2
Suppose -8*b - 40*b**2 + 12*b - 5*b**3 + 35*b**2 + 6*b = 0. What is b?
-2, 0, 1
What is x in 92/7*x**2 - x**4 + 26/7*x**3 + 0 + 24/7*x = 0?
-2, -2/7, 0, 6
Let q(t) be the second derivative of 0*t**3 + 0 - 1/100*t**5 + 0*t**2 + 2*t + 1/60*t**4. Factor q(u).
-u**2*(u - 1)/5
Let q(o) be the third derivative of o**7/525 + 7*o**6/300 - 9*o**5/50 + 29*o**4/60 - 2*o**3/3 + 222*o**2 + 2. Factor q(z).
2*(z - 1)**3*(z + 10)/5
Let j(a) be the third derivative of -1/240*a**5 + 1/840*a**7 + 0*a + 0*a**3 + 1/480*a**6 + 43*a**2 - 1/1344*a**8 + 0 + 0*a**4. Solve j(d) = 0 for d.
-1, 0, 1
Suppose 0 = -11*i + 12*i - 2. What is c in 19*c + 2*c**3 - 9*c**i - 3*c + 2*c**4 + 3*c**2 - 8 - 6*c**3 = 0?
-2, 1, 2
Let k(m) = -m**3 - 14*m**2 - 25*m - 10. Let f be k(-12). Factor -8*x**2 - x**4 - 12*x**3 - x**5 + f*x - 7*x**4 - x**5 - 4*x.
-2*x*(x + 1)**4
Let k(p) be the second derivative of -p**4/9 - 100*p**3/9 - 98*p**2/3 + 36*p + 1. Solve k(c) = 0 for c.
-49, -1
Suppose 0*l + 99 = -3*l. Let w be ((-11)/l)/((-2)/(-12)). Factor -5*o**5 + 6*o**3 - 5*o**3