1
Factor -363/2 + 1/2*w**2 + 59*w.
(w - 3)*(w + 121)/2
Let s(u) be the second derivative of -u**4/24 - 3*u**3/2 - 1577*u. Factor s(j).
-j*(j + 18)/2
Let u(p) be the second derivative of 0 - 47*p - 1/120*p**4 - 144/5*p**2 + 4/5*p**3. Suppose u(r) = 0. What is r?
24
Let j = -31478 + 94468/3. What is s in 2/3*s**3 - 20/3*s**2 - 16/3 + j*s = 0?
1, 8
Let m(b) be the first derivative of b**5/35 - 13*b**4/14 + 25*b**3/21 + 2091. Solve m(o) = 0 for o.
0, 1, 25
Let z(n) = -2*n**2. Let r = -49 + 48. Let c(s) = -3*s**2 + 24*s + 45. Let b(d) = r*c(d) + 3*z(d). Factor b(t).
-3*(t + 3)*(t + 5)
Let y = -14 + 17. Solve -3*o + 10*o**2 - 5*o**y - o**3 - 18*o**2 + o**5 = 0.
-1, 0, 3
Let -40*f**2 - 24*f - 50 + 41*f + 5*f**3 + 68*f = 0. Calculate f.
1, 2, 5
Find b, given that -2364*b - 771*b - 326*b - 1590*b**2 + 6196*b**2 + 126 - 1151*b**3 - 120 = 0.
2/1151, 1, 3
Let z be 116*6/36*(-18)/4. Let r = -84 - z. Suppose 0*t - t**3 + t**4 + 3*t**2 - 4*t**2 + r*t - 2*t = 0. Calculate t.
-1, 0, 1
Let f(l) be the second derivative of l**3 + 1/8*l**4 - 1 - 72*l - 3/40*l**5 - 3*l**2. Let f(b) = 0. Calculate b.
-2, 1, 2
Solve -33*m + 0 + 3/5*m**3 + 162/5*m**2 = 0 for m.
-55, 0, 1
Suppose 11*p - 16 = 9*p. Suppose -5*a = f - 11, -2*a - p = f - 10. Suppose 1/2*n + 1/4*n**a - 3/4*n**2 + 0 = 0. What is n?
0, 1, 2
Let h be 10/2*(18 + -1 + -16) - 2. Suppose 4*d + 173 = 5*i - 183, 5*i - d - 359 = 0. Factor h - 7*n + i*n**2 - 24*n**3 - 20*n - 19*n**3 - 5*n**3.
-3*(n - 1)*(4*n - 1)**2
Let h(r) be the third derivative of 9*r**8/56 - 888*r**7/35 + 582*r**6/5 - 3472*r**5/15 + 2308*r**4/9 - 512*r**3/3 - 977*r**2. Factor h(m).
2*(m - 96)*(3*m - 2)**4/3
Let v(t) be the second derivative of -2/9*t**3 - 1/63*t**7 + 1/9*t**6 + 0 - 3/10*t**5 - 22*t + 0*t**2 + 7/18*t**4. What is i in v(i) = 0?
0, 1, 2
Determine z so that -60*z**2 + 7/4*z**4 - 28 + 5/4*z**3 + 115*z = 0.
-7, 2/7, 2, 4
Let s = 3/1084 - -3749/16260. Let p(m) be the second derivative of 0 + 0*m**2 + 2/3*m**3 - s*m**5 - 1/18*m**4 - 6*m. Determine q, given that p(q) = 0.
-1, 0, 6/7
Let f(w) = 340*w**2 + 48365*w - 13024980. Let k(t) = 37*t**2 + 5374*t - 1447220. Let i(h) = 6*f(h) - 55*k(h). Factor i(q).
5*(q - 538)**2
Let x(r) be the third derivative of r**2 + 0*r**4 + r + 1/10*r**5 + 0*r**3 + 1/40*r**6 - 1/70*r**7 + 0. Factor x(b).
-3*b**2*(b - 2)*(b + 1)
Factor -39248*m - 596748/5 + 889/5*m**2 - 1/5*m**3.
-(m - 446)**2*(m + 3)/5
Let h = -575636 - -1734106/3. Factor -h*a - 242/3*a**2 - 2/3*a**3 + 7442/3.
-2*(a - 1)*(a + 61)**2/3
Suppose -1/3*y**5 - 13/12*y**3 - 5/4*y**4 + 17/12*y + 3/4*y**2 + 1/2 = 0. What is y?
-2, -1, -3/4, 1
Let c(a) be the third derivative of -a**7/630 + a**6/45 + 53*a**5/180 - 5*a**4/6 - 682*a**2. Let c(j) = 0. What is j?
-5, 0, 1, 12
Let t be 1 + -8 + 100/10. Suppose 3*f = -0*f + 9. Determine o so that -7*o**4 + 7*o**f - t*o**3 + 11*o**4 + o**5 = 0.
-2, 0
Let g be (-69)/54 + (-12)/(-27) + (10540/840 - 6). Factor -2/7*h**2 + g - 2/7*h.
-2*(h - 4)*(h + 5)/7
Suppose 6*v - 2931 = v - 2921. Let n(s) be the second derivative of 5*s + 3/8*s**3 - 3/2*s**v + 0 + 1/16*s**4. Suppose n(k) = 0. Calculate k.
-4, 1
Let m be (48/648)/(8/30). Let r = m - 8/45. Factor -3/10*f + 3/10*f**2 - r*f**3 + 1/10.
-(f - 1)**3/10
Let h be ((-12)/(-20))/((-19)/10 + 2). Factor h + 0*k**2 - 1 + k**2 - k + 11*k + 4*k**2.
5*(k + 1)**2
Let v(r) be the second derivative of 1/9*r**3 - 4/45*r**6 + 54*r - 1/15*r**5 - 4/3*r**2 + 1/63*r**7 + 4/9*r**4 + 2. Let v(p) = 0. What is p?
-1, 1, 4
Let l(j) be the second derivative of j**5/100 - 3*j**4/4 + 45*j**3/2 + 95*j**2/2 + 4*j + 5. Let n(p) be the first derivative of l(p). What is a in n(a) = 0?
15
Let w(v) = -2*v**3 - 5*v**2 + v - 1. Let t(i) = 9*i**3 + 515*i**2 + 60503*i - 185999. Let y(a) = t(a) + 4*w(a). Factor y(s).
(s - 3)*(s + 249)**2
Let q = 163 - 283. Let x be (-19)/((-4389)/(-14))*q. Factor 9/11 - 192/11*y**3 + 21/11*y - x*y**2.
-(3*y - 1)*(8*y + 3)**2/11
Let h(f) be the second derivative of -f**5/180 + f**4/24 + 2*f**3/9 - 19*f**2/2 + 12*f. Let g(q) be the first derivative of h(q). Find o such that g(o) = 0.
-1, 4
Let s(f) be the first derivative of -4*f**5/5 + 14*f**4 + 128*f**3 - 1692*f**2 + 5508*f - 4097. Find x such that s(x) = 0.
-9, 3, 17
Factor 737*x**2 - x**5 - 9827*x**2 + 45225*x + 6394*x**3 - 6162*x**3 + 128250 + 24*x**4.
-(x - 15)**3*(x + 2)*(x + 19)
Let p(l) = 2*l**2 + 28*l - 72. Let n(y) = -y**2 - 27*y + 72. Let h = 6 - 9. Let z = -730 - -726. Let t(c) = h*p(c) + z*n(c). Factor t(u).
-2*(u - 6)**2
Let d(z) be the third derivative of z**8/1680 - z**7/105 + 3*z**6/200 + 9*z**5/25 - 9*z**4/10 - 973*z**2. Factor d(j).
j*(j - 6)**2*(j - 1)*(j + 3)/5
Let x = 37 - 39. Let v(s) = s + 4. Let o be v(x). Factor 6*r - 5*r**2 - 2*r**3 - 3*r**o + 15 + 17 + 4.
-2*(r - 2)*(r + 3)**2
Solve 36/7*c - 2/7 + 444/7*c**2 + 324/7*c**5 + 1014/7*c**4 + 1096/7*c**3 = 0.
-1, -1/6, 1/27
Suppose 14 - 2 = -3*r - 4*b, -b - 3 = -2*r. Let n(q) be the third derivative of 1/66*q**5 + 1/330*q**6 + 0*q**3 + r*q + 1/44*q**4 + 6*q**2 + 0. Factor n(y).
2*y*(y + 1)*(2*y + 3)/11
Let w(k) be the second derivative of 1/3*k**3 - 1/10*k**5 - 4*k + 2*k**2 - 1/2*k**4 - 2 + 1/15*k**6. Suppose w(f) = 0. Calculate f.
-1, 1, 2
Let n(q) = 14*q**2 - 425*q + 830. Let j(x) = -55*x**2 + 1700*x - 3320. Let t(i) = 9*j(i) + 35*n(i). Factor t(d).
-5*(d - 83)*(d - 2)
Let r(y) = 3*y**3 + 15*y**2 - 18*y + 9. Let h be r(14). Suppose -8101 + 2*b**2 - 7*b**2 - h - 17950 - 860*b = 0. Calculate b.
-86
Suppose -11*u + 5 = -50. Factor 0*z**2 + u*z - 17 + 3*z + 23 + 2*z**2.
2*(z + 1)*(z + 3)
Let z = -192303 - -384607/2. What is n in -1/6*n**2 - z + 2/3*n = 0?
1, 3
Let d(p) be the third derivative of -1/5*p**5 + 2/15*p**6 + 1/168*p**8 - p**2 - 3/4*p**4 + 2/35*p**7 + 24 + 0*p**3 + 0*p. Factor d(b).
2*b*(b - 1)*(b + 1)*(b + 3)**2
Let s(v) be the first derivative of v**5/20 - v**4/3 - v**3/6 + 2*v**2 + 36*v + 16. Let f(i) be the first derivative of s(i). Let f(u) = 0. Calculate u.
-1, 1, 4
Let t(q) = -34*q + 64. Let w(s) = -s**2 - 34*s + 66. Let h(a) = 3*t(a) - 2*w(a). Let v(z) = -z - 1. Let r(n) = -h(n) + 6*v(n). What is g in r(g) = 0?
3, 11
Let g(t) be the second derivative of -t**4/54 - 65*t**3/27 + 350*t**2/9 - 18*t - 27. Factor g(v).
-2*(v - 5)*(v + 70)/9
Let z = 319201 - 2553605/8. Suppose 5/4*i - z - 1/4*i**5 - 3/4*i**2 + 9/8*i**4 - i**3 = 0. What is i?
-1, 1/2, 1, 3
Let t(a) = -4*a**2 + 1. Let d be t(1). Let f be 6*((-6 - d) + (-14)/(-4)). Solve 2*p**5 + f*p**3 - 13*p**3 + p**2 - 2*p**4 - 7*p**2 + 0*p**2 = 0.
-1, 0, 3
Suppose -5*k - 13*n + 9*n + 8 = 0, -26 = -5*k + 2*n. Factor 23*u**2 + 24*u**3 + 77*u**2 - 4*u**3 - 5*u**k - 6*u**4 + 12*u**4.
u**2*(u + 10)**2
Let x(i) = 3*i**3 + 2*i**2 - 9*i + 7. Let z be x(1). Determine v, given that 21*v - 30*v**z - 2*v + 27*v**3 + 35*v - 21*v**2 = 0.
-9, 0, 2
Let p(b) be the second derivative of 8/3*b**3 + 0 + 7*b**2 + 4*b + 1/6*b**4. Factor p(v).
2*(v + 1)*(v + 7)
Let 414 + 282*g + 50*g**2 + 2/3*g**3 = 0. Calculate g.
-69, -3
Let -1/4*o**2 - 559504 - 748*o = 0. Calculate o.
-1496
Let y(g) be the first derivative of 5*g**3/3 - 5*g**2 - 40*g - 645. Factor y(u).
5*(u - 4)*(u + 2)
Let g(u) = 2*u**3 + 80*u**2 + 1170*u + 5404. Let d(a) = 2*a**3 + 78*a**2 + 1170*a + 5402. Let h(f) = 2*d(f) - 3*g(f). Factor h(n).
-2*(n + 13)**2*(n + 16)
Let a(w) be the first derivative of -w**3/12 - 15*w**2/4 - 50*w + 11658. Factor a(q).
-(q + 10)*(q + 20)/4
Factor -21*d**3 - 83*d - 2*d**2 + 84*d + 20*d**3 + 2.
-(d - 1)*(d + 1)*(d + 2)
Let l(i) be the first derivative of -i**4/12 + 43*i**3/3 - 85*i**2/2 + 127*i/3 - 4476. Factor l(r).
-(r - 127)*(r - 1)**2/3
Let g = -57499/4 - -57517/4. Let 0 - g*x - 1/4*x**2 = 0. What is x?
-18, 0
Let t(y) be the first derivative of -2*y**7/63 + 2*y**6/15 - 3*y**5/20 + y**4/18 + 57*y + 54. Let w(f) be the first derivative of t(f). Factor w(l).
-l**2*(l - 2)*(2*l - 1)**2/3
Let h(t) be the first derivative of t**6/39 - 12*t**5/65 - 17*t**4/26 + 92*t**3/13 - 236*t**2/13 + 240*t/13 + 1778. Find o such that h(o) = 0.
-5, 1, 2, 6
Determine u, given that -2/3*u**4 + 6560/3*u - 3362/3 - 1012*u**2 - 160/3*u**3 = 0.
-41, 1
Suppose 7*a + 2 = g + 3*a, 2*g - 17*a = 4. Find o, given that 2*o - 1/2*o**3 - 4 + o**g = 0.
-2, 2
Let c(t) be the first derivative of -t**4 + 3*t**6 - 96 + 0*t**2 + 14/5*t**5 + 0*t**3 + 0*t.