 second derivative of -50*v**2 + 3/2*v**4 - 89*v + 1 + 223/3*v**3. Factor z(s).
2*(s + 25)*(9*s - 2)
Let x = 51/373 - -3695/2984. Factor 1/4 + 13/8*z**2 + 1/2*z**3 + x*z.
(z + 1)*(z + 2)*(4*z + 1)/8
Suppose 3*a**3 + 19*a**2 + 43431*a + 284*a**2 - 42837*a = 0. Calculate a.
-99, -2, 0
Let s(r) be the second derivative of -r**5/4 + 5*r**4/4 + 15*r**3/2 - 135*r**2/2 + 1221*r. Factor s(y).
-5*(y - 3)**2*(y + 3)
Let k(q) be the second derivative of -11*q**4/4 - 31*q**3/2 + 9*q**2 - 3399*q. Determine t so that k(t) = 0.
-3, 2/11
Let s be 2 - ((-1)/4 + 35/(-20)). Suppose 0 = -4*d + d - 6, -t + 8 = -s*d. Factor -9/4*k**4 + 0*k + t - 3/2*k**3 - k**5 - 1/4*k**2.
-k**2*(k + 1)**2*(4*k + 1)/4
Factor 3 - 589*w**2 - 3 - w**3 - 555*w**2 - 285975*w - 41209*w.
-w*(w + 572)**2
Factor 3/2*v**3 + 18711/2*v - 234*v**2 - 17787.
3*(v - 77)**2*(v - 2)/2
Let n(w) be the first derivative of w**8/1344 - w**7/168 + w**6/80 + 45*w**2 - 87. Let d(a) be the second derivative of n(a). Factor d(u).
u**3*(u - 3)*(u - 2)/4
Suppose 0 = -46*l - 0*l + 4186. Let j = l + -89. What is f in -f**j + 1/2 + 1/2*f = 0?
-1/2, 1
Suppose 8*c - 7*c + 10 = 0. Let s be (3 + c/(-5))*1. Factor s*x + 20*x + 15 + 5*x**2 + 6*x - 11*x.
5*(x + 1)*(x + 3)
Suppose 8*r + 3072 + 0 = 0. Let x = r - -795/2. Find a such that -9/2*a - 3/8*a**2 - x = 0.
-6
Factor -140/3 + 142/3*k - 2/3*k**2.
-2*(k - 70)*(k - 1)/3
Let s(j) be the third derivative of -11*j**6/180 - 163*j**5/90 + 5*j**4/6 + 7997*j**2. Factor s(n).
-2*n*(n + 15)*(11*n - 2)/3
Let v(i) be the first derivative of 5*i**4/8 - 35*i**2 - 120*i + 88. Find m such that v(m) = 0.
-4, -2, 6
Let p(f) be the first derivative of 5*f**4/24 - 13*f**3/18 + 11*f**2/12 - f/2 - 76. Suppose p(g) = 0. What is g?
3/5, 1
Suppose -20188/3*s - 4/3*s**3 - 86436 - 500/3*s**2 = 0. Calculate s.
-49, -27
Let u(j) be the second derivative of -2/3*j**4 - 6*j**2 - 14/3*j**3 + 2/3*j**6 + 2/21*j**7 - 32 - j + 6/5*j**5. Suppose u(m) = 0. Calculate m.
-3, -1, 1
Let u(y) = -15*y + 528. Suppose 22*o - 47 = -n + 25*o, -o + 31 = n. Let c be u(n). Let -4/3*k**2 + 10/3*k**4 - 2 + 4*k**c - 14/3*k + 2/3*k**5 = 0. Calculate k.
-3, -1, 1
Determine p, given that -2080 - 3200/3*p - 5/3*p**3 - 430/3*p**2 = 0.
-78, -4
Suppose -2*m - 14 = 3*t, -5*t - 22 = 8. Let a(x) be the first derivative of 0*x + 2/3*x**2 + m*x**3 + 15. Factor a(i).
2*i*(9*i + 2)/3
Let t(s) = 2*s**2 - 4*s - 135. Let r be t(-28). Let f = 1547 - r. Determine p so that 0*p + 1/2*p**f - 1/2 = 0.
-1, 1
Let j(k) be the second derivative of -k**6/15 - 31*k**5/5 + 130*k**4/3 - 88*k**3 + 3*k - 13. Factor j(w).
-2*w*(w - 2)**2*(w + 66)
Let d(f) be the first derivative of f**4/46 - 936*f**3/23 + 491397*f**2/23 + 1976836*f/23 + 3278. Solve d(w) = 0 for w.
-2, 703
Let q be 6*((-20)/8)/(-5). Let p = 779/1028 + -2/257. Let -3/2*b + 3/4*b**2 + 0 + p*b**q = 0. What is b?
-2, 0, 1
Factor 135 - 135 + 519*w**3 - 521*w**3 + 69*w**2 + 595*w**2.
-2*w**2*(w - 332)
Suppose -40*p + 68 + 22 = 5*p. Let w(d) be the first derivative of -5/3*d**3 + 24 + 40*d - 5*d**p. Factor w(f).
-5*(f - 2)*(f + 4)
Suppose 106*t + 23 - 640*t + 18 + 175 - 15*t**2 = 0. What is t?
-36, 2/5
Suppose b + 4*d = 84, 0 = 3*b - 3*d - 135 - 192. Let a be (-38)/(-24) - 26/b. Factor a*j + 2/9*j**2 + 0.
2*j*(j + 6)/9
Suppose 2599*v - 183503 - 189741 + 8428 - 4*v**2 - 183*v = 0. What is v?
302
Let j be 342 - 337 - 6/(1 - -1). Let v(u) be the first derivative of -3 + 10/3*u**3 + 0*u**j + 0*u**5 - 15/4*u**4 + 5/6*u**6 + 0*u. Factor v(h).
5*h**2*(h - 1)**2*(h + 2)
Let u(r) be the third derivative of -r**6/60 + 3*r**5/2 + 34*r**4 + 848*r**3/3 + 1409*r**2. Let u(c) = 0. What is c?
-4, 53
Let v(s) = s**3 - s**2. Let b(h) = -3*h**3 + 152*h**2 - 7500*h + 125000. Let n be 3 + -2 + (2 - 1). Let x(g) = n*v(g) + b(g). Factor x(m).
-(m - 50)**3
Let o(i) be the first derivative of -2/9*i**3 - 1/3*i**4 + 2/15*i**5 + 1/18*i**6 + 0*i + 115 + 1/2*i**2. Factor o(f).
f*(f - 1)**2*(f + 1)*(f + 3)/3
Let o(g) be the third derivative of -11/16*g**4 - 13/2*g**3 - 85*g**2 + 0*g + 1/40*g**5 + 0. Solve o(k) = 0.
-2, 13
Let u(p) be the third derivative of p**7/840 - 2*p**6/45 + 8*p**5/15 + 77*p**3/6 - p**2 - 109*p. Let q(m) be the first derivative of u(m). Factor q(j).
j*(j - 8)**2
Let g(m) be the first derivative of m**4/6 - 5*m**3 - 89*m - 95. Let k(u) be the first derivative of g(u). Find z such that k(z) = 0.
0, 15
Let z = 387 - 391. Let x be ((-2)/(-6))/((28/(-49))/z). Let -x*s**3 + 5/3*s**4 - 1/3*s**2 + 8/3*s - 1/3*s**5 - 4/3 = 0. What is s?
-1, 1, 2
Factor -3/4*a**3 - 3/8*a**2 + 0 + 0*a - 3/8*a**4.
-3*a**2*(a + 1)**2/8
Let f(t) = -55*t**3 + 1183*t**2 + 313*t. Let n(h) = -19*h**3 + 395*h**2 + 104*h. Let m(g) = 6*f(g) - 17*n(g). Suppose m(r) = 0. What is r?
-2/7, 0, 55
Let z = -99 - -104. Factor g**2 - z*g**4 + 3*g**3 + 6*g + 3*g - 16*g**2 + 8*g**4.
3*g*(g - 1)**2*(g + 3)
Suppose -43*u = 2319 - 2405. Factor -3/7 - 12/7*s**u - 12/7*s.
-3*(2*s + 1)**2/7
Let t(z) be the first derivative of -2/15*z**5 - 1312/5*z**2 - 5092/45*z**3 - 81 - 768/5*z + 233/30*z**4. Find o, given that t(o) = 0.
-1, -2/5, 24
Let f(g) be the third derivative of 0*g + 1/360*g**6 - 1/18*g**3 + 1/180*g**5 - 1/72*g**4 - 10*g**2 - 1. Suppose f(u) = 0. Calculate u.
-1, 1
Let x(t) be the second derivative of -t**4/36 - 53*t**3/6 + 212*t. Find b, given that x(b) = 0.
-159, 0
Let a(i) = -2*i + 8. Let y(u) = 10*u - 41. Let t(x) = -22*a(x) - 4*y(x). Let d be t(15). Factor 4*c**5 + 23 + d*c**3 - 40*c**2 - 23 - 24*c**4 + 12*c.
4*c*(c - 3)*(c - 1)**3
Let r(x) = -6*x**3 + 24*x**2 + 33*x - 57. Let c(w) = -13*w**3 + 54*w**2 + 68*w - 115. Let n(y) = -3*c(y) + 7*r(y). Factor n(p).
-3*(p - 3)*(p - 2)*(p + 3)
Factor 4/3*h**4 + 8*h**3 + 16/3*h**2 - 32*h - 128/3.
4*(h - 2)*(h + 2)**2*(h + 4)/3
Let d be (-1175)/(-125) + (-36)/4. Factor d*v**4 + 2/5*v**3 - 8/5*v + 0 - 8/5*v**2.
2*v*(v - 2)*(v + 1)*(v + 2)/5
Let r(c) be the third derivative of c**6/24 + 47*c**5/6 + 155*c**4/8 - 1129*c**2. Factor r(v).
5*v*(v + 1)*(v + 93)
Let k(o) = -69*o**2 - 4409*o - 41. Let z(l) = 5*l**2 + 315*l + 3. Let d(s) = -6*k(s) - 82*z(s). Factor d(x).
4*x*(x + 156)
Suppose 2704/15 - 1144/15*a - 2/15*a**4 - 484/5*a**2 - 106/15*a**3 = 0. Calculate a.
-26, -2, 1
Factor -66/7*r**2 + 138/7 - 75/7*r + 3/7*r**3.
3*(r - 23)*(r - 1)*(r + 2)/7
Let x = -51 - -67. Suppose 0 = 5*a - 2*a + 2*n - x, 0 = a - 3*n + 13. Factor 2*m**3 - 6*m**2 + m**4 - 2*m**4 + a*m**2 + 2*m**3.
-m**2*(m - 2)**2
Let k be (-2)/(-10) - 614/307*2/20. Factor 2*h**2 + 2/3*h**4 - 8/3*h**3 + k*h + 0.
2*h**2*(h - 3)*(h - 1)/3
Let v = -49 - -103. Let q(x) = -v*x**3 + 45*x**3 + x + 16*x - 25*x**4 - 17. Let h(o) = -3*o**4 - o**3 + 2*o - 2. Let b(m) = 51*h(m) - 6*q(m). Solve b(t) = 0.
0, 1
Let p(a) = 1642*a - 6566. Let x be p(4). Factor 1/6*c**4 - 1/3*c**3 + 3*c + 9/2 - x*c**2.
(c - 3)**2*(c + 1)*(c + 3)/6
Factor 1366*l**2 + 23*l**4 + 25*l**4 - 2888 + 28*l**4 - 72*l**4 + 222*l**2 - 1140*l - 156*l**3.
4*(l - 19)**2*(l - 2)*(l + 1)
Let w = -65 + 69. Let u be w/2*(12 + -5). Factor -18*h**3 + 2*h**2 + u*h**4 - 9*h**2 - 6*h**3 - h**2.
2*h**2*(h - 2)*(7*h + 2)
Let v(d) be the second derivative of d**5/30 - d**4/6 - d**3 - 26*d**2 + 66*d. Let z(p) be the first derivative of v(p). What is n in z(n) = 0?
-1, 3
Let d(a) be the second derivative of a**4/42 + 26*a**3/3 + 175*a**2 + 10*a + 162. Let d(g) = 0. What is g?
-175, -7
Suppose 2*f = 6, -2*n + 2*f - 3 = -n. Factor 2 + 12 + n*l**2 - 3 + 7 - 21*l.
3*(l - 6)*(l - 1)
Suppose -108 + 134*x**3 - 20/3*x**4 - 2380/3*x**2 + 1158*x = 0. What is x?
1/10, 2, 9
Suppose -2*o - 237 = -3*c, 0*c = 3*c - 3*o - 237. Suppose -40*b - c*b - 144*b**2 - 24*b**2 - 28*b - 48*b**3 = 0. Calculate b.
-7/4, 0
Let p(o) = 46*o**3 + 6800*o**2 - 10984*o - 5464. Let y(q) = -30*q**3 - 4533*q**2 + 7322*q + 3643. Let l(j) = -5*p(j) - 8*y(j). Factor l(s).
2*(s - 2)*(s + 228)*(5*s + 2)
Let t = -30 + 14. Let d = -6 - t. Find v, given that -3*v**3 - d*v**3 + 17*v**3 - 4*v = 0.
-1, 0, 1
Let d = 8894372/23 + -386710. Solve 2/23*f**2 - d*f + 76/23 = 0.
2, 19
Factor 7*o - 183*o**2 - 903*o - 268*o - 3*o**3 - 934 - 645 - 41.
-3*(o + 2)*(o + 5)*(o + 54)
Determine n so that 775*n**2 + 1627 + 2820*n - 731*n**3 + 741*n**3 + 1073 - 5*n**4 = 0.
-9, -2, 15
Suppose -42*q - 21*q - 137 = -137. Factor -3/4*s**5 + 0*s + 3/2*s**4 + 6*s**3 + q + 0*s**2.