505/4 - b. Factor 3 + n - q*n**2.
-(n - 6)*(n + 2)/4
Factor 195*y**2 - 226*y + 413*y - 12*y**3 - 119 + 217*y**2 + 859 + 977*y.
-4*(y - 37)*(y + 1)*(3*y + 5)
Let u(l) be the second derivative of 4/9*l**3 + 2/9*l**4 + 0*l**2 - 61 - 2*l + 1/30*l**5. Determine d so that u(d) = 0.
-2, 0
Let b(o) be the first derivative of -1922/3*o + 82 - 310/3*o**2 - 50/9*o**3. Suppose b(k) = 0. What is k?
-31/5
Let i(l) be the third derivative of l**6/15 + 17*l**5/45 + l**4/2 - 4*l**3/9 - 172*l**2. Factor i(v).
4*(v + 1)*(v + 2)*(6*v - 1)/3
Let i(c) be the second derivative of -1/2*c**5 - 7*c**4 + 40*c**2 + 162*c + 28*c**3 + 0. Factor i(u).
-2*(u - 2)*(u + 10)*(5*u + 2)
Factor 36963 - 222*f + 1/3*f**2.
(f - 333)**2/3
Let f(a) be the second derivative of 46*a**4 - 728/3*a**3 + 2/15*a**6 - 4*a**5 + 490*a**2 + 5*a + 10. Determine g so that f(g) = 0.
1, 5, 7
Factor -13*n**2 - 163 + 5*n**2 + 6*n**2 + 43 + 64*n.
-2*(n - 30)*(n - 2)
Let m = -204 - -230. Factor -m*o**2 - 27*o**2 - 11*o + 85*o**2 - 31*o**2 + 24.
(o - 8)*(o - 3)
Suppose -6*p + 562 - 382 = 0. Factor 33 - 2027*b**2 + 1007*b**2 + p*b + 1017*b**2.
-3*(b - 11)*(b + 1)
Let q(k) be the first derivative of k**6/900 + k**5/300 - k**4/3 + 47*k**3/3 + 300. Let d(c) be the third derivative of q(c). Let d(i) = 0. What is i?
-5, 4
Let m(x) be the first derivative of -3*x**4/4 - 29*x**3 + 183*x**2/2 - 93*x + 2627. Solve m(r) = 0.
-31, 1
Suppose -d + 4*q = -26, -6*d + 4*q + 56 = -2*d. Solve -8*v**2 + d*v**3 + 10*v**2 + 14 - 6*v**2 + 2 - 40*v = 0 for v.
-2, 2/5, 2
Factor 3/4*f**3 - 69/2*f**2 - 72*f + 0.
3*f*(f - 48)*(f + 2)/4
Let c(x) be the first derivative of 69 - 3/40*x**5 - 9/8*x**2 + 0*x - 9/16*x**4 - 11/8*x**3. Factor c(z).
-3*z*(z + 1)*(z + 2)*(z + 3)/8
Solve -92*c**3 - 100*c**3 + 57*c + 90 - 99*c**3 + 288*c**3 = 0.
-3, -2, 5
Let z be -3*(-5 - (70/21 + -7)). Suppose c = 3*i - 4, 0 = i + 5*c - 10*c + 22. Factor -29*y**4 + z*y**i + 61*y**4 - 28*y**4.
4*y**3*(y + 1)
Let k = -782 + 786. What is h in -105 + 3*h**4 - 7*h**k + 92*h**3 - 92*h - 4 - 505*h**2 + 13 + 605*h**2 = 0?
-1, 1, 24
Let x be (-47)/(12502/(-47120)) + (-1 - 0)*-8. What is c in -2/7*c**4 + x - 108/7*c**2 + 30/7*c**3 - 216/7*c = 0?
-3, 6
Factor -256*m**3 - 1/2*m**5 + 254*m**2 + 0 + 131/2*m**4 + 0*m.
-m**2*(m - 127)*(m - 2)**2/2
Let c(u) be the second derivative of -u**7/2100 - u**6/450 - u**5/300 - 31*u**3/3 - u**2/2 - 8*u + 4. Let a(r) be the second derivative of c(r). Factor a(i).
-2*i*(i + 1)**2/5
Suppose -103*s + 97*s = -162. Solve 1 - s*q**2 - 5*q + 5*q - 21*q**2 + 9*q**3 + 29 + 9*q = 0.
-2/3, 1, 5
Let c = -141 - -173. Factor -224*k**2 + 18*k**4 + 180*k**2 + c*k**3 - 16 + 100*k - 90*k**2.
2*(k - 1)**2*(k + 4)*(9*k - 2)
Let p(y) = 11*y**2 - 112*y - 33. Let u(g) = g**2 - 4*g + 5. Let q(k) = 2*p(k) - 18*u(k). Suppose q(a) = 0. Calculate a.
-1, 39
Let 448/3*w + 1336/9 + 38*w**2 + 2/9*w**3 = 0. Calculate w.
-167, -2
Let x(b) be the third derivative of 11*b**5/240 - 31*b**4/8 - 17*b**3/6 - 721*b**2. Factor x(l).
(l - 34)*(11*l + 2)/4
Let d = -160 + 167. Let r(u) = -3*u**4 - 15*u**3 - 9*u**2. Let x(m) = -6*m**4 - 30*m**3 - 17*m**2. Let q(b) = d*r(b) - 3*x(b). Determine i so that q(i) = 0.
-4, -1, 0
Let i(l) = -2*l**3 + 37*l**2 - 98*l + 292. Let x be i(16). Find v such that -18*v - 105/2*v**x - 157/2*v**3 - 111/2*v**2 - 27/2*v**5 - 2 = 0.
-1, -2/3, -2/9
Let a = -1601 - -1603. Let c(m) be the first derivative of -4/5*m + 16 + 2/15*m**3 + 1/5*m**a. Let c(q) = 0. Calculate q.
-2, 1
Suppose -354*g + 82 = -313*g. Let t(d) be the second derivative of 2*d**4 - g*d + 0 - 3/4*d**5 + 0*d**2 - 3/2*d**3. Suppose t(x) = 0. Calculate x.
0, 3/5, 1
Let z = -7994961/5 + 1598993. Suppose 3*s - 6 = -0*s. Factor -z*k**s - 4/5*k + 0.
-4*k*(k + 1)/5
Let l(b) be the second derivative of -b**5/140 - 2075*b**4/84 - 1077443*b**3/42 - 1075369*b**2/14 - b - 1996. Factor l(z).
-(z + 1)*(z + 1037)**2/7
Let m(h) = 80*h**3 + 655*h**2 - 1555*h - 7040. Let b(y) = -5*y**3 - 41*y**2 + 98*y + 440. Let z(d) = -65*b(d) - 4*m(d). Factor z(k).
5*(k - 4)*(k + 2)*(k + 11)
Let r(x) be the second derivative of -x**7/399 + x**6/285 + 3*x**5/95 - 2*x**4/57 - 8*x**3/57 - 678*x. Solve r(g) = 0.
-2, -1, 0, 2
Let l(i) be the second derivative of -i**7/504 + 7*i**6/144 + 4*i**4 - 2*i + 6. Let p(b) be the third derivative of l(b). Factor p(w).
-5*w*(w - 7)
Let i(x) be the first derivative of x**6 + 21*x**5/5 - 9*x**4/2 - 7*x**3 + 6*x**2 + 2655. Suppose i(m) = 0. What is m?
-4, -1, 0, 1/2, 1
Let q(f) be the second derivative of 8 + 1/36*f**4 - 11/18*f**3 - f + 3*f**2. Factor q(m).
(m - 9)*(m - 2)/3
Let u = -4465 + 4468. Solve -3/7*v**5 - 114/7*v**2 + 0 - 30/7*v**4 + 108/7*v**u + 39/7*v = 0.
-13, 0, 1
Let z(v) be the third derivative of -1/1848*v**8 - 4/33*v**4 + 0*v**3 + 0*v**7 - 5*v**2 - 3 + 0*v + 0*v**5 + 2/165*v**6. Suppose z(k) = 0. Calculate k.
-2, 0, 2
Let p = 51931/1470 - -3/490. Let u = -35 + p. Solve -2 - u*q**2 + 5/3*q = 0 for q.
2, 3
Determine j, given that 3201*j**3 - 279*j**5 + 2565*j**4 + 290*j**5 + 3467*j**2 + 462*j + 2358*j**3 = 0.
-231, -1, -2/11, 0
Let o(v) be the third derivative of v**6/24 + 2*v**5 + 125*v**4/8 - 250*v**3/3 + 3*v**2 + 23*v. Solve o(k) = 0 for k.
-20, -5, 1
Let m(q) be the second derivative of -q**5/5 - 17*q**4/3 + 2*q**3/3 + 34*q**2 - 843*q. Factor m(n).
-4*(n - 1)*(n + 1)*(n + 17)
Let m = 220 - 218. Suppose -3*j - m = 4*u + 4, -u - 5 = -j. Factor 1/2*d**j + 0 + 1/4*d**5 + 0*d**3 - 1/2*d**4 - 1/4*d.
d*(d - 1)**3*(d + 1)/4
Let j = -108 - -127. Determine d so that 62*d**3 + 16*d**2 - j*d**2 + d - 59*d**3 - 7*d = 0.
-1, 0, 2
Let b(f) = 6*f - 63. Let d be b(11). Let t(l) be the third derivative of 1/270*l**5 + 1/360*l**6 + 0 - 7/216*l**4 - 11*l**2 + 1/27*l**d + 0*l. Factor t(u).
(u - 1)*(u + 2)*(3*u - 1)/9
Let k(d) = d**3 + 9*d**2 - 25*d - 114. Let t be k(-9). Let a be -17 + t/6 + (-1)/(-2). Factor -4/3*f**a - 48 - 16*f.
-4*(f + 6)**2/3
Let q be -4*(-5 - (-150)/18)*153/(-408). Factor 2*o**2 + 30/7*o**3 + 18/7*o**4 + 0*o + 0 + 2/7*o**q.
2*o**2*(o + 1)**2*(o + 7)/7
Factor 279 + 463*j - 63 + 221*j - 363*j**3 + 187*j**2 + 142*j**2 + j**2.
-3*(j - 2)*(11*j + 6)**2
Let v(j) = 3*j**2 + 2044*j - 208080. Let y(o) = -7*o**2 - 6131*o + 624240. Let k(d) = -11*v(d) - 4*y(d). Solve k(w) = 0.
204
Let o(p) = p**2 - 4*p - 117. Let m be o(-9). Let w(j) be the first derivative of -20/3*j**3 - 2*j**5 + m*j - 5/2*j**2 - 25/4*j**4 + 23. Factor w(n).
-5*n*(n + 1)**2*(2*n + 1)
Suppose 90 = -r - 4*m, 89*r - 88*r - 4*m = 94. What is u in 45 + 5/4*u**r + 75/4*u = 0?
-12, -3
Suppose 0 = 45*w - 49*w + 1404. Let g = w - 1748/5. Factor 1/5*c**4 - 6/5 - g*c**2 + 13/5*c - 1/5*c**3.
(c - 2)*(c - 1)**2*(c + 3)/5
Let x(n) be the third derivative of n**8/168 + n**7/105 - 2*n**6/15 - 4*n**5/15 + 4*n**4/3 + 16*n**3/3 + 80*n**2. Find c such that x(c) = 0.
-2, -1, 2
Suppose 3*u + 4*o = 3*o + 8, 0 = -5*u - 3*o + 20. Let d be (19 - 20) + (5 - u). Find h, given that 2/3*h**4 + 0 + 1/3*h**5 + 0*h - 2/3*h**2 - 1/3*h**d = 0.
-2, -1, 0, 1
Let j(v) = v**3 - 34*v**2 - 173*v + 2. Let d be j(39). Let h = d - 854. Suppose -6*l**4 + 3/2*l + 0 - 3/2*l**3 + h*l**2 = 0. What is l?
-1, -1/4, 0, 1
Factor 6/5*l**5 + 0 + 8*l**3 + 16/5*l**2 + 0*l + 28/5*l**4.
2*l**2*(l + 2)**2*(3*l + 2)/5
Let v(x) be the first derivative of 12/5*x + 2/3*x**3 + 17/5*x**2 + 102. Determine y so that v(y) = 0.
-3, -2/5
Let p(o) be the third derivative of -o**6/320 - 157*o**5/160 - 195*o**4/2 - 1521*o**3/4 + 29*o**2 - 31. Solve p(g) = 0 for g.
-78, -1
Suppose 20 = -5*b, 4200 - 451 = 3*p - 5*b. Suppose 6*j + p - 1261 = 0. Factor -2 + 21/2*o - 9/4*o**j - 25/4*o**2.
-(o - 1)*(o + 4)*(9*o - 2)/4
Let q(o) be the second derivative of -3*o**6/320 + o**5/32 + o**4/32 - 21*o**2/2 - 44*o. Let b(u) be the first derivative of q(u). Factor b(t).
-3*t*(t - 2)*(3*t + 1)/8
Let o be -6 + 132 + 2 + -3. Determine i so that -o*i + 9216 - 165*i - 94*i + 4*i**2 = 0.
48
Let u(v) = 22*v - 393. Let x be u(18). Let w(c) = -c**3 + c**2 - c - 1. Let f be w(-1). Factor 1 - 11*n**2 + 2 + x*n**3 + 14*n**f + 9*n + 6*n**2.
3*(n + 1)**3
Let h(p) = -3*p**5 + p**4 - p**2 - p - 1. Let i(z) = -11*z**5 + 10*z**4 + 12*z**3 + 4*z**2 - 4*z - 4. Let s(x) = 4*h(x) - i(x). Factor s(v).
-v**2*(v + 2)**3
Suppose -15 = 2*n - 7*n. Suppose -5*y + 237 = 2*k - 58, 3*y = n*k - 495. Solve -690*x**3 + 40*x + 22