 i(w) be the third derivative of -w**5/360 - 7*w**4/72 - 13*w**3/36 - 1860*w**2. Factor i(g).
-(g + 1)*(g + 13)/6
Let z(i) = 3*i**3 - i**2 - 2*i + 1. Let q(o) = -o**5 - 166*o**4 - 513*o**3 - 483*o**2 - 149*o - 7. Let x(p) = -3*q(p) - 21*z(p). Factor x(w).
3*w*(w + 1)**3*(w + 163)
Let o be 2/(-78)*(-22)/143*13. Let n(f) be the first derivative of -2/13*f**2 - 2/13*f - o*f**3 - 15. Factor n(l).
-2*(l + 1)**2/13
Solve -62/13*i**3 - 2/13*i**5 - 80/13*i + 102/13*i**2 + 18/13*i**4 + 24/13 = 0.
1, 2, 3
Let d(s) be the second derivative of -s**4/42 - 71*s**3/21 + 300*s**2/7 - 1835*s. Factor d(b).
-2*(b - 4)*(b + 75)/7
Let l(k) = -k**3 + 3*k**2 - 5669*k + 17009. Let u be l(3). Factor -4*m - 1/4*m**u + 0.
-m*(m + 16)/4
Solve 2/3*o**4 + 496/3*o + 44/3*o**3 - 542/3*o**2 + 0 = 0 for o.
-31, 0, 1, 8
Factor 2/11*h**2 + 0 + 372/11*h.
2*h*(h + 186)/11
Let m(h) be the third derivative of -2*h**7/525 + h**6/75 + 11*h**5/25 - 3*h**4 + 6765*h**2. Find g, given that m(g) = 0.
-6, 0, 3, 5
Factor 0 + 47*k**3 + 0*k**2 + 1/4*k**4 + 0*k.
k**3*(k + 188)/4
Let p(g) be the first derivative of 27*g - 5*g**3 + 3/4*g**4 - 45 + 9/2*g**2. Let p(n) = 0. What is n?
-1, 3
Let h(v) be the first derivative of 3*v**4/8 - 17*v**3/2 + 99*v**2/2 + 325. Factor h(u).
3*u*(u - 11)*(u - 6)/2
Let v = -64 + 65. Let w = 2 + v. Factor -2*o**5 - 48*o**w + 19*o**3 + 19*o**3 + 4*o**4 + 16*o**3.
-2*o**3*(o - 3)*(o + 1)
Let u(z) be the third derivative of z**5/30 + 37*z**4/12 + z**2 + 19. What is k in u(k) = 0?
-37, 0
Let d(p) be the second derivative of 23*p**5 + p + 128*p**2 + 2/21*p**7 + 11 + 38/15*p**6 + 241/3*p**4 + 416/3*p**3. Factor d(f).
4*(f + 1)**3*(f + 8)**2
Let p be ((18/(-4))/((-13020)/(-9920)))/(33/(-14)). Solve -2/11*f**4 + 0 + p*f**2 - 4/11*f**3 + 0*f = 0 for f.
-4, 0, 2
Factor -389/2*j + 1 - 195/2*j**2.
-(j + 2)*(195*j - 1)/2
Let t = 101534 + -304598/3. Factor -t*b**2 + 1/3*b**3 + 0 - 5/3*b.
b*(b - 5)*(b + 1)/3
Let v be -4*4/(-8) - 0. Let k = -245 + 253. Factor 5*p**2 + p + k*p**2 - 11*p - 11*p**v.
2*p*(p - 5)
Factor 31939/2*l - 1/2*l**4 + 0 + 101/2*l**3 - 3239/2*l**2.
-l*(l - 41)**2*(l - 19)/2
Let r(d) = -13*d - 49. Let x be r(-6). Factor 9*t**2 + 18*t**3 - 48*t**4 + 41*t**4 - x*t**2 + 8*t + t**5.
t*(t - 2)**3*(t - 1)
Let -1/6*x**2 - 163/2*x - 487/3 = 0. What is x?
-487, -2
Let z = 4935/8 - 39791/72. Factor -170/3*n - 22/3*n**2 - 2/9*n**3 + z.
-2*(n - 1)*(n + 17)**2/9
Let o(a) be the third derivative of 6/5*a**5 + a**4 - 2/5*a**6 + 130*a**2 + 0*a**3 + 0*a + 0 - 3/35*a**7 + 1/32*a**8. Solve o(r) = 0 for r.
-2, -2/7, 0, 2
Let k = 23772 - 23768. Let s(l) be the first derivative of 0*l - 2*l**2 - 10/3*l**3 - 2/5*l**5 + 33 - 2*l**k. Factor s(w).
-2*w*(w + 1)**2*(w + 2)
Let c(r) be the second derivative of 7921*r**5/5 + 13083*r**4 - 1184*r**3 + 40*r**2 - 2950*r. Factor c(w).
4*(w + 5)*(89*w - 2)**2
Factor -101/2*t + 1/2*t**3 + 1/2*t**2 + 99/2.
(t - 9)*(t - 1)*(t + 11)/2
Let j = 919 - 1095. Let k be 1*(j/(-20) + -7). Factor k*q**2 - 3/5 + 6/5*q.
3*(q + 1)*(3*q - 1)/5
Let j(g) be the first derivative of -2/15*g**3 + 16/15*g + 23/15*g**2 - 88. Factor j(o).
-2*(o - 8)*(3*o + 1)/15
Let c be (2 - 1)/((255/20)/51). Let l(t) be the second derivative of 0 + 0*t**3 + 0*t**2 + c*t + 1/33*t**4 - 1/165*t**6 - 1/110*t**5. Factor l(h).
-2*h**2*(h - 1)*(h + 2)/11
Let t = 143456 + -430352/3. Determine r so that 10/3*r**2 + t*r + 2 = 0.
-1, -3/5
Let g(m) be the first derivative of -m**5/20 + m**4 - 6*m**3 + 16*m**2 + 44*m + 78. Let v(j) be the first derivative of g(j). Determine r, given that v(r) = 0.
2, 8
Let t(l) be the third derivative of 0*l - 7/8*l**4 + 0 + 119*l**2 - 1/60*l**5 - 10/3*l**3. Factor t(k).
-(k + 1)*(k + 20)
Let j(z) be the second derivative of 3*z**6/55 - 93*z**5/55 - 237*z**4/22 - 72*z**3/11 + 2241*z. Find r, given that j(r) = 0.
-3, -1/3, 0, 24
Solve 24536*x**2 + 1604*x**4 - 120 + 24540*x**2 - 436*x + 560*x**5 - 49104*x**2 + 1332*x**3 = 0 for x.
-1, -2/5, 15/28
Let z(d) be the third derivative of -3*d**5/80 + 253*d**4/48 - 14*d**3/3 + 1081*d**2. Factor z(r).
-(r - 56)*(9*r - 2)/4
Let b be (-10)/(-4)*102/(-255)*0/(-7). Let n be 0 - 0 - (-4 + 1). Find g such that -5/4*g**n - 3*g**2 + b - g = 0.
-2, -2/5, 0
Let p(a) be the first derivative of a**7/1680 - 7*a**5/160 - 5*a**4/48 - 115*a**2/2 - 93. Let m(j) be the second derivative of p(j). Factor m(h).
h*(h - 5)*(h + 1)*(h + 4)/8
Let p(s) be the first derivative of s**4/2 + 247*s**3/9 + 41*s**2/6 + 438. Factor p(u).
u*(u + 41)*(6*u + 1)/3
Let u(f) be the first derivative of -4*f**3/21 + 10868*f**2/7 - 29528356*f/7 + 5487. Find o such that u(o) = 0.
2717
What is k in 0 - 13/3*k**3 + 100/3*k - 1/3*k**4 - 20/3*k**2 = 0?
-10, -5, 0, 2
Let z = -595 - -606. Suppose -29*p = z*p. Let 1/4*c**4 - c**2 + p - c**3 + 0*c + 1/4*c**5 = 0. What is c?
-2, -1, 0, 2
Determine x, given that 222*x - 334*x**3 - 13*x**2 + 109*x**4 + 122*x**2 - 106*x**4 = 0.
-2/3, 0, 1, 111
Let f be ((-372)/(-3255) - 275/(-5250))/(-1 + (-29)/(-24)). Determine i so that 0*i + f*i**5 + 0*i**2 + 0 + 52/5*i**4 - 56/5*i**3 = 0.
-14, 0, 1
Let r(a) be the first derivative of -a**3/7 + 1143*a**2/14 + 920. Find u, given that r(u) = 0.
0, 381
Let t(g) = 27*g**3 + 269*g**2 + 367*g - 96. Let o(a) = -135*a**3 - 1344*a**2 - 1836*a + 480. Let p(b) = -5*o(b) - 24*t(b). Factor p(q).
3*(q + 2)*(q + 8)*(9*q - 2)
Let y = -31 - -49. Suppose -11*z + 2*z + y = 0. Factor 2*p + 129*p**z - 125*p**2 - 2*p**3 + p**4 - 5*p**4.
-2*p*(p - 1)*(p + 1)*(2*p + 1)
Let m(x) be the first derivative of -16*x**4/9 - 352*x**3/27 - 34*x**2 - 36*x - 5394. Let m(v) = 0. What is v?
-9/4, -1
Let p(s) = -s**3 - 25*s**2 - 47*s - 19. Let k be p(-23). Let w(c) = -7*c**2 - 20*c + 4. Let i(y) = 9*y**2 + 21*y - 5. Let x(z) = k*i(z) + 5*w(z). Factor x(d).
d*(d - 16)
Solve 920 - 12*l**4 + 49*l**2 - 101*l**2 + 10*l**4 + 1186*l**2 - 1832*l - 220*l**3 = 0.
-115, 1, 2
Let s(h) be the third derivative of -2 - 1/24*h**4 - 1/30*h**5 - 26*h**2 + 0*h + 0*h**3 - 1/120*h**6. Factor s(n).
-n*(n + 1)**2
Let u be 9/(90/(-76)) - (-4 + -4). Let x(n) = n + 12. Let q be x(-8). Factor -q*c - 10 - u*c**2.
-2*(c + 5)**2/5
Let l(i) = 2*i**3 + 177*i**2 + 85*i - 260. Let c be l(-88). Let v(z) be the first derivative of z**2 - 7 - 2/3*z**3 + c*z. Factor v(n).
-2*(n - 2)*(n + 1)
Let b be (9 + -18 + 10)*(-2 - -4) - 2384/(-745). Factor 1/5*v**2 - 5*v - b.
(v - 26)*(v + 1)/5
Let u(n) be the first derivative of -n**4/36 - 34*n**3/27 - 83*n**2/6 - 24*n + 1286. Solve u(f) = 0 for f.
-24, -9, -1
Let h(l) = l**2 + 16*l + 30. Let q be h(-14). Suppose 0 = -3*w + c + q*c + 72, -5*c - 8 = -w. Factor -w*s - 3 - 21 + 6*s**2 + 16*s + 3*s**3.
3*(s - 2)*(s + 2)**2
Let v(t) be the third derivative of -t**7/175 - 9*t**6/100 - 12*t**5/25 - 4*t**4/5 - 680*t**2. Factor v(b).
-6*b*(b + 1)*(b + 4)**2/5
Let i = -1336/63 + 1448/63. Solve i*m - 2/9*m**4 - 10/9*m**3 - 4/9*m**2 + 0 = 0 for m.
-4, -2, 0, 1
Let d be (-2)/(-63)*-21 + 8/3. Factor 20/9*t + 2/9*t**d + 2.
2*(t + 1)*(t + 9)/9
Let m be (25/2400*-12)/(10/(-4)). Let y(f) be the second derivative of 0 + 1/2*f**2 + m*f**5 + 33*f + 1/4*f**4 + 1/2*f**3. Factor y(g).
(g + 1)**3
Suppose 1/4*g**5 + 0*g - 1/2*g**2 + 1/2*g**4 + 0 - 1/4*g**3 = 0. What is g?
-2, -1, 0, 1
Let o(y) be the second derivative of 2*y**6/15 - 3*y**5 + 26*y**4 - 320*y**3/3 + 192*y**2 - 14*y + 122. What is f in o(f) = 0?
1, 4, 6
Factor 5835*y + 4*y**2 + 553798 + 934602 - 955*y.
4*(y + 610)**2
Let c(q) be the third derivative of -q**5/15 - 77*q**4/6 - 1340*q**3/3 + 4*q**2 + 361*q + 1. Suppose c(y) = 0. Calculate y.
-67, -10
Let f = 3799/494 + 694/247. Factor 9 + 3/2*s**2 + f*s.
3*(s + 1)*(s + 6)/2
Let q be (-399)/(-1463) - (-96)/132. Factor 5/7*w**2 + q - 13/7*w + 1/7*w**3.
(w - 1)**2*(w + 7)/7
Let n(t) be the third derivative of 19*t**3 + 1/30*t**5 - 192*t**2 + 0 + 29/6*t**4 + 0*t. Solve n(a) = 0.
-57, -1
Factor 4/7*w**5 + 1056/7*w - 156/7*w**4 + 120*w**3 - 1616/7*w**2 + 0.
4*w*(w - 33)*(w - 2)**3/7
Let b be (-72)/(-15) + 20/(-25). Factor 3*d**2 + 18*d + 16*d**3 - d**2 - b*d**4 - 34*d + 2*d**4.
-2*d*(d - 8)*(d - 1)*(d + 1)
Let y = -3277 - -3297. Let t(q) be the second derivative of 3/4*q**4 + 0 - y*q - 1/40*q**5 - 9*q**3 + 54*q**2. Determine o so that t(o) = 0.
6
Factor 193*s**2 + 270*s**2 - 2 + 315*s + 605*s**2 + 756*s + 5.
3*(s + 1)*(356*s + 1)
Let z = 86212 +