2*u. Let z(m) = 90*m**2 + 163*m - 580. Let l(w) = -7*q(w) - z(w). Factor l(p).
(p - 145)*(p - 4)
Let z = 33173/159000 + -2/6625. Let i(g) be the third derivative of 2/3*g**3 + 0 - z*g**4 + 0*g + 1/60*g**5 - 3*g**2. Factor i(w).
(w - 4)*(w - 1)
Let v = 39249 + -39249. Let -8/3*l**2 + 2/3*l**3 + 0 + v*l = 0. What is l?
0, 4
Let b = -381 + 390. Let c be ((-4)/15)/((-60)/b - -6). Suppose c*u + 2/5*u**2 + 0 = 0. Calculate u.
-1, 0
Suppose -15*g + 223 = -14*g - 2*u, 0 = 5*g - u - 1097. Let j = -4159/19 + g. Suppose 6/19*y - 6/19*y**3 + j*y**2 + 2/19*y**4 - 4/19 = 0. What is y?
-1, 1, 2
Let w(h) be the first derivative of 0*h**2 - 25*h + 0*h**4 - 18 - 1/150*h**6 - 2/15*h**3 + 3/100*h**5. Let n(m) be the first derivative of w(m). Factor n(p).
-p*(p - 2)**2*(p + 1)/5
Let k = -194 + -168. Let y = k + 362. Suppose y*w + 0 + 0*w**2 + 0*w**3 - 2/15*w**5 + 4/15*w**4 = 0. Calculate w.
0, 2
Let x(h) be the first derivative of h**3/6 + 19*h**2/4 - 3055. Solve x(y) = 0.
-19, 0
Let n = 9057999/10786895 - 2/1540985. Let p = -11/41 + n. Factor 2/7*m**2 + 0 - p*m + 2/7*m**3.
2*m*(m - 1)*(m + 2)/7
Let b(v) = 11*v**3 + 36*v**2 - 63*v - 211. Let c be b(-3). Solve -i**4 + 0 - 5/2*i**3 + 1/6*i**c - 4/3*i**2 + 0*i = 0.
-1, 0, 8
Suppose 0 = -2*k + z + 1673, -9*z + 10*z + 3349 = 4*k. Let n = k + -2512/3. Factor 4/3*a**3 - 2/3*a**2 + 4/3*a**4 - 5/3*a - n + 1/3*a**5.
(a - 1)*(a + 1)**3*(a + 2)/3
Let s(h) be the second derivative of 4 - 3*h + 8/9*h**3 + 7/3*h**2 + 1/18*h**4. Factor s(j).
2*(j + 1)*(j + 7)/3
Let o = 24/19 + -241/266. Let k(p) be the first derivative of o*p**2 + 10 - 6/7*p - 1/21*p**3. Factor k(u).
-(u - 3)*(u - 2)/7
Let u(t) = -t**2 - 19*t - 88. Let i(b) = 5*b + 79. Let k be i(-18). Let h be u(k). Factor -6/5*j**3 + h + 0*j + 18/5*j**2.
-6*j**2*(j - 3)/5
Suppose 0 = -b + 4*q + 15, 34*b + q = 30*b + 9. Find s, given that 3*s**2 + 0 - 1/5*s**b + 0*s - 3*s**4 + 1/5*s**5 = 0.
-1, 0, 1, 15
Let d(b) be the third derivative of b**5/15 - 125*b**4/6 - 84*b**3 - 2*b**2 - 3*b + 330. Suppose d(p) = 0. What is p?
-1, 126
Let g(c) be the third derivative of -c**8/80640 + c**7/2880 - c**6/288 + 43*c**5/30 - 5*c**2 + 8*c. Let k(m) be the third derivative of g(m). Factor k(n).
-(n - 5)*(n - 2)/4
Let t = 1/1123212 + 2246417/7862484. Let -t*p**2 - 12/7*p - 16/7 = 0. What is p?
-4, -2
Let o(r) be the second derivative of 12*r**4/5 - 136*r**3 + 2890*r**2 + 1205*r. Factor o(s).
4*(6*s - 85)**2/5
Let h(b) be the first derivative of 0*b + 102 - 44/3*b**3 + 28/5*b**5 + 10*b**4 - 12*b**2. Factor h(j).
4*j*(j - 1)*(j + 2)*(7*j + 3)
Let z(r) = 55*r**2 - 100*r + 110. Let p(f) be the first derivative of -5/3*f**3 + 11 - 10*f + 9/2*f**2. Let l(x) = -65*p(x) - 6*z(x). Factor l(q).
-5*(q - 2)*(q - 1)
Let j(c) be the first derivative of -24 + 1/20*c**5 + 0*c - 1/8*c**4 - 9*c**2 - c**3. Let f(o) be the second derivative of j(o). Find n such that f(n) = 0.
-1, 2
Let v = 130777 - 1050057/8. Let x = -479 - v. Find q, given that 0 + 3/4*q - x*q**2 + 3/8*q**3 = 0.
0, 1, 2
Suppose 2*o + 2*o**4 - 373*o**3 - 274*o**3 + 653*o**3 + 6*o**2 = 0. What is o?
-1, 0
Let v = 426193 - 257846553/605. Let p = 6/121 + v. Factor 4/5*t**2 - 2/5*t - p*t**3 + 0.
-2*t*(t - 1)**2/5
Let n be 0/(-2*3/2). Let i = n + 3. Find u such that -27*u**3 + 2*u + 17*u**i + 11*u**3 - 3*u**2 = 0.
0, 1, 2
Factor -20/3*s**2 + 4/9*s**3 - 176/9 + 64/3*s.
4*(s - 11)*(s - 2)**2/9
Let l(r) be the third derivative of 5*r**8/336 - 5*r**7/21 + 61*r**6/96 + 191*r**5/48 - 545*r**4/48 + 35*r**3/3 - 18*r**2 - 12*r. Solve l(f) = 0.
-2, 1/2, 4, 7
Let s(w) be the second derivative of -46225*w**4/42 - 860*w**3/21 - 4*w**2/7 - 1124*w. Find n such that s(n) = 0.
-2/215
Let n be (-657)/(-33) + (-511)/(-5621). Factor 4/3 + n*g**2 - 64/3*g.
4*(g - 1)*(15*g - 1)/3
Let b(g) be the third derivative of -3*g**6/8 + 179*g**5/6 + 2245*g**4/24 + 205*g**3/3 + 119*g**2 - 7*g. Factor b(d).
-5*(d - 41)*(d + 1)*(9*d + 2)
Let o = -2312454526/1573 + 1470092. Let x = o - -4/121. What is r in -18/13 + 12/13*r - x*r**2 = 0?
3
Let -5354596/7 - 1/7*y**2 - 4628/7*y = 0. What is y?
-2314
Determine q so that -92 - 183*q**3 - 40*q**4 - 140*q + 22 - 284*q**2 - q**5 + 70 = 0.
-35, -2, -1, 0
Let b(x) be the second derivative of x**5/50 - 19*x**4/10 + 18*x**3/5 + 112*x**2/5 - 314*x. Factor b(c).
2*(c - 56)*(c - 2)*(c + 1)/5
Suppose -3*l = -4*g + 4, 3*g + 19 = 7*l + 3. Let v(f) be the second derivative of 1/3*f**g - 2/3*f**3 - 8*f + 0*f**2 + 0. Find c, given that v(c) = 0.
0, 1
Let 52*p**3 - 249*p**2 + 311*p**4 + 194*p - 80*p**5 + 209*p**4 - 251*p**2 - 577*p**3 + 431*p = 0. What is p?
-1, 0, 5/4, 5
Let x be (-1 + 1)*(41924/282 - 149). Let s be 15/28 - (-6)/(-21). Factor 3/2*a**3 + 0 - s*a**4 + 7/4*a**2 + x*a.
-a**2*(a - 7)*(a + 1)/4
Let u(m) = m**2 + 5*m. Let w = 478 + -483. Let b be u(w). Suppose -2/5*o**2 - 8/5*o + b = 0. Calculate o.
-4, 0
Let y(o) be the second derivative of -o**7/168 - 29*o**6/120 - 39*o**5/16 + 89*o**4/48 + 163*o**3/6 + 99*o**2/2 - 10403*o. Determine v so that y(v) = 0.
-18, -11, -1, 2
Let h(i) = 2*i**2 - 2*i + 4. Let s be h(0). Suppose -s*d + 23 - 11 = 0. Factor 1 + 217*y**2 + 2*y**d + 3*y**4 - 2 - 3*y + y**5 - 219*y**2.
(y - 1)*(y + 1)**4
Solve -4095*f + 3632 + 340 - 2*f**2 + 421*f - 296 = 0 for f.
-1838, 1
Suppose 8 = 2*p, 5*a - 3*p - 10 + 7 = 0. Let m be (0 + 0)*(6 - 5). Solve -2/11*w**4 + 0*w**a + m*w + 4/11*w**2 - 2/11 = 0 for w.
-1, 1
Factor -17787/4 - 213/4*v**2 - 3/4*v**3 - 3597/4*v.
-3*(v + 11)**2*(v + 49)/4
Let s = -43/17 - -189/68. Determine b, given that -3/2*b - 9/4 - s*b**2 = 0.
-3
Let k(n) = 3*n**2 + 39*n - 3. Suppose 0 = -4*d - 4*g - 28, 41 - 17 = -3*d - 4*g. Let l(q) = 5*q**2 + 38*q - 4. Let p(u) = d*k(u) + 3*l(u). Factor p(b).
3*b*(b - 14)
Let t(x) be the second derivative of 11 + 1/50*x**6 + 11/10*x**4 + 27/100*x**5 - 48/5*x**2 + x + 0*x**3. Factor t(p).
3*(p - 1)*(p + 2)*(p + 4)**2/5
Let f be -4 - ((-23970)/5990 + 0). Let o = f + 595/2396. Factor -1/4*c**2 + 0 + 0*c + o*c**4 + 0*c**3.
c**2*(c - 1)*(c + 1)/4
Let p = 1262302/21 - 180274/3. Let q = 7 - 5. Factor p - 32/7*c + 2/7*c**q.
2*(c - 8)**2/7
Let r(a) = a**2 - 374*a + 5387. Let f be r(15). Let 2/13 - 4/13*o**3 + 4/13*o + 0*o**f - 2/13*o**4 = 0. Calculate o.
-1, 1
Let w(a) be the first derivative of 5*a**6/6 - a**5 - 55*a**4/4 + 145*a**3/3 - 65*a**2 + 40*a + 1527. Factor w(v).
5*(v - 2)*(v - 1)**3*(v + 4)
Suppose -55*g - 42 = -69*g. Factor -161*a**2 - 405 + 5*a**g + 4*a**2 + 495*a + 62*a**2.
5*(a - 9)**2*(a - 1)
Let 220/19*g - 6*g**2 + 6*g**4 - 218/19*g**3 - 2/19*g**5 + 0 = 0. What is g?
-1, 0, 1, 2, 55
Let l(k) be the first derivative of 321 - 1/14*k**6 - 6/7*k**5 - 96/7*k - 80/7*k**3 - 30/7*k**4 - 120/7*k**2. Solve l(q) = 0.
-2
Let u = -4/42643 - -1620446/127929. Factor 1/3*j**3 + u*j - 7*j**2 + 0.
j*(j - 19)*(j - 2)/3
Factor 17*r**2 + 1/4*r**4 + 35/2*r - 69/4 - 35/2*r**3.
(r - 69)*(r - 1)**2*(r + 1)/4
Factor -4*a - 26625*a**3 - a**2 - 2*a**4 + 3*a**4 + 0*a**4 + 26629*a**3.
a*(a - 1)*(a + 1)*(a + 4)
Let a(t) = 3*t**4 - 87*t**3 - 123*t**2 + 11*t - 11. Let p(r) = r**4 - 21*r**3 - 31*r**2 + 3*r - 3. Let s = 19 + -13. Let l(w) = s*a(w) - 22*p(w). Factor l(y).
-4*y**2*(y + 1)*(y + 14)
Suppose 16*k = -49 - 79. Let d be ((-2)/10)/((80/25)/k). Factor -1/2*a + a**2 + 0 - d*a**3.
-a*(a - 1)**2/2
Let y(s) be the second derivative of -1/3*s**4 + 0*s**2 + 20*s + 0 + 2/3*s**3. Find p such that y(p) = 0.
0, 1
Let y(b) be the first derivative of -7/12*b**3 + 1/16*b**4 - 225 + 3/2*b**2 + 0*b. Factor y(q).
q*(q - 4)*(q - 3)/4
Let m = -1543887/2170 + -57/434. Let t = 712 + m. Factor -t*r**2 + 0 + 2/5*r.
-2*r*(r - 1)/5
Let b be (-1)/14*8*(24 - 26). Let 0 - 8/7*g**2 + b*g + 2/7*g**3 = 0. Calculate g.
0, 2
Suppose -4*b - 2 + 22 = 4*q, -5*q = -b - 25. Let z be 10 - (2/(-10) - 9/(-45)). Suppose -2 - 50*d - q*d**2 - z + 5*d - 28 = 0. What is d?
-8, -1
Let t(o) be the second derivative of o**4/3 - 448*o**3/3 - 2828*o. Factor t(v).
4*v*(v - 224)
Let d(z) be the second derivative of z**5/4 + 15*z**4/2 + 50*z**3 + 140*z**2 - 95*z + 2. Determine k so that d(k) = 0.
-14, -2
Suppose 2311*d**2 - 8973 + 4037059*d**3 - 9750 + 2426*d**2 - 186756*d - 4037089*d**3 = 0. What is d?
-1/10, 79
Factor 3476/3*x - 1/3*x**2 - 3020644/3.
-(x - 1738)**2/3
Let w(d) be the first derivative of -5*d**4/4 - 6815*d**3/3 + 4515. Factor w