 19. Let k = 51 + -37. Let a(l) = 64*l**3 + 116*l**2 - 246*l + 94. Let u(d) = k*c(d) - 3*a(d). Factor u(p).
-2*(p - 1)*(p + 4)*(5*p - 2)
Let j(x) be the first derivative of 3*x**5/10 - 3*x**4/2 - 47*x**3/2 + 315*x**2/2 - 12381. Factor j(w).
3*w*(w - 6)*(w - 5)*(w + 7)/2
Let g(j) = -75*j**3 + 114*j**2 + 248*j + 52. Let o(r) = -50*r**3 + 75*r**2 + 165*r + 35. Let v(n) = -5*g(n) + 7*o(n). Suppose v(q) = 0. Calculate q.
-1, -1/5, 3
Factor 108446 - 16*k**2 + 13*k**2 - 108446 - 54*k.
-3*k*(k + 18)
Let y(f) = -5*f**2 + 1000*f - 6419. Let p(o) = o**2 - 200*o + 1287. Let b(c) = 21*p(c) + 4*y(c). Let b(q) = 0. Calculate q.
7, 193
Suppose -20 = -2*z + 2*d, 2*z - d - 2 - 13 = 0. Factor v**z + 0*v**5 + 45*v + 2*v**4 - 18*v**3 - 34*v - 34*v + 32*v**2 + 6.
(v - 1)**4*(v + 6)
Let u = 2648/3909 - 14/1303. Find h such that -4*h**3 + 0 + 6*h**2 + u*h**4 + 0*h = 0.
0, 3
Let 1/3*z**3 + 3*z + 4*z**2 - 22/3 = 0. Calculate z.
-11, -2, 1
Let u = 349/10 - 8528/245. Let p = 5/98 + u. Factor c - p*c**3 + 4/7 + 2/7*c**2.
-(c - 4)*(c + 1)**2/7
Let q = 2319/15521 - 29/913. Factor q*b**2 + 2/17*b + 0.
2*b*(b + 1)/17
Let i(c) = -c**2 - 37*c + 596. Let a(m) = -5*m**2 - 142*m + 2383. Let b(v) = 4*a(v) - 18*i(v). Find w such that b(w) = 0.
23, 26
Let k be 38/(21546/14715) + 160/28 + -5. Factor -k - 4/3*o**2 + 12*o.
-4*(o - 5)*(o - 4)/3
Suppose -19 - 13 - 33 = -5*i. Let u(z) be the first derivative of 1/10*z**5 - 5/6*z**3 - i + 2*z + 3/4*z**2 - 3/8*z**4. Suppose u(l) = 0. What is l?
-1, 1, 4
Let b(v) be the first derivative of 1/22*v**4 + 0*v + 128 - 14/33*v**3 + 6/11*v**2. Factor b(a).
2*a*(a - 6)*(a - 1)/11
Factor 39*t - 21*t + 31*t + t**2 + 2*t.
t*(t + 51)
Let 13182000 - 3/4*r**3 - 152100*r + 585*r**2 = 0. Calculate r.
260
Suppose 86*i - 14*i + 20592 = 0. Let d = -857/3 - i. Solve -d*o**2 + 0*o + 1/3*o**3 + 0 = 0.
0, 1
Let n(a) = a**3 + 13*a**2 + 23*a + 86. Let z be n(-9). Solve -z*v**5 - v**4 + 160 - 136*v**2 - 48*v - 4*v**3 + 25*v**4 + 207*v**5 = 0.
-5, -2, 1, 2
Let r(s) be the first derivative of -s**3/15 - 3*s**2/2 + 16*s/5 + 1463. Factor r(m).
-(m - 1)*(m + 16)/5
Suppose -572*d - 2/3*d**2 + 1718/3 = 0. What is d?
-859, 1
Let t(g) be the first derivative of g**5/330 + 5*g**4/66 - 8*g**3/11 - 81*g**2/2 - 50. Let f(b) be the second derivative of t(b). Factor f(k).
2*(k - 2)*(k + 12)/11
Let x(k) be the first derivative of -k**4/6 - 656*k**3/9 - 26228*k**2/3 + 220448*k/3 - 14316. Factor x(t).
-2*(t - 4)*(t + 166)**2/3
Let g(x) = 5*x**3 - 2*x**2 + 1. Let l(d) = -40*d**5 - 62*d**4 + 114*d**3 + 266*d**2 + 64*d - 30. Let y(c) = -6*g(c) - l(c). Determine f so that y(f) = 0.
-2, -1, -3/4, 1/5, 2
Let f(z) be the second derivative of z**5/270 + 7*z**4/54 + 40*z**3/27 - 126*z**2 + 71*z - 1. Let j(m) be the first derivative of f(m). What is c in j(c) = 0?
-10, -4
What is s in 53138/3 + 2/3*s**2 + 652/3*s = 0?
-163
Let f(x) be the third derivative of 0 - 1/70*x**6 + 0*x**3 - 3/70*x**5 + 0*x**4 + 1/245*x**7 + 147*x**2 + 0*x. Determine u, given that f(u) = 0.
-1, 0, 3
Let b(j) be the second derivative of j**6/60 + j**5/4 - 13*j**4/6 + 14*j**3/3 - 7858*j. Find u, given that b(u) = 0.
-14, 0, 2
Suppose -4*t - 2*s + 26 = 0, -3*s - 17 = -2*t - 0. Suppose -16 - 13 + 5 + a**2 - t*a**2 - 40*a = 0. What is a?
-6, -2/3
Suppose -131*y - 76 + 534 + 590 = 0. Determine k so that -4/7*k**2 + 20/7*k + y = 0.
-2, 7
Let p(z) = -z**3 - 44*z**2 - 29*z - 1. Let j(y) = 6*y**2 + 4*y. Let h(l) = -15*j(l) - 2*p(l). Factor h(i).
2*(i - 1)**2*(i + 1)
Let m(i) = i**2 + 140*i - 2325. Let c be m(15). Let l(w) be the second derivative of 8*w - 16/3*w**3 - 1/3*w**4 + c - 14*w**2. Suppose l(b) = 0. What is b?
-7, -1
Let d(i) be the second derivative of i**6/360 + i**5/120 - i**4/4 + 13*i**3/6 - 3*i**2/2 + 26*i. Let n(f) be the second derivative of d(f). Factor n(c).
(c - 2)*(c + 3)
Let n be ((-35)/30 + 1)*16989/(-4045). Factor n*t + 1/2*t**2 + 3/10 + 1/10*t**3.
(t + 1)**2*(t + 3)/10
Let w = 4026 - 20118/5. Let q be 0 - (-7)/(140/16). Suppose -q*b**3 + 12/5*b**2 - w + 4/5*b = 0. Calculate b.
-1, 1, 3
Let l be 19*36/(-1368)*0. Solve -j**4 + 0*j - 1/3*j**5 + 4/3*j**2 + 0 + l*j**3 = 0.
-2, 0, 1
Let b(g) be the first derivative of g**3/3 + 11*g**2/2 + 21*g + 13. Let o be b(-9). Factor 408*i - 404*i - o*i**2 - i**2.
-4*i*(i - 1)
Let y(i) be the second derivative of i**5/5 - i**4 - 20*i**3/3 + 5857*i. Suppose y(g) = 0. Calculate g.
-2, 0, 5
Suppose 0 = 4*s - 7 - 1. Let u be s*5/(-10) + 4. Determine n so that 1 - u*n**3 - 9*n + 0 - 3 - 1 - 9*n**2 = 0.
-1
Let f(l) be the third derivative of -l**5/20 + 17*l**4/8 - 30*l**3 + 835*l**2. Solve f(n) = 0 for n.
5, 12
Suppose 0 = 32*l - 7*l - 125. Let h be -7 + ((-114)/(-9) - l). Find y such that 7/3*y**2 + 5/3*y**4 - 1/3*y**5 - 3*y**3 - h*y + 0 = 0.
0, 1, 2
Let a(m) be the second derivative of -m**7/210 + m**5/25 - m**4/30 - m**3/10 + m**2/5 - 3573*m. Factor a(z).
-(z - 1)**3*(z + 1)*(z + 2)/5
Let d = -335627 - -2349390/7. Let -1/7 + 2/7*c**2 - d*c**4 - 2/7*c**3 + 1/7*c + 1/7*c**5 = 0. What is c?
-1, 1
Let v(z) be the third derivative of z**9/90720 - z**7/1890 + 3*z**5/10 - 44*z**2. Let m(a) be the third derivative of v(a). Determine j so that m(j) = 0.
-2, 0, 2
Let h(k) be the third derivative of -k**9/151200 + k**8/8400 + 2*k**7/1575 - 5*k**5/6 + 19*k**2. Let n(c) be the third derivative of h(c). Factor n(b).
-2*b*(b - 8)*(b + 2)/5
Let h = -94 + 136. Let a = -11479 - -11481. Solve -11*b**3 + 3*b**3 + a*b**4 - 36*b**2 + h*b**2 = 0 for b.
0, 1, 3
Let u = 5267 + -5263. Find n such that 0 - 5/6*n**u + 0*n + 5/6*n**3 + 5/3*n**2 = 0.
-1, 0, 2
Let w = 928 + -933. Let s(c) = -3*c**2 - 17*c - 6. Let i be s(w). Factor 2/19*z**3 - 2/19*z**2 - 2/19*z + 0 + 2/19*z**i.
2*z*(z - 1)*(z + 1)**2/19
Let l(d) be the third derivative of d**6/60 + 89*d**5/30 + 506*d**4/3 + 1936*d**3/3 + 349*d**2 + 6. Factor l(p).
2*(p + 1)*(p + 44)**2
Let u be (-4)/(-18) + ((-5089)/9)/(-7). Find o, given that -79*o**4 + 0*o**3 + u*o**4 + 4*o**3 = 0.
-2, 0
Let -84/5 + 42/5*o**3 - 9/5*o**2 - 132/5*o + 3/5*o**4 = 0. What is o?
-14, -1, 2
Solve -6110*d**3 + 974*d + 243*d**2 + 275 + 241*d**2 + 6108*d**3 + 213 = 0 for d.
-1, 244
Let g = 115 + -111. Factor -33*w - g*w**3 - 50*w - 24*w**2 + 63*w.
-4*w*(w + 1)*(w + 5)
Let p(j) be the first derivative of j**6/2 - 39*j**5/5 + 153*j**4/4 - 67*j**3 + 42*j**2 - 1927. Find c such that p(c) = 0.
0, 1, 4, 7
Suppose -4*l + v + 122 = 6*v, -l + 2*v = -24. Let r be 38/l + 1/7. Factor 3/4*n**4 - 3/2*n + 0*n**2 - 3/4 + r*n**3.
3*(n - 1)*(n + 1)**3/4
Let w(q) be the third derivative of q**7/735 + 15*q**6/28 + 6154*q**5/105 - 475*q**4 - 17328*q**3/7 + q**2 + 9*q - 19. Suppose w(v) = 0. What is v?
-114, -1, 4
Let r(q) be the second derivative of q**5/220 + 173*q**4/132 - 349*q**3/66 + 175*q**2/22 + 11664*q. Factor r(y).
(y - 1)**2*(y + 175)/11
Suppose 4*n - 12*n - 1840 = 0. Let r = -2528/11 - n. Factor 14/11*q - 10/11*q**2 - 6/11 + r*q**3.
2*(q - 3)*(q - 1)**2/11
Suppose -5*w + 3*c - 17487 = -6*w, 2*w - 34981 = c. Let w + 2*y**2 + 31*y + 7*y - 17530 = 0. What is y?
-20, 1
Let w(v) be the first derivative of -4/7*v + 4/21*v**3 + 29 - 1/14*v**4 + 1/7*v**2. Find y such that w(y) = 0.
-1, 1, 2
Suppose 7 = -u + 81861*d - 81860*d, 2*d - 20 = -u. Find h such that -4/3*h - 1/3*h**u + 4 = 0.
-6, 2
Suppose r = 3*r + 5*w + 7, 0 = -5*r + 4*w - 1. Let t(b) = -4*b**3 - 20*b + 8. Let k = -6 - -22. Let x(h) = -h**2. Let o(i) = k*x(i) + r*t(i). Factor o(a).
4*(a - 2)*(a - 1)**2
Suppose 3/4*b**2 - b**3 + 91/4*b + 69/2 = 0. Calculate b.
-3, -2, 23/4
Let g(j) be the third derivative of 6*j + 0 + 2/3*j**3 + j**2 - 1/15*j**5 + 1/30*j**6 - 1/6*j**4. Solve g(c) = 0 for c.
-1, 1
Let t(l) be the first derivative of -9*l**3 + 190 + 3/4*l**4 + 30*l**2 + 0*l. Find p, given that t(p) = 0.
0, 4, 5
Let y be -6 + -7 + (-6 - -21). Suppose -3 - 10 - 22 - 29 - 4*w**y - 40*w = 0. Calculate w.
-8, -2
Let x = -31006 - -91181/3. Let n = -609 - x. Solve -20/3 + 40/3*b - 5*b**2 - n*b**3 + 5/3*b**4 = 0.
-2, 1, 2
Let p = -43 - -45. Determine s, given that -18*s**p + 4800 + 72*s - 312*s + 21*s**2 = 0.
40
Factor 70823 - 35526 - 232*o - 2*o**2 - 35527.
-2*(o + 1)*(o + 115)
Let v be (17 - 22)*1*-13. Let -14*c**2 - 58*c**2 + 27*c**2 - 15*c**5 - 20 - v*c**3 + 80*c + 65*c**4 = 0. Calculate c.
-1, 1/3, 1, 2
Let m(p) be the first derivative of -