d. Suppose -4*r + d = -b + 42, -b - 3*r = -14. Let 126/5*k**3 + 0 + 12/5*k - 66/5*k**2 - 102/5*k**4 + 6*k**b = 0. What is k?
0, 2/5, 1
Let h(j) be the third derivative of j**5/160 - 17*j**4/8 + 399*j**3/16 - 881*j**2 - 2. Factor h(n).
3*(n - 133)*(n - 3)/8
Let n(o) = 3*o**2 - 3755*o + 2. Let r(v) = -39*v**2 + 48621*v - 27. Let u(s) = -27*n(s) - 2*r(s). Factor u(b).
-3*b*(b - 1381)
Let o(t) = -1 - 3*t**4 + 9437*t**3 + t**5 + 3*t**4 - 9436*t**3. Let k(f) = 7*f**5 + 8*f**4 + 8*f**3 - 4. Let n(j) = -5*k(j) + 20*o(j). Let n(z) = 0. What is z?
-2, -2/3, 0
Let b(h) be the second derivative of 79*h**6/150 - 159*h**5/100 - 77*h**4/60 + 53*h**3/10 - h**2/5 - 6667*h. Determine n so that b(n) = 0.
-1, 1/79, 1, 2
Suppose c = -5*x - 3, 10*c - 8*c + 5*x = -1. Factor 14*l + 3*l**3 + 139*l**c + 4*l - 160*l**2.
3*l*(l - 6)*(l - 1)
Let p(t) = 4*t**3 - 391*t**2 - 1659*t - 9. Let j(n) = n**3 - 102*n**2 - 415*n - 2. Let h(v) = -9*j(v) + 2*p(v). Let h(i) = 0. Calculate i.
-3, 0, 139
Find l such that 159/2*l - 486 + 1/4*l**2 = 0.
-324, 6
Let i be 80/64 + (-7)/(-4). Suppose -104*h**3 + 8*h + 2 - 110*h**i + 226*h**3 - 22*h**2 = 0. Calculate h.
-1/6, 1
Let w = 13 + -38. Let n = 40 + w. Factor -n*r**2 - 17*r**2 - 12*r**4 + 60*r**3 - 18*r**4 + 5*r**5 - 18*r**2 + 15*r.
5*r*(r - 3)*(r - 1)**3
Let s(g) = -g**3 + 18*g**2 - 52*g - 19. Let x be s(14). Factor 184*u - 60 + x*u**4 + 21*u + 160*u**3 - 77*u**4 - 68 + 4*u**5 + 115*u - 320*u**2.
4*(u - 2)**5
Let o(p) be the third derivative of 0*p + 2 - 1/120*p**4 - 1/300*p**5 - 5*p**2 + 1/15*p**3. Factor o(m).
-(m - 1)*(m + 2)/5
Let c(s) = 372*s - 356. Let u be c(1). Let o(v) = -2*v**3 - 2*v**2 - 9*v - 1. Let a be o(-6). Let a*y + u*y**2 + 15 - 448*y + 9*y**2 - 5*y**3 = 0. Calculate y.
1, 3
Suppose 43/8*q**2 - 11 + 1/8*q**3 - 23/4*q = 0. Calculate q.
-44, -1, 2
Suppose 37*w - 675 = 11*w - 571. Factor 744*c**2 - 8192 + 95/4*c**3 + 1/4*c**w + 7424*c.
(c - 1)*(c + 32)**3/4
Let c be 7 - 24/10 - (158 - 154). Let 3*n**3 - c*n**4 + 0 + 0*n + 0*n**2 = 0. What is n?
0, 5
Factor 150*w - 201/4 + 3/4*w**4 + 48*w**3 - 297/2*w**2.
3*(w - 1)**3*(w + 67)/4
Let c = 76914/13 - 153815/26. Factor -c*x + 1/4 + 1/4*x**2.
(x - 1)**2/4
Let p(h) be the second derivative of -4/9*h**3 + 0 - 1/8*h**4 + 1/3*h**2 - 22*h. Factor p(t).
-(t + 2)*(9*t - 2)/6
Suppose 20*c - 119 - 281 = 0. Suppose 25*u - 10*u**5 - c*u**2 - 5 - 3*u**3 - 7*u**3 + 25*u**4 + 7*u - 12*u = 0. Calculate u.
-1, 1/2, 1
Let t be ((-20)/30)/(4/6). Let k(f) = -f**2 - 1. Let u(m) = -25*m**3 + 8*m**2 - 2. Let l(y) = t*u(y) + 2*k(y). Factor l(z).
5*z**2*(5*z - 2)
Let u be (-276)/42*(-6391)/132. Let h = u - 318. Factor 0 - h*j**2 + 1/3*j.
-j*(j - 2)/6
Let t = 4319/783 - 146/29. Let l = -11/135 + t. Factor -l - 2*v**2 - 12/5*v.
-2*(v + 1)*(5*v + 1)/5
Let l be (-201)/(-134) + (3 - 4 - 0/1). Let m = 15 - 13. Factor 0 - q + l*q**m.
q*(q - 2)/2
Let f(x) be the first derivative of x**9/1008 - x**7/140 + x**5/40 + x**3 - 42*x + 68. Let i(k) be the third derivative of f(k). Factor i(p).
3*p*(p - 1)**2*(p + 1)**2
Let w(o) be the third derivative of 1/1344*o**8 + 7/24*o**6 + 11/420*o**7 - 147*o**2 + 0*o**4 + 1 + 0*o + 0*o**3 + 5/6*o**5. Factor w(m).
m**2*(m + 2)*(m + 10)**2/4
Let l be 42/(-7)*(-3)/12*14. Factor 18*d + l*d**2 + 5095 + 3*d**3 - 5095.
3*d*(d + 1)*(d + 6)
Factor 3/5*n**2 + 0 + 6*n.
3*n*(n + 10)/5
Factor 0 + 49*z**3 - 1/3*z**4 + 3425/3*z - 465*z**2.
-z*(z - 137)*(z - 5)**2/3
Suppose 4*w - 32 = -12*w. Factor -2231*u**w + 2238*u**2 - u**3 + 6*u + 2*u.
-u*(u - 8)*(u + 1)
Let m(b) be the first derivative of b**6/10 + 66*b**5/25 + 273*b**4/20 + 102*b**3/5 - 12123. Determine d, given that m(d) = 0.
-17, -3, -2, 0
Let w(f) be the second derivative of -11/2*f**4 + 0 - 235*f + 47/2*f**3 - 3*f**2 - 69/20*f**5. Suppose w(t) = 0. Calculate t.
-2, 1/23, 1
Let o be -24 + 19 + 27 + (-2 - -2). Let c(p) be the third derivative of 1/12*p**3 + 3/10*p**5 + 0 + o*p**2 + 0*p - 1/4*p**4. Factor c(b).
(6*b - 1)**2/2
Let z be (-33 - (1044/(-378) + -31))/(4*(-6)/(-140)). Factor 0 - z*g - 2/9*g**2.
-2*g*(g + 20)/9
Let w(s) = 43 + 49 - 8*s - 114*s**2 - 122*s**2 + 237*s**2 - 13*s. Let k be w(15). Factor 78/5*r**k + 66/5*r + 12/5 + 24/5*r**3.
6*(r + 1)*(r + 2)*(4*r + 1)/5
Let f(r) be the second derivative of -r**5/25 + 7*r**4/15 - 28*r**3/15 + 16*r**2/5 - 759*r. Solve f(z) = 0 for z.
1, 2, 4
Let c be 1*(-27)/((-1323)/(-973)) - -20. Factor -c*l**2 - 10/7*l + 1/7*l**3 - 8/7.
(l - 4)*(l + 1)*(l + 2)/7
Let y(s) be the third derivative of -s**7/42 + 67*s**6/24 - 1015*s**5/12 - 6125*s**4/8 - 9*s**2 + 28. Factor y(i).
-5*i*(i - 35)**2*(i + 3)
Let g be (-2)/(-1*(-2)/(-4)). Let u be (20/26)/(41 + 4 - 40). Find k, given that 6/13*k**3 + 0*k**2 + 0 - 4/13*k**g + 0*k - u*k**5 = 0.
-3, 0, 1
Let i = 92/2303 - -18148/6909. Let 3 - 2/3*x**3 - 1/3*x**4 + 6*x + i*x**2 = 0. What is x?
-3, -1, 3
Suppose -211*j = -780 - 64. Let 4/3*l**2 - 4/3*l**3 + 0*l + 0 + 1/3*l**j = 0. What is l?
0, 2
Let s(n) be the second derivative of n**4/30 - 5*n**3 + 146*n**2/5 - 7035*n. What is q in s(q) = 0?
2, 73
Let v(w) = w**2 + 11*w + 2*w**3 - 2*w - 24*w**2. Let g(z) = z**3 - 24*z**2 + 7*z. Let a be (-4)/(-3)*(-4 + 3 - -4). Let b(o) = a*v(o) - 3*g(o). Factor b(r).
5*r*(r - 3)*(r - 1)
Suppose -d - h + 3*h = 2606, 0 = 2*d + 5*h + 5239. Let f = 15673/6 + d. Factor -5/6*w - f*w**2 - 1.
-(w + 2)*(w + 3)/6
Let m(b) = -27*b**4 + 9*b**3. Suppose 0 = 5*g - g + 3*u - 49, -3*g + 40 = -u. Let c(h) = -55*h**4 + 17*h**3 - h**2. Let j(s) = g*m(s) - 6*c(s). Factor j(l).
-3*l**2*(l - 1)*(7*l + 2)
Suppose 24 = -4*a - 12*i + 4*i, 0 = -a - i - 3. Let b(j) be the first derivative of a*j + 1/10*j**4 + 4/15*j**3 - 4/5*j**2 - 22 - 1/25*j**5. Factor b(m).
-m*(m - 2)**2*(m + 2)/5
Let p(h) be the third derivative of -1/300*h**6 + 1/60*h**4 + 1/150*h**5 + 0 - 1/525*h**7 + 0*h**3 - 20*h**2 + 0*h. Factor p(z).
-2*z*(z - 1)*(z + 1)**2/5
Let a = 229316 + -1605211/7. Suppose -a*i**2 - 13/7 - 2*i = 0. Calculate i.
-13, -1
Let o(b) be the third derivative of -1/64*b**4 + 0*b**3 + 0 - 1/320*b**6 + 0*b + 1/80*b**5 - 60*b**2. Solve o(r) = 0 for r.
0, 1
Let c(n) = -7*n - 133. Let g be c(-21). Suppose -12 = g*w - 15*w. Let -w*x**2 - 2/3*x**4 - 14/3*x**3 - 16/3 - 40/3*x = 0. Calculate x.
-2, -1
Let q(n) be the first derivative of 0*n**2 + 5/3*n**3 + 6 + 0*n. Factor q(z).
5*z**2
Solve -59/3*c**2 + 237*c - 12 = 0.
3/59, 12
Suppose 15*i + 33270 = -15*i. Let o = i - -3331/3. Let -4*l**2 + 4 + 2*l**3 + o*l**4 - 10/3*l = 0. Calculate l.
-2, -3/2, 1
Find j, given that 88*j**3 + 1366 - 397*j**2 + 37*j**4 + 117*j**2 - 432*j - 1222 - 167*j**5 + 160*j**5 = 0.
-2, 2/7, 3, 6
Let n(s) be the third derivative of 5*s**4/6 + 10*s**3/3 + 30*s**2 + 3*s. Let l be n(-1). Factor -6/13*w**4 + 0*w + l*w**2 + 0 - 4/13*w**3 - 2/13*w**5.
-2*w**3*(w + 1)*(w + 2)/13
Let u(i) be the second derivative of 7*i**4/15 - 146*i**3/5 + 3644*i. Determine o, given that u(o) = 0.
0, 219/7
Let v(k) = 107*k**2 + 40*k - 264. Let t(h) = 61*h**2 + 20*h - 133. Let x(p) = -7*t(p) + 4*v(p). Let x(j) = 0. Calculate j.
-25, 5
Let y be 27*(170/(-25) - 196/(-28)) + -5. Factor 0 - y*k**2 - 12/5*k.
-2*k*(k + 6)/5
Suppose -12*c + 24576 = -10416. Let p be (15 - 9) + (0 - 4). Suppose -c + 596*i + 294*i + 4*i**3 + 82*i - 108*i**p = 0. What is i?
9
Let m(k) be the first derivative of -9*k**4/26 - 100*k**3/39 - 92*k**2/13 - 112*k/13 - 66. Factor m(g).
-2*(g + 2)**2*(9*g + 14)/13
Let r(n) be the third derivative of -n**5/12 - 45*n**4/8 + 390*n**3 + 5*n**2 - 8*n. Determine q, given that r(q) = 0.
-39, 12
Suppose 4*o + 0*o = -7*o. Let b(u) be the second derivative of 0*u**3 + 1/72*u**4 - 17*u + 0*u**2 + o + 1/120*u**5. What is h in b(h) = 0?
-1, 0
Let k(w) = 31218*w**3 - 7922*w**2 + 562*w + 4. Let b(a) = 93653*a**3 - 23766*a**2 + 1687*a + 10. Let x(r) = -6*b(r) + 17*k(r). Determine s so that x(s) = 0.
1/54, 2/17
Let x(d) = -2*d**2 - 132*d - 2176. Let h(g) = 4*g**2 + 264*g + 4351. Let c be ((-6)/(-27))/(2/18). Let o(b) = c*h(b) + 5*x(b). Factor o(m).
-2*(m + 33)**2
Suppose -2 + 1 = 2*h - 3*o, 2*h + 5*o = 23. Let i be 30/70*(-20)/(-9)*18. Solve -i*x**2 - h*x**3 - 144/7*x - 32/7 = 0.
-2, -2/7
Let f(n) be the first derivative of 18/7*n**2 + 56 + 1/28*n**4 + 0*n + 4/7*n**3. Determine m so that f(m) = 0.
-6, 0
Let z = 889821 - 2669438/3. Factor -490/3 + 5/6*o**3 - 35/6*o