= 195 - 1. Suppose 1/2 + 1/2*k**w - k = 0. What is k?
1
Let l(m) be the third derivative of m**5/240 - 33*m**4/8 + 395*m**3/24 + 120*m**2 + 25. Solve l(x) = 0 for x.
1, 395
Solve -12*p + 0 + 86/5*p**2 - 24/5*p**3 - 2/5*p**4 = 0 for p.
-15, 0, 1, 2
Let q = 737245/7 + -105295. Factor q*b - 675/7 + 78/7*b**2 - 3/7*b**4 - 12/7*b**3.
-3*(b - 3)**2*(b + 5)**2/7
Let j(q) be the second derivative of q**5/40 - 9*q**3/4 - 149*q**2/2 - 18*q - 1. Let o(h) be the first derivative of j(h). Factor o(g).
3*(g - 3)*(g + 3)/2
Let i(w) be the third derivative of -w**6/120 + 13*w**5/10 - 51*w**4/8 + 38*w**3/3 - 2247*w**2. Factor i(f).
-(f - 76)*(f - 1)**2
Let c(p) = -p**3 - 5*p**2 - 4. Let q be c(-5). Let o be -4*1 - 64/q. Factor -13 + 6 + o*a - 2 - 3*a**2.
-3*(a - 3)*(a - 1)
Let n(j) be the first derivative of j**4/8 + 69*j**3 + 42849*j**2/4 - 12004. Let n(b) = 0. Calculate b.
-207, 0
Let o be 4/(32/12)*(-3 - (-38)/6). Let g(l) be the second derivative of l + 3/80*l**o + 3/16*l**4 - 3/2*l**2 + 0*l**3 + 0. Determine j so that g(j) = 0.
-2, 1
Let u(t) = 4008*t**2 - 5025*t + 1026. Let p(d) = -4*d**3 - 12023*d**2 + 15074*d - 3071. Let l(z) = 3*p(z) + 8*u(z). Determine n, given that l(n) = 0.
-335, 1/4, 1
Let x(z) be the third derivative of -7/18*z**4 - 33*z - 3*z**2 - 1/60*z**6 + 0*z**3 + 0 - 23/90*z**5. Factor x(y).
-2*y*(y + 7)*(3*y + 2)/3
Suppose 4*l - 4*m = 24, -3*l + 4*m + 16 = -2. Suppose 180*g - 4 + 3*g**2 - 89*g - 56 - 100*g + l = 0. What is g?
-3, 6
Let u be (1 - (-55)/(-60))/((-9)/(-228)). Let s = 239/45 - u. Factor -6/5*j**2 - s - 28/5*j.
-2*(j + 4)*(3*j + 2)/5
Let f be (-4 - -4) + 1 - -35. Let t be ((-16)/18)/((-8)/f). Factor -160 + 304*d - 64*d - 148*d**2 + 16 + 40*d**3 - t*d**4.
-4*(d - 3)**2*(d - 2)**2
Let a(r) be the first derivative of 1/8*r**4 - 7/3*r**3 + 0*r + 0*r**2 - 35. Suppose a(v) = 0. Calculate v.
0, 14
Let r(n) = -2*n**2 - n. Let z(a) = 7*a**2 - 6*a - 136. Let w(q) = -3*r(q) - z(q). Let k be w(17). Factor 1/4*c**5 + 0 - 1/2*c**2 + k*c - 3/4*c**3 + 0*c**4.
c**2*(c - 2)*(c + 1)**2/4
Let i(m) = 21*m**3 - 3*m**2 - 6*m + 18. Let w(v) = v**3 + 1. Let p(n) = 6*n - 6. Let y be p(-2). Let o(r) = y*w(r) + i(r). Find b, given that o(b) = 0.
-1, 0, 2
Let b(x) be the second derivative of -x**4/18 + x**3 + 4*x + 562. Determine r so that b(r) = 0.
0, 9
Find j, given that -1/3*j**4 + 14/3*j**3 - 11/3 + 34/3*j - 12*j**2 = 0.
1, 11
Suppose -114*w - 1338 = -1566. Determine i so that 2/3*i**3 - 38/3*i + 32/3*i**w - 68/3 = 0.
-17, -1, 2
Let c(v) = -11*v**3 - 12*v**2 + 56*v + 187. Let n(g) = -13*g**3 - 10*g**2 + 56*g + 186. Let j(k) = -6*c(k) + 5*n(k). Suppose j(y) = 0. What is y?
-24, -2, 4
Let g = 2256/101 + 33/202. Let l(q) be the second derivative of 1/6*q**6 + g*q**2 + 0 - 5/6*q**4 - 15*q - q**5 + 10*q**3. Factor l(o).
5*(o - 3)**2*(o + 1)**2
Let n(x) = -10*x**3 + 76*x**2 - 96*x. Let d(c) = -2*c**3 + 15*c**2 - 19*c. Let w be ((-30)/(-50))/((-4)/(-20)). Let a(u) = w*n(u) - 16*d(u). Factor a(l).
2*l*(l - 4)*(l - 2)
Let v(r) = -208*r**2 + 840*r - 894. Let q(y) = 2*y**2 - 1. Let h = 173 + -172. Let k(c) = h*v(c) + 6*q(c). Factor k(u).
-4*(7*u - 15)**2
Let k = -183/10534 + -2646197/12609198. Let u = 10/171 - k. Suppose -6/7*a**3 + 6/7*a - u + 4/7*a**4 - 2/7*a**2 = 0. What is a?
-1, 1/2, 1
Let s be (7/(-28))/((-16)/(-40) - (-672)/(-1664)). Let 1/3*x**3 + s*x - 9*x**2 - 169/3 = 0. Calculate x.
1, 13
Let f(j) be the first derivative of j**4/6 - 8*j**3/9 - 59*j**2 + 120*j - 11828. Find t such that f(t) = 0.
-12, 1, 15
Suppose -302816 = 37*o - 302927. Factor o - 28/3*a - 11*a**2 + 4/3*a**3.
(a - 9)*(a + 1)*(4*a - 1)/3
Let 53/2*g**3 + 5194*g + 1/4*g**4 + 9604 + 3201/4*g**2 = 0. Calculate g.
-49, -4
Let z(q) = 137*q**2 + 86*q - 84. Let b(i) = 119*i**2 + 87*i - 83. Let t(r) = -4*b(r) + 3*z(r). Determine k so that t(k) = 0.
-2, 8/13
Factor 587/7*q**2 - 1/7*q**3 - 86435/7*q + 85849/7.
-(q - 293)**2*(q - 1)/7
Let i(x) be the first derivative of -1/450*x**6 + 0*x + 0*x**2 - 5/3*x**3 - 1/150*x**5 + 1 + 1/15*x**4. Let b(l) be the third derivative of i(l). Factor b(n).
-4*(n - 1)*(n + 2)/5
Let r(h) = h**2 + 3*h. Let n(z) = -185*z + 465. Let g(w) = n(w) + 5*r(w). Let g(j) = 0. What is j?
3, 31
Suppose 0 = 2*x - 152 - 402. Let h = 1943/7 - x. Let -2/7*g + h - 2/7*g**2 = 0. Calculate g.
-2, 1
Suppose -8954*b**2 + 2*b**3 + 7 + 2*b**4 + 8946*b**2 - 8*b - 7 = 0. What is b?
-2, -1, 0, 2
Let m(r) be the first derivative of 2*r**5/55 - 2*r**3/33 - 1220. Solve m(j) = 0.
-1, 0, 1
Factor 149*a**2 + 101*a**3 + 2 - 101*a - 26*a**4 - 73*a**4 + 168*a**2 - 220*a**2.
-(a - 1)**2*(a + 1)*(99*a - 2)
Let u(q) be the third derivative of -q**8/3360 - q**7/525 + q**6/40 - q**5/30 - 29*q**4/240 + 2*q**3/5 - 25*q**2 + 34*q + 1. Let u(b) = 0. Calculate b.
-8, -1, 1, 3
Factor 4*u**3 + 201*u**2 - 1384*u**2 + 842700*u - 74438500 - 1954*u**2 - 43*u**2.
4*(u - 265)**3
Let j(u) be the third derivative of u**6/720 + 43*u**5/360 + 391*u**4/144 - 145*u**3/12 + 124*u**2 - 16*u - 2. Find w such that j(w) = 0.
-29, -15, 1
Suppose -220*w + 210 = -217*w. Let y = w + -67. Factor -3/2*r**3 + 0*r + 0 + 0*r**2 - 3/2*r**5 + y*r**4.
-3*r**3*(r - 1)**2/2
Let m(l) be the third derivative of -l**6/40 + 257*l**5/10 - 511*l**4/2 + 1020*l**3 - 26*l**2 - 43*l. Factor m(a).
-3*(a - 510)*(a - 2)**2
Let t(d) = -2*d**3 + 11*d**2 - 5*d**4 + 219*d - 3 - 203*d + d**3. Let s(k) = 4*k**4 + 2*k**3 - 10*k**2 - 16*k + 2. Let b(y) = 3*s(y) + 2*t(y). Factor b(r).
2*r*(r - 2)*(r + 2)**2
Determine j, given that -2/7*j**2 - 324818/7 - 1612/7*j = 0.
-403
Let j(t) = -t**2 + 3*t + 4. Let r be j(1). Let b be (-3)/r*(0/1)/(-2). Solve -3/5*z**2 + b - 3*z = 0 for z.
-5, 0
Suppose 15*a - 265 = 10*a + 3*c, 5*a - 275 = 5*c. Factor 38*i**3 - 5*i**4 - 54*i**3 + 15*i**2 - 40 - a*i + 36*i**3.
-5*(i - 4)*(i - 2)*(i + 1)**2
Let 1094/21 - 2/21*v**3 - 730/7*v + 366/7*v**2 = 0. Calculate v.
1, 547
Let a(s) be the first derivative of 5*s**4/16 + 100*s**3/3 - 10615*s**2/8 + 30855*s/2 - 7764. Factor a(h).
5*(h - 11)**2*(h + 102)/4
Let o be ((-11)/(-66))/(25 + -15). Let w(z) be the third derivative of 0*z**4 + 0*z - 14*z**2 - 2/3*z**3 + 0 + o*z**5. Factor w(y).
(y - 2)*(y + 2)
Let g = 378770 - 378768. Suppose -a**3 - 2 + 20/3*a**g - 11/3*a = 0. What is a?
-1/3, 1, 6
Factor 16/3*d + 16/3*d**2 + 1.
(4*d + 1)*(4*d + 3)/3
Let n(m) = -m**3 + 120*m**2 - 499*m - 622. Let w(o) = -10*o**3 + 1320*o**2 - 5485*o - 6838. Let u(f) = -23*n(f) + 2*w(f). Let u(a) = 0. Calculate a.
-1, 6, 35
Let m(j) be the second derivative of -j**5/20 + 11*j**4/4 + j + 1372. Factor m(f).
-f**2*(f - 33)
Suppose -41*p = 69*p. Let y(b) be the first derivative of 0*b**3 + 0*b**4 + 3/25*b**5 + 1/10*b**6 + 0*b + p*b**2 - 7. Let y(s) = 0. What is s?
-1, 0
Let s be -4 + (-5)/1 + 6. Let b be (-14)/s*100/210 - 2. Solve b*w + 2/9*w**2 + 0 = 0 for w.
-1, 0
Solve 2/3*m**2 - 40*m - 264 = 0 for m.
-6, 66
Let z = 372 + -363. Suppose -5*v + 2*n + 4 = 0, -4*v - 7 = -z*n + 4*n. Solve 0*r + 0*r**v - 2/7*r**3 - 8/7*r**5 - 10/7*r**4 + 0 = 0 for r.
-1, -1/4, 0
Suppose w + 2*d - d - 15 = 0, -3*d = -2*w + 55. Suppose 5*v - w = 0, -5*u + 5*v - 12 = -2. Factor 4/7*g**u + 1/7*g**3 + 0 + 3/7*g.
g*(g + 1)*(g + 3)/7
Let g(k) = -12*k**4 - 26*k**3 + 6*k**2 - 3*k + 3. Let j(q) = -45*q**4 - 105*q**3 + 16*q**2 - 11*q + 11. Let n(c) = -22*g(c) + 6*j(c). Factor n(f).
-2*f**2*(f + 9)*(3*f + 2)
Suppose 2*u + 35 = -77. Let h = -54 - u. Find n, given that -45*n**4 + 10 + 35*n + 12*n**h + 25*n**3 + 50*n**4 + 33*n**2 = 0.
-2, -1
Find u such that 22*u**2 + 1583323 - 18*u**2 + 11088*u + 5500010 + 600651 = 0.
-1386
Let d be 714/(-255)*(-20)/12. Suppose 26/3*y + 8/3 + d*y**3 + 10*y**2 + 2/3*y**4 = 0. What is y?
-4, -1
Let i(n) = n**4 + 3*n**2 + 1. Let w be 1 - 8/(0 - 2). Let z(b) = 3*b**4 + 22*b**3 - 71*b**2 + 138*b - 67. Let g(a) = w*i(a) - z(a). Factor g(r).
2*(r - 4)*(r - 3)**2*(r - 1)
Suppose -6*j - 82 = b, 2*j = -29*b + 29*b - 30. Factor 10*p + b + 1/2*p**3 + 4*p**2.
(p + 2)**2*(p + 4)/2
Factor -669135*b - 708990*b - 1471*b**2 - 3779*b**2 - 5*b**3.
-5*b*(b + 525)**2
Let v(a) = -a**2 + 12*a - 9. Let w = -37 - -46. Let n be v(w). Solve 0*s**3 + 0*s**3 + 6*s - 5*s**4 - n*s**3 - 7*s**2 = 0.
-3, -1, 0, 2/5
Let o be ((10 - 10 - 0)/((-10)/2))/(-3). Suppose 1/4*b**2 + 3/4*b + o = 0. What is b?
-3, 0
Suppose 18 - 8 = -l + 5*n, 2*l - 19 = -3*n. Su