2
Let g be ((-154)/70 + 2/10)*-12. Factor 58*x**2 - 35*x + 50*x + 49*x + g - 11*x**4 + 13*x**4 + 20*x**3.
2*(x + 1)**2*(x + 2)*(x + 6)
Let j = 57176/3 - 57172/3. Find r such that j - 5/3*r + 1/3*r**2 = 0.
1, 4
Solve 213 + 1/3*n**2 - 640/3*n = 0 for n.
1, 639
Let t = 10052/22851 - -1140/2539. Determine b, given that -4 - 68/9*b + t*b**2 = 0.
-1/2, 9
Let m = 51939/8 - 6492. Let s(d) be the first derivative of -3 + 5/8*d + 1/24*d**3 + m*d**2. Factor s(v).
(v + 1)*(v + 5)/8
Let u = 65743 + -65738. Find l such that 1/5*l**u + 0 + 1/5*l**3 - 6/5*l**2 + 4/5*l**4 + 0*l = 0.
-3, -2, 0, 1
Factor -33*b**2 - 147/2 - 1/6*b**4 + 4*b**3 + 308/3*b.
-(b - 9)*(b - 7)**2*(b - 1)/6
Let d be ((-3)/5)/((-120)/1200). Let l(v) be the third derivative of -2*v**2 + 0 + 3/2*v**3 + 0*v + 7/20*v**5 - 17/16*v**4 - 3/80*v**d. Solve l(r) = 0.
2/3, 1, 3
What is i in -21*i**3 + 19*i**3 + 466 - 50*i**2 + i + 25*i**4 - 441 + i**5 = 0?
-25, -1, 1
Let v = -2100883 - -10504431/5. Determine b, given that 37/5*b**2 - 42/5*b - 12/5*b**3 + v + 1/5*b**4 = 0.
1, 2, 8
Let w(m) be the second derivative of 3*m**5/140 - 365*m**4/14 - 209*m**3/2 - 1098*m**2/7 + 3*m - 349. Let w(j) = 0. Calculate j.
-1, 732
Suppose -3*p - 24 = -7*p + 3*x, -2*x = -3*p + 18. Factor 12*b**3 + 3*b**4 - 12*b**2 + 9*b**2 - 6*b**2 - p*b**5.
-3*b**2*(b - 1)**2*(2*b + 3)
Suppose 0 = 2*q - 38 + 2. Let g(r) = 2*r - 34. Let x be g(q). Let -12302 - 2*h + 12302 + h**x = 0. Calculate h.
0, 2
Let c = 3140 - 7760. Let l be 10/6*(-504)/c. Let 0*q + 2/11*q**2 + l*q**4 + 0 + 4/11*q**3 = 0. What is q?
-1, 0
Find s, given that -12/5*s**4 - 162/5*s**2 + 0 + 3/5*s**5 + 0*s - 117/5*s**3 = 0.
-3, -2, 0, 9
Let a(o) be the first derivative of -o**3/3 - 17*o**2/2 + 3*o - 76. Let g(q) = -q + 1. Let f(c) = -2*a(c) + 6*g(c). Factor f(n).
2*n*(n + 14)
Factor 9*h + 3/4*h**2 + 0.
3*h*(h + 12)/4
Let o = -226/93 + 1901/744. Let k(c) be the second derivative of 1/80*c**5 + 0 + 1/8*c**3 + o*c**2 + 19*c + 1/16*c**4. Let k(l) = 0. Calculate l.
-1
Suppose -2*v - 2*c + 16 = 0, -4*v - 3*c + 12 = -5*v. Let -6*b**2 - 32*b - 8*b**2 - v*b**2 - 128 + 15*b**2 = 0. Calculate b.
-8
Let c(q) = 2*q**3 + 17*q**2 - 835*q - 7430. Let b be c(-9). Suppose 55*g**2 - 54*g - 53/2*g**3 + 20 - 1/2*g**5 + 6*g**b = 0. Calculate g.
1, 2, 5
Let q be 2/(-4)*(0 - 10). Suppose 16*c - q*c - 44 = 0. Solve -2*u**2 + 3 - u**4 + 3*u**3 + 0 - c*u + u**3 = 0.
-1, 1, 3
Let y(k) = -36*k**3 + 32*k**2 + 10*k - 126. Let i(w) = -3*w**3 - w**2 - w - 7. Let x(l) = 36*i(l) - 2*y(l). Suppose x(p) = 0. What is p?
-2, -7/9, 0
Factor w**2 - 360*w + 2190*w + 428 + 1526 + w**2 - 126.
2*(w + 1)*(w + 914)
Let s(a) be the second derivative of a**5/50 + 19*a**4/30 - 4*a**3/3 + 1026*a. What is o in s(o) = 0?
-20, 0, 1
Let t(j) be the third derivative of j**7/945 - j**6/108 - j**5/45 - 227*j**2 + 5. Solve t(o) = 0.
-1, 0, 6
Let z be (1 + -3)/((-8)/(5 + -1)). Let h be ((-132)/(-24))/(z/2). Factor -2*k**4 - 14*k**5 - 9*k**3 + h*k**5 - 3*k**2 - 7*k**4.
-3*k**2*(k + 1)**3
Let y(k) be the third derivative of -21*k**2 + 7/12*k**4 + 0*k - k**3 + 0 - 1/6*k**5 + 1/60*k**6. Factor y(g).
2*(g - 3)*(g - 1)**2
Find b, given that 230*b + 12*b**3 + 1/4*b**4 - 1587/4 + 309/2*b**2 = 0.
-23, -3, 1
Let c be (-2786)/28 - -67 - -40. Factor -3/2*o**3 + 12*o**2 - 75 - c*o.
-3*(o - 5)**2*(o + 2)/2
Let b(q) be the third derivative of -q**7/630 - 2*q**6/15 - 149*q**5/90 - 19*q**4/3 - 205*q**3/18 - 7*q**2 + 139*q + 2. Factor b(k).
-(k + 1)**2*(k + 5)*(k + 41)/3
Let y = -1239 + 1243. Suppose -26 = -5*z + y*a, -3*z + 3 = -2*a - 11. Determine l so that 4/7*l**3 + 84*l - 12*l**z - 196 = 0.
7
Let r(f) be the third derivative of 4*f**7/15 + 47*f**6/6 + 787*f**5/15 - 107*f**4/3 - 80*f**3 + 1557*f**2. Determine w so that r(w) = 0.
-12, -5, -2/7, 1/2
Let b(j) be the first derivative of 2*j**5/35 + j**4 + 46*j**3/7 + 144*j**2/7 + 216*j/7 + 5017. Factor b(k).
2*(k + 2)*(k + 3)**2*(k + 6)/7
Let w(b) be the first derivative of 0*b**3 + 3*b**2 - 38 + 0*b - 3/8*b**4. Factor w(f).
-3*f*(f - 2)*(f + 2)/2
Let g = 1550 + -2885. Let c = 14695/11 + g. Find h, given that c*h**2 + 0*h + 2/11*h**3 + 0 = 0.
-5, 0
Let c(u) be the third derivative of 1/420*u**6 + 16*u**2 + 0*u - 1/210*u**5 - 3 + 0*u**3 - 1/42*u**4. Solve c(i) = 0 for i.
-1, 0, 2
Let g(o) be the second derivative of -5*o + 0*o**5 - 2 + 0*o**3 - o**2 + 1/3*o**4 - 1/15*o**6. Find a such that g(a) = 0.
-1, 1
Let j(y) be the first derivative of 3*y**5/5 - 219*y**4/4 + 1366*y**3 - 1728*y**2 - 7776*y - 2031. Factor j(i).
3*(i - 36)**2*(i - 2)*(i + 1)
Factor -1232*i - 20077*i**3 + 11104*i**2 - 2104*i**3 + 324*i**4 - 2911*i**3.
4*i*(i - 77)*(9*i - 2)**2
Let z(s) be the third derivative of 1/105*s**7 + 0*s**3 + 0*s + 0 - 180*s**2 + 0*s**4 - 1/15*s**5 - 1/60*s**6. Factor z(q).
2*q**2*(q - 2)*(q + 1)
Let t(j) be the third derivative of j**8/112 + 141*j**7/280 - 257*j**6/160 + 15*j**5/16 + 37*j**4/32 + 10*j**2 + 10*j. Find s such that t(s) = 0.
-37, -1/4, 0, 1
Let -2*v**2 - 91 - 84*v + 262 + 405 = 0. What is v?
-48, 6
Let l be ((-1224)/(-30))/(-17)*(-505)/404. Factor 2 + 10/3*z**l + 26/3*z**2 + 22/3*z.
2*(z + 1)**2*(5*z + 3)/3
Find y such that -61*y**2 + 62*y**2 + y**3 + 374*y - 386*y = 0.
-4, 0, 3
Let d(g) = 5*g**4 + 16*g**3 - 27*g**2 - 152*g + 6. Let o(n) = -41*n**4 - 127*n**3 + 216*n**2 + 1211*n - 51. Let t(i) = -17*d(i) - 2*o(i). What is y in t(y) = 0?
-6, -3, 0, 3
Let p(q) = 3*q**2 + 10*q + 1. Let o be p(-4). Suppose -13 - 23 = -o*r. Let -16/3*z + 4*z**3 + 10/3*z**r + 0 - 8/3*z**2 + 2/3*z**5 = 0. What is z?
-2, 0, 1
Let r = 84/65 - 10977/8645. Let n = r - -4377/532. Factor -n*z**2 - 27/4*z**3 + 3 + 12*z.
-3*(z - 1)*(z + 2)*(9*z + 2)/4
Factor -3/5*t**3 - 156/5*t**2 - 336*t + 9408/5.
-3*(t - 4)*(t + 28)**2/5
Let j = -83 + 90. Suppose -j*u - 31 = -45. Factor -2*p**4 - 3/2*p**5 - 1/2*p**3 + 0 + 0*p**u + 0*p.
-p**3*(p + 1)*(3*p + 1)/2
Suppose -9*o + 52*o - 5*o = 12*o. Let 1/6*j**5 - 1/3*j**2 + 1/3*j**4 + 0 - 1/6*j + o*j**3 = 0. Calculate j.
-1, 0, 1
Suppose 5*u - 18850 + 4190 = 0. What is h in -8*h**2 + 2932*h**4 + 4*h**5 + 12*h + 8 - u*h**4 - 16*h**3 = 0?
-1, 1, 2
Let u = 480691/98 + -4905. Let n(l) be the second derivative of 0*l**3 + 0 + 0*l**4 - 1/35*l**6 + u*l**7 + 0*l**2 + 0*l**5 - 28*l. Factor n(c).
3*c**4*(c - 2)/7
Let o(d) be the third derivative of -5*d**8/224 - 5*d**7/21 - 19*d**6/24 - d**5 + 5*d**4/48 + 5*d**3/3 + 23*d**2 + 4*d - 24. Let o(v) = 0. What is v?
-4, -1, 1/3
Suppose 200 + 106*v - 536 - 97406*v**2 + 97408*v**2 = 0. Calculate v.
-56, 3
Let c(t) be the first derivative of t**4/8 + 11*t**3 + 191*t**2/4 + 63*t - 3716. Let c(n) = 0. Calculate n.
-63, -2, -1
Factor -2/15*m**3 + 108/5 + 66/5*m + 8/5*m**2.
-2*(m - 18)*(m + 3)**2/15
Let r be 2/(-17) - 837672/(-408). Find c, given that -1547 - r + 136*c + 87*c - 4*c**2 + 17*c = 0.
30
Suppose -43*j + 39*j = 2*a + 2, 5*j + 2*a = -2. Determine h so that 0*h**2 + 0*h**3 - 15/4*h**4 + j + 3/4*h**5 + 0*h = 0.
0, 5
Let x(p) be the second derivative of 1/54*p**4 - 7 - p + 0*p**2 - 7/27*p**3. What is u in x(u) = 0?
0, 7
Suppose 13668 = -13*z - 4*z. Let k = z - -5638/7. Let 8/7*d + 0 + 0*d**2 - k*d**3 + 0*d**4 + 2/7*d**5 = 0. Calculate d.
-2, -1, 0, 1, 2
Let l(t) be the second derivative of -t**6/195 - 7*t**5/130 + t**4/26 + 19*t**3/39 - 14*t**2/13 - 83*t + 3. Determine i so that l(i) = 0.
-7, -2, 1
Let g(w) be the second derivative of w**7/294 - 53*w**6/105 + 2701*w**5/140 + 477*w**4/7 + 486*w**3/7 - 459*w + 1. Suppose g(o) = 0. What is o?
-1, 0, 54
Factor 6/7*z**4 - 24/7*z**3 + 0 + 0*z**2 + 0*z.
6*z**3*(z - 4)/7
Let o(b) be the first derivative of -4 + 0*b**2 + 16*b + 1/30*b**4 + 1/5*b**3. Let h(n) be the first derivative of o(n). Factor h(k).
2*k*(k + 3)/5
Let d(a) be the third derivative of -69*a**2 + 1/90*a**5 + 0 + 0*a - 7/36*a**4 - 8/9*a**3. Find t such that d(t) = 0.
-1, 8
Let t(r) be the third derivative of -1/210*r**5 + 0*r + 5*r**2 - 1/42*r**4 + 3 - 1/21*r**3. Factor t(p).
-2*(p + 1)**2/7
Let j(n) be the third derivative of 1/21*n**8 + 0*n**3 + 0*n**6 + 0*n**4 + 0*n + 51*n**2 + 0 + 0*n**5 + 2/105*n**7. Let j(w) = 0. Calculate w.
-1/4, 0
Suppose -1119/8*d**2 - 9/8*d**4 - 849/4*d**3 + 849/4*d + 141 = 0. Calculate d.
-188, -1, -2/3, 1
Suppose -588 = 7*j - 105. Let o = -66 - j. Factor -15*y + 83 + 3*y**4 - 3*y**2 - 6*y**2 + o*y**3 - 89.
3*(y