 so that m(d) = 0.
-49, -1/3, 0, 3
Suppose -d + 12 - 11 = 0. Let l(q) = 2*q**2 + q - 1. Let w(z) = -z**3 - z**2 - 4*z - 4. Let i(p) = d*w(p) - 4*l(p). What is t in i(t) = 0?
-8, -1, 0
Suppose 0 = -9*j + 14*j. Factor 2*i**3 + j*i**3 + i**2 + 4*i**3 - 5*i**3.
i**2*(i + 1)
Let v(y) be the third derivative of y**8/1680 - y**7/350 - y**6/200 + 11*y**5/300 - y**4/20 - 1413*y**2. Factor v(u).
u*(u - 3)*(u - 1)**2*(u + 2)/5
Let z(q) be the first derivative of -q**4/18 - 20*q**3/27 + q**2/9 + 20*q/9 - 676. What is l in z(l) = 0?
-10, -1, 1
Suppose -303*v + 1720 = -0*v + 41*v. What is q in -v*q**3 - 4/3*q**4 + 0 - 8/3*q**2 + q = 0?
-3, -1, 0, 1/4
Solve 26/7*k + 60/7 - 2/7*k**2 = 0 for k.
-2, 15
Let n(g) be the first derivative of -g**6/168 + 61*g**5/280 - 3*g**4/14 + 8*g**3/3 + g + 71. Let b(r) be the third derivative of n(r). Factor b(d).
-3*(d - 12)*(5*d - 1)/7
Let q = 554 - 522. Let k(i) be the second derivative of -4*i**4 - 3/20*i**5 + 0*i**2 - 26*i + 0 - q*i**3. Factor k(w).
-3*w*(w + 8)**2
Let z(m) = -376*m + 4518. Let l(h) = 5*h**2 + h - 18. Let k(j) = -l(j) - z(j). Let k(g) = 0. Calculate g.
15, 60
Let k(b) = b**2 - 10*b + 3. Let u be k(9). Let n be 3 + (u - -4)/2. Factor -r**n + 12*r - 10 + r**2 + r**3 + 2 - 6*r**2.
(r - 2)**3
Let r(n) be the first derivative of -5*n**4/8 - 29*n**3/12 + 25*n**2/8 + 7*n/2 + 855. Find b, given that r(b) = 0.
-7/2, -2/5, 1
Let v = -346 - -514. Let t be ((-12)/20)/(v/(-70)). Factor 9/2*z**2 - 27*z + 54 - t*z**3.
-(z - 6)**3/4
Factor -384000 + 1600*b - 5/3*b**2.
-5*(b - 480)**2/3
Let c(l) be the second derivative of 3*l**5/40 + 153*l**4/8 - 309*l**3/4 + 465*l**2/4 + 370*l + 2. Suppose c(i) = 0. Calculate i.
-155, 1
Suppose -s + 5*a = -1004, -4*s + 6*s - 2019 = -a. Let n = s - 5044/5. Factor -2/5*u**2 + 0 - n*u**3 + 0*u.
-u**2*(u + 2)/5
Let v be 24258/260 - 74 - 1/10. Factor -4/5*u**2 - 20*u - v.
-4*(u + 1)*(u + 24)/5
Let q(y) be the first derivative of -y**7/42 + 7*y**6/24 - 2*y**5/3 - 10*y**4/3 - y**2/2 - 4*y - 83. Let m(v) be the second derivative of q(v). Factor m(d).
-5*d*(d - 4)**2*(d + 1)
Suppose -386*a + 379*a = 0. Suppose a = -9*w + 7*w + 4. Factor -2/3*l**2 - 8/3*l - w.
-2*(l + 1)*(l + 3)/3
Let t be (((-5712)/60)/17)/(2/(-455)). Let n = t - 1270. Find y such that -2*y**2 - 2/3*y**3 - 2/3*y**5 + 0 + 4/3*y + 2*y**n = 0.
-1, 0, 1, 2
Let l(n) = -3*n**3 - 50*n**2 + 65*n - 124. Let g be l(-18). Factor -1/5*u**g + 5 + 0*u.
-(u - 5)*(u + 5)/5
Let d be 1992/800 + (-666)/2775. Let -1/4*g**3 + 25/4 - d*g**2 - 15/4*g = 0. Calculate g.
-5, 1
Let m be 2 + (-8 - 8) + (3 - 3). Let n be (12/14)/((-4)/m). Factor 10/3*q**4 - 10/3*q**2 - 5/3*q**5 + 0 + 0*q**n + 5/3*q.
-5*q*(q - 1)**3*(q + 1)/3
Let r(i) = -i**2 + 13*i + 18. Let h be r(14). Suppose -10*d + 12 = -h*d. Solve 3*v**3 - 3*v - 2*v**2 + 3*v**2 + 2 + 1 - 4*v**d = 0 for v.
-1, 1
Suppose 72*s + 28 = 74*s. Let a be (s + (-111)/9)/((-10)/(-12)). Determine i, given that -2/9*i**a + 14/9*i - 4/3 = 0.
1, 6
Let k(a) = -9*a**2 - 84*a - 17. Let n be k(-9). Factor -n - 281*h**3 - 600*h**2 - 14*h**3 + 509*h - 400*h - 424*h.
-5*(h + 1)**2*(59*h + 2)
Let c(y) be the first derivative of 1/10*y**5 + 7/9*y**3 + 1/3*y**2 + 63 - 13/24*y**4 - 4/3*y. Factor c(q).
(q - 2)**2*(q - 1)*(3*q + 2)/6
Suppose 4*d - x - 16 = 0, -341*d + 12 = -338*d + 2*x. Factor 4/9 - 2/9*z**3 + 2/9*z**d + 2/9*z - 2/3*z**2.
2*(z - 2)*(z - 1)*(z + 1)**2/9
Let u(v) be the third derivative of v**7/1050 + v**6/40 + 19*v**5/100 + 73*v**4/120 + v**3 - v**2 + 553*v. Solve u(z) = 0 for z.
-10, -3, -1
Let o(y) = -8*y + 6 - y**2 + 2*y**2 + 4*y + y. Let a be o(2). Solve -42*h**5 + 1572*h**3 - 3*h**2 + 6*h + 0*h**4 + 93*h**a - 1626*h**3 = 0 for h.
-2/7, 0, 1/2, 1
Suppose -561*y - 36 = -570*y. Let g be 3*(-4)/6 - -5. Factor v**5 - v**2 - 6*v**5 + 2 + 4*v**y + 4*v**g - v + 2*v**5 - 5*v**2.
-(v - 1)**3*(v + 1)*(3*v + 2)
Let d(l) = 30*l**2 - 3306*l - 10089. Let k(p) = -7*p**2 + 827*p + 2522. Let g(u) = 2*d(u) + 9*k(u). Factor g(r).
-3*(r - 280)*(r + 3)
Let k = -7315 + 7319. Let w(a) be the third derivative of 0*a + 1/16*a**k + 0 - 23*a**2 + 3/16*a**3 + 1/160*a**5. Factor w(t).
3*(t + 1)*(t + 3)/8
Let 2/9*k**2 - 70/3*k + 2392/9 = 0. What is k?
13, 92
Let y(l) be the first derivative of 5*l**3/3 + 90*l**2 - 1505*l - 1276. Let y(j) = 0. Calculate j.
-43, 7
Let v = 714 - 660. Suppose 0 = -v*i + 68*i. Let 3/2*n**2 + i + 3/2*n = 0. What is n?
-1, 0
Factor v - v + 374*v**3 - 186*v**2 - 39481*v**5 - 190*v**4 + 39483*v**5.
2*v**2*(v - 93)*(v - 1)**2
Let s(v) be the second derivative of v**5/40 - 5*v**4/8 + 4*v**3 + 16*v**2 + 17*v - 24. Solve s(l) = 0 for l.
-1, 8
Suppose -31*c = -28*c - 9. Suppose -2*r - 2*r = 5*w + 2, c*w + 3*r + 3 = 0. Factor 6/11*s - 6/11*s**4 - 4/11*s**3 + 4/11*s**w - 2/11*s**5 + 2/11.
-2*(s - 1)*(s + 1)**4/11
Let u(w) = -2*w**3 + 3*w**2 + 2*w + 2. Let f(b) = 9*b**3 + 57*b**2 + 351*b + 288. Let y(k) = f(k) + 3*u(k). Determine d, given that y(d) = 0.
-14, -7, -1
Let w(r) be the third derivative of 29*r**6/1200 - 11*r**5/60 + 23*r**4/60 + 2*r**3/5 + 612*r**2. Factor w(n).
(n - 2)**2*(29*n + 6)/10
Suppose 5*p - 211 = -51. Let x be 0 + 0 - p/(-16). Let 6*o**2 + o**2 - o**x + 12 - 3*o**2 - 12*o = 0. Calculate o.
2
Let c(t) be the second derivative of -t**4/132 + 56*t**3/33 + 113*t**2/22 - 11*t - 1. Let c(k) = 0. What is k?
-1, 113
Let d be (26 - 132) + 53 - -58. Find z such that 79/4*z - 4*z**4 - 29*z**2 + 37/2*z**3 - 1/4*z**d - 5 = 0.
-20, 1
Suppose -38*r = r - 468. Solve 8*l**2 - r*l**2 + 5*l - 5*l**2 + 14*l**2 - 150 = 0 for l.
-6, 5
Let a(t) be the first derivative of 0*t - 41 + 3*t**2 + 5/3*t**3 + 1/4*t**4. Factor a(k).
k*(k + 2)*(k + 3)
Let o(l) be the third derivative of l**6/960 + 19*l**5/40 + 227*l**4/192 - 1749*l**2. What is i in o(i) = 0?
-227, -1, 0
Let m(n) be the first derivative of -5*n**2/2 - 13*n - 17. Let r be m(-3). Factor 4*y**r - 2*y**2 - 5*y**2 + 3*y**4 + 6*y + 3*y**5 - 6*y**3 - 3*y**3.
3*y*(y - 1)**2*(y + 1)*(y + 2)
Find d, given that 56/3 - 2/9*d**3 - 176/9*d + 50/9*d**2 = 0.
2, 21
Let u(s) be the first derivative of s**6/60 + 3*s**5/40 - s**4 - 20*s**3/3 - 34*s - 55. Let g(y) be the first derivative of u(y). Find x, given that g(x) = 0.
-4, 0, 5
Let n be 207 + -230 + 18667*5. Factor -n*l + 3888*l**2 + 839808 + 1/2*l**4 - 72*l**3.
(l - 36)**4/2
Let z(p) = 34*p**3 - 87*p**2 + 72*p - 19. Let l(j) = -11*j**3 + 29*j**2 - 24*j + 6. Let a = 248 + -241. Let k(u) = a*l(u) + 2*z(u). Factor k(s).
-(s - 2)*(s - 1)*(9*s - 2)
Let k(r) be the second derivative of r**5/80 - 23*r**4/48 + 67*r**3/12 - 14*r**2 - 772*r. Factor k(v).
(v - 14)*(v - 8)*(v - 1)/4
Factor 46/3*a + 20/3*a**3 + 0 - 1/3*a**4 + 67/3*a**2.
-a*(a - 23)*(a + 1)*(a + 2)/3
Let w(l) be the first derivative of -l**2/2 + 15*l + 3. Let f be w(9). Find i such that 200*i**3 - 36*i**2 - 12*i**4 - 160*i**3 + f*i + 2*i = 0.
0, 1/3, 1, 2
Let w(q) be the first derivative of -15/4*q**2 + 31/4*q + 117 - 1/12*q**3. Find u such that w(u) = 0.
-31, 1
Let y(f) = -f + 1. Let l be y(-3). Suppose -67*u = -71*u - 20, -2*u - l = 2*i. Determine a so that -i*a**4 + 21/2*a**5 + 0*a + 0 - 21/2*a**3 + 3*a**2 = 0.
-1, 0, 2/7, 1
Let t(h) be the second derivative of 2166/5*h**2 - 38/5*h**3 - 2*h + 23 + 1/20*h**4. Determine f, given that t(f) = 0.
38
Let i be (21/35)/(1161/430). Let -32/3*w + 128/9 - i*w**3 + 8/3*w**2 = 0. Calculate w.
4
Let f(b) be the first derivative of 3*b**5/35 - 3*b**4/7 - 2225. Factor f(m).
3*m**3*(m - 4)/7
Let m(t) be the second derivative of -t**5/35 + 2*t**4/21 + 22*t**3/21 - 24*t**2/7 + 3*t - 105. Find u such that m(u) = 0.
-3, 1, 4
Let f(n) = 2*n + 21. Let d be f(-12). Let v be (-16 + 7 + -3)*d. Let -q**4 + 4*q - 3*q**4 + 7*q**3 + v*q**2 - 20*q - 13*q**3 = 0. Calculate q.
-4, 0, 1/2, 2
Suppose 1 = -8*p - 11*p + 1. Let b = -76 + 155/2. Find c, given that p + 3/2*c**2 - b*c = 0.
0, 1
Let h be 1/(-27)*(-1015)/10150. Let p(v) be the third derivative of -1/12*v**4 + 2*v**2 + 0*v**3 + h*v**5 + 0*v + 0. Solve p(b) = 0.
0, 9
Let a be (-14)/12 + 2 + 590/(-885). Let a*j**4 + 0 + 1/6*j**2 - 2/3*j**3 + j = 0. Calculate j.
-1, 0, 2, 3
Let x be (27 + (-1921)/153)*90/(-75)*6/(-14). Suppose 30/7*k + x + 2/7*k**2 = 0. What is k?
-13, -2
Let f(j) be the second derivative of j**5/100 - 299*j**4/60 - 151*j**3/15 + 60*j**2 - 5254*j. Factor f(r).
(r - 300)*(r - 1)*(r + 2