). Solve f + 1/3*y + 1/6*y**2 - 1/6*y**3 = 0 for y.
-1, 0, 2
Let k(c) = -2*c**3 - 4*c**2 - 6*c - 7. Let g be k(-2). Suppose -10*l**4 + 3*l**g + l**2 - l**5 + 2*l**4 - 3*l**4 + 12*l**3 - 4*l = 0. What is l?
-1/2, 0, 1, 4
Let r(y) be the second derivative of -1/3*y**3 - 3/40*y**5 + 0*y**2 - 51*y + 5/16*y**4 + 0 - 1/120*y**6. Factor r(c).
-c*(c - 1)**2*(c + 8)/4
Let s = 217/214 - -5231/856. Suppose -s*c**2 + 57/8 + 3/8*c**3 - 3/8*c = 0. Calculate c.
-1, 1, 19
Let m be (35/(-63))/((-2 + 39/20)*(-3200)/(-1536)). Find y such that 2*y - 22/3*y**2 + m = 0.
-8/11, 1
Let r(f) be the first derivative of -2*f**3/3 + 235*f**2 - 932*f - 3922. Factor r(w).
-2*(w - 233)*(w - 2)
Let m = 3061/7887 - 144/2629. Suppose -m*a**2 - 3 + 2*a = 0. Calculate a.
3
Let u be -15 - ((-6399)/790)/(2/4). Solve -a**2 + u*a - 1/5 = 0 for a.
1/5, 1
Let x = -5585 - -5590. Let i(k) be the third derivative of 0*k + 8*k**2 + 0 + 6*k**3 + 1/15*k**x - k**4. Factor i(w).
4*(w - 3)**2
Let x(w) be the first derivative of 223 + 10/3*w**3 - 8*w**2 - 1/2*w**4 + 8*w. What is v in x(v) = 0?
1, 2
Let k(h) = 11*h**2 - 121*h + 1550. Let m(v) = -5*v**2 + 43*v + 17*v - 957 + 42 + 139. Let b(r) = 4*k(r) + 9*m(r). Factor b(u).
-(u - 28)**2
Let s(i) = 15*i**3 + 11952*i**2 + 3041937*i + 263639979. Let w(o) = 3*o**3 + 2388*o**2 + 608388*o + 52727996. Let f(h) = -4*s(h) + 21*w(h). Factor f(u).
3*(u + 260)**3
Let z(c) = 2*c**2 - 26*c - 40. Let s be z(15). Factor -7*w**3 - 38559*w**4 - s*w**2 + 38563*w**4 + 12*w + 16 - 5*w**3.
4*(w - 4)*(w - 1)*(w + 1)**2
Let 2560/3 + 3712*b - 104/3*b**3 - 584*b**2 + 6*b**4 = 0. Calculate b.
-10, -2/9, 8
Let t(f) be the first derivative of 8*f**2 + 115 + 2/15*f**3 + 78/5*f. Factor t(z).
2*(z + 1)*(z + 39)/5
Factor -3*h**2 + 573 - 1338 + 1278 + 162*h.
-3*(h - 57)*(h + 3)
Let u be 4 + 126/28 + -4 + 9/8. Solve u + 21/4*h - 3/8*h**2 = 0 for h.
-1, 15
Let w(s) be the second derivative of -s**4/60 + 43*s**3/15 + 87*s**2/10 + 1795*s. Factor w(b).
-(b - 87)*(b + 1)/5
Let d(f) be the second derivative of 5*f**4/12 - 235*f**3/6 - 1260*f**2 + 6590*f. Solve d(b) = 0 for b.
-9, 56
Let q(v) be the third derivative of 35*v**8/144 + 61*v**7/18 + 305*v**6/36 + 71*v**5/18 - 415*v**4/72 + 35*v**3/18 - 2*v**2 - 123*v. Let q(t) = 0. Calculate t.
-7, -1, 1/7
Let w(m) be the second derivative of m**6/120 + 3*m**5/20 + 5*m**4/8 + 7*m**3/6 - 5*m**2/2 - 88*m. Let k(p) be the first derivative of w(p). Solve k(y) = 0.
-7, -1
Let u be ((-19)/4)/(12/(-720)*15). Let y(m) be the third derivative of u*m**2 - 1/12*m**4 + m**3 + 1/60*m**6 + 0*m + 0 - 1/10*m**5. Factor y(j).
2*(j - 3)*(j - 1)*(j + 1)
Suppose 85 = -30*i + 175. Suppose 16*b + i*o - 14 = 15*b, -5*o = -b - 10. Solve -2/5*q**2 + 1/5*q**3 - 1/5*q**b + 0*q + 0 + 2/5*q**4 = 0 for q.
-1, 0, 1, 2
Suppose 0 = -2*r - 2. Let a(v) = -4*v**3 - 2*v - 2. Let m be a(r). Solve 0*s**2 + 0 + 0*s - 2/3*s**m + 1/3*s**3 + 1/3*s**5 = 0 for s.
0, 1
Let w be 253/77 + ((-32)/(-28))/(-4). Let a(k) be the second derivative of 1/4*k**5 + 0*k**2 - 5/4*k**4 + 9*k + 5/3*k**w + 0. Factor a(p).
5*p*(p - 2)*(p - 1)
Let f(r) be the second derivative of 0*r**2 - 103*r + 0 + 17/12*r**4 + 2/5*r**5 + 5/3*r**3 + 1/30*r**6. Let f(s) = 0. What is s?
-5, -2, -1, 0
Let l(r) be the first derivative of -4*r**2 + 61 + 2/3*r**3 + 1/2*r**4 - 8*r. Factor l(p).
2*(p - 2)*(p + 1)*(p + 2)
Let p(d) be the second derivative of d**4/42 - 1063*d**3/21 - 152*d**2 - 2062*d + 2. Solve p(u) = 0 for u.
-1, 1064
Solve -400/7*t + 220/7*t**2 - 24/7*t**3 - 500/7 = 0.
-5/6, 5
Let g be (-24)/(-40)*(9 + (-34)/6). Factor -12*p**g - 18*p - 3/2*p**3 + 0.
-3*p*(p + 2)*(p + 6)/2
Let v(i) be the second derivative of 1/36*i**4 - 300*i - 5*i**2 - 1/18*i**3 + 0. Let v(x) = 0. What is x?
-5, 6
Let k(u) be the second derivative of u**7/168 - u**6/24 - 21*u**5/80 - 23*u**4/48 - u**3/3 - u - 865. Suppose k(l) = 0. What is l?
-1, 0, 8
Let l = -3232 + 3232. Let y(b) be the third derivative of 0 + 0*b**4 - 1/140*b**7 + l*b**6 + 0*b**3 - 9/448*b**8 + 0*b**5 + 0*b - 14*b**2. Factor y(d).
-3*d**4*(9*d + 2)/4
Let p = -13380/11 + 13388/11. Factor -2/11*a**2 - p - 8/11*a.
-2*(a + 2)**2/11
Factor 449*n - 219*n + 59*n**2 - 118*n**2 + 55*n**2 + 702*n.
-4*n*(n - 233)
Determine a, given that -56/9*a + 14/9*a**3 - 2/9*a**4 - 64/9 + 8/3*a**2 = 0.
-2, -1, 2, 8
Suppose 0 = 130*l - 97*l. Let t(p) be the second derivative of -1/16*p**4 + 0 + 22*p + l*p**2 + 1/80*p**5 + 1/12*p**3. Factor t(n).
n*(n - 2)*(n - 1)/4
Let 67 + 72/5*w + 1/5*w**2 = 0. Calculate w.
-67, -5
Find v such that 4/7*v**2 - 8 + 20/7*v = 0.
-7, 2
Let u(y) be the first derivative of 5/2*y**2 + 150*y - 202 - 50*y**3 - 5/4*y**4. Factor u(l).
-5*(l - 1)*(l + 1)*(l + 30)
Let d(s) = -7*s**3 + 10*s**2 - 3*s - 8. Let v(p) = p**3 - p**2 + p + 1. Let y(m) = -d(m) - 6*v(m). Let j be y(0). Factor 0*x**3 + j*x + 7/3*x**2 + 0 - 1/3*x**4.
-x*(x - 3)*(x + 1)*(x + 2)/3
Let a(r) be the third derivative of -r**5/150 + 257*r**4/10 - 198147*r**3/5 - r**2 + 526*r. Factor a(s).
-2*(s - 771)**2/5
Suppose -27*k**4 + 24*k + 96*k**4 - 64633*k**3 + 64231*k**3 + 156*k**2 + 15*k**5 + 138*k**5 = 0. What is k?
-2, -2/17, 0, 2/3, 1
Let i be -2 - (1390/39615 + 460/(-114)). Factor -512/3 - 2/3*u**3 - 22*u**i - 192*u.
-2*(u + 1)*(u + 16)**2/3
Let n = -2308 - -5433. Factor 36*d**3 + n*d + 68*d**2 - 31*d**3 + 182*d**2.
5*d*(d + 25)**2
Let l(h) = -6*h**3 + h**2 + 10*h + 9. Let o be l(-1). Let w(t) be the first derivative of 0*t + o - 1/3*t**3 - 5/2*t**2. Find g such that w(g) = 0.
-5, 0
Let b(y) = 20*y**3 + 980*y**2 + 1990*y + 982. Let f(v) = 4*v**3 - 2*v**2 - v - 3. Let a(w) = -b(w) + 6*f(w). Determine i so that a(i) = 0.
-1, 250
Let y(t) be the second derivative of t**6/30 + 207*t**5/10 - 415*t**4/12 - 1829*t. Factor y(c).
c**2*(c - 1)*(c + 415)
Let z(t) = -t**3 + 17*t**2 + t - 247. Let l be z(16). Suppose -21*v = -l*v + h + 9, 3*v + 3*h = 18. Solve -1/6 + 1/2*u - 1/2*u**2 + 1/6*u**v = 0.
1
Let q(b) be the first derivative of -b**6/6 + 25*b**4/12 - 10*b**2 - b + 210. Let n(i) be the first derivative of q(i). Determine f, given that n(f) = 0.
-2, -1, 1, 2
Let o(p) be the first derivative of 5*p**4/8 + 775*p**3/3 + 770*p**2 - 2926. Let o(i) = 0. What is i?
-308, -2, 0
Factor -1/2*v**2 + 15/2*v - 27.
-(v - 9)*(v - 6)/2
Let p be 15/11*-2*(22/32)/((-242)/968). Suppose -p*d + 13 + 1/2*d**2 = 0. Calculate d.
2, 13
Factor 14*q**2 - 136*q + 8*q**2 + 11*q**2 - 12*q**2 - 19*q**2 + 630.
2*(q - 63)*(q - 5)
Let g(y) be the first derivative of -y**6/10 + 19*y**5/15 - 11*y**4/2 + 6*y**3 + 3*y**2/2 + 8*y + 41. Let r(o) be the second derivative of g(o). Factor r(a).
-4*(a - 3)**2*(3*a - 1)
Suppose 48*q - 28*q = 40. Solve c**4 + 1517*c**2 + 14175*c + 4311*c**3 - 4170*c**3 + 20250 + q*c**4 + 778*c**2 = 0.
-15, -2
Let a = -21420 + 150012/7. What is i in 6/7*i**2 + a*i - 78/7 = 0?
-13, 1
Let b(f) be the first derivative of 5/2*f**2 + 5/3*f**3 - 58 + 0*f. Factor b(z).
5*z*(z + 1)
Let z(u) be the first derivative of -u**5/15 - u**4/4 + 22*u**3/9 + 4*u**2 - 543. Determine a, given that z(a) = 0.
-6, -1, 0, 4
Let w be (0/((-3510)/(-195)))/((-1)/(-1) + 0). Factor 2*s**2 + 1/4*s**4 + 4*s + w - 7/4*s**3.
s*(s - 4)**2*(s + 1)/4
Let k(a) = a**2 + 36*a + 99. Let d be k(-3). Let 0 + 3*n**3 + d*n**2 - 3/2*n - 3/2*n**5 + 0*n**4 = 0. Calculate n.
-1, 0, 1
Let z be ((-8)/(-6) - -2)/(3/216). Suppose w - z = b, 571 = 4*w - b - 404. Factor -10*s**3 + 6*s**3 - w - s**3 - 315*s - 75*s**2.
-5*(s + 1)*(s + 7)**2
Solve -5*z**4 + 48/7 + 491/7*z**2 + 290/7*z + 214/7*z**3 = 0.
-1, -3/5, -2/7, 8
Let s(f) be the third derivative of -f**5/270 - f**4/54 + 7*f**3/3 + 2*f**2 - 22. Factor s(j).
-2*(j - 7)*(j + 9)/9
Suppose -8*h - 80 = -13*h. Find u, given that -3*u**2 - 668*u + 330*u - 9*u**2 - h - 2*u**3 + 314*u = 0.
-2
Let x(b) be the second derivative of -2*b**7/21 - 16*b**6/15 + 44*b**5/5 - 16*b**4 + 164*b. Solve x(t) = 0 for t.
-12, 0, 2
Suppose r + 95 = -o, 485 = -5*o - 0*r - 3*r. Let v = -100 - o. Let -3/8*f**4 - 1/2 + 1/8*f**5 + v*f - 1/8*f**3 + 7/8*f**2 = 0. Calculate f.
-1, 1, 2
Let j = -257 + 259. Determine k, given that 82 + 70 - 252*k - 260*k**j - 144 = 0.
-1, 2/65
Let p = -46 + 28. Let x be (p/(-14) - 1)*119. Factor 4*g**2 - g**2 - 16 - x - 20*g - 5*g**2.
-2*(g + 5)**2
Let j(a) be the first derivative of 4/35*a**5 + 12*a**2 + 12/7*a**4 + 45 + 148/2