, 1
Let b(z) = z**2 + z + 1. Let a = -14 - -13. Let n = a + 2. Let t(l) = -6*l**2 - 6*l - 3. Let w(h) = n*t(h) + 3*b(h). Determine m so that w(m) = 0.
-1, 0
Let m(n) be the second derivative of 0*n**3 + 0*n**2 - 1/14*n**4 + 17/98*n**7 - 18/35*n**6 + 5*n + 3 + 9/20*n**5. Factor m(g).
3*g**2*(g - 1)**2*(17*g - 2)/7
Let b = -163 - -168. Suppose -4*d + 5*c = -d - 29, -b*d + 27 = -3*c. Determine a, given that 4/5 - 4/5*a**2 - 2/5*a + 2/5*a**d = 0.
-1, 1, 2
Let k(c) = -4*c**5 - 64*c**4 - 368*c**3 - 812*c**2 - 804*c - 312. Let f(m) = m**3 - m**2 - m + 2. Let a(w) = 12*f(w) + k(w). Let a(d) = 0. What is d?
-6, -2, -1
Let i(g) = 9*g + 21. Let s(b) = 14*b + 32. Let m(a) = -8*i(a) + 5*s(a). Let k be m(-5). Suppose 5*j**3 - j**2 - 8*j**3 - j**3 - j**k - 2*j**4 = 0. What is j?
-1, 0
Factor 220*d + 242 - 43/2*d**2 + 1/2*d**3.
(d - 22)**2*(d + 1)/2
Let i(m) be the third derivative of 0 - 10/3*m**3 + 0*m - m**2 + m**4 - 1/15*m**5. Factor i(d).
-4*(d - 5)*(d - 1)
Let b be 0*(17/68)/(10/(-8)). Let n(j) be the first derivative of -3 + 1/4*j**2 + b*j + 1/12*j**3. Factor n(l).
l*(l + 2)/4
Solve 15/4*z**3 + 0 - 1/4*z**4 + 49/4*z - 63/4*z**2 = 0.
0, 1, 7
Let b(i) be the third derivative of -i**8/110880 + i**7/27720 + 11*i**5/60 + 13*i**2. Let n(c) be the third derivative of b(c). Suppose n(u) = 0. What is u?
0, 1
Let y(h) be the third derivative of -5*h**6/84 - h**5/42 + 4*h**4/21 - 4*h**3/21 + 56*h**2. Solve y(j) = 0.
-1, 2/5
Suppose 32*k + 16 = 36*k. Factor 11*d**2 + 11*d**2 - 5*d**k - 17*d**2.
-5*d**2*(d - 1)*(d + 1)
Find z such that 21*z**3 - z**2 - 3*z**2 + 24*z**3 - 47*z**3 = 0.
-2, 0
Let k(v) be the second derivative of 2/25*v**3 + 4/75*v**4 + 1/375*v**6 - 3/125*v**5 - 9/25*v**2 + 0 + 9*v. Let k(b) = 0. What is b?
-1, 1, 3
Let p(j) = 26*j**3 - 53*j**2 + 3*j + 2. Let z be p(2). Let -4/3*y**2 - 8/3 + z*y = 0. Calculate y.
1, 2
What is k in 16/9*k**4 + 14/9*k**2 + 2/9*k + 0 + 28/9*k**3 = 0?
-1, -1/2, -1/4, 0
Let p(o) be the second derivative of 1/3*o**4 - 2*o**3 + 0 - 13*o + 4*o**2. Factor p(q).
4*(q - 2)*(q - 1)
Suppose 0 = n + n. Suppose n = 2*w - 5*u + 13 - 47, -5*w + 85 = -4*u. Solve 0*r - 52*r**2 - 8*r - w*r + 30*r**3 - 5*r + 56*r**4 - 4 = 0.
-1, -2/7, -1/4, 1
Let q(z) be the first derivative of -27/2*z**4 - 12/7*z**2 + 0*z - 28 + 21/5*z**5 + 60/7*z**3. Let q(j) = 0. Calculate j.
0, 2/7, 2
Let r(i) be the third derivative of -i**6/120 + i**5/20 + i**4 + 14*i**3/3 + 15*i**2 + 6*i. What is t in r(t) = 0?
-2, 7
Determine v, given that -2*v**5 + 52*v**3 + 1639640 - 1639640 - 50*v = 0.
-5, -1, 0, 1, 5
Suppose 2*g + 11 = 2*a - 7*a, -2*g - 3*a - 5 = 0. Find r such that 3*r**g + 21/5*r + 3/5*r**3 + 9/5 = 0.
-3, -1
Let z(t) = 3*t**4 + t**3 + 12*t**2 + 7*t. Let p(d) = -d**4 - d**3 - 6*d**2 - 3*d. Let k(y) = 14*p(y) + 6*z(y). Find f, given that k(f) = 0.
-1, 0, 3
Let h = 971 + -964. Let x(l) be the second derivative of -1/14*l**7 + 3/2*l**3 + 1/2*l**4 + h*l + 0 - 3/10*l**6 - 3/10*l**5 + 3/2*l**2. Factor x(b).
-3*(b - 1)*(b + 1)**4
Let w(t) be the second derivative of -t**7/28 - 3*t**6/10 - 39*t**5/40 - 3*t**4/2 - t**3 - 88*t + 2. Factor w(u).
-3*u*(u + 1)**2*(u + 2)**2/2
Let y(i) be the second derivative of -i**5/20 + 11*i**4/4 - 31*i**3/3 - 30*i. Factor y(v).
-v*(v - 31)*(v - 2)
Suppose 2*t = -9 + 15. Find k, given that -3*k**2 + 17*k**2 + 4*k**t + 64 + 12*k**2 + 6*k**2 + 80*k = 0.
-4, -2
Let m(g) be the first derivative of -g**4/4 - 7*g**3/3 - 11*g**2/2 - 5*g + 55. Factor m(s).
-(s + 1)**2*(s + 5)
Suppose -8*b = 5*b + 19*b. Let v(q) be the first derivative of b*q + 1/6*q**4 - 7 + 0*q**2 + 2/9*q**3. Let v(j) = 0. What is j?
-1, 0
Let g = -59 - -62. Factor -4*d**3 + d**g + 3*d**2 + 3*d - 6*d + 3*d**2.
-3*d*(d - 1)**2
Let z be -1 + -4 - 425/(-60). Let j = -17/12 + z. Factor 1/3*w + 1/3*w**2 - j.
(w - 1)*(w + 2)/3
Solve -344/17*k**3 - 2/17*k**5 + 44/17*k**4 + 1168/17*k**2 - 1792/17*k + 1024/17 = 0.
2, 8
Let k = -1768 - -1773. Factor 1/7*i**2 + 3/7*i**3 + 0 + 3/7*i**4 + 0*i + 1/7*i**k.
i**2*(i + 1)**3/7
Let v(k) be the first derivative of 5*k**3/3 - 45*k**2 - 95*k - 14. Let f(p) = -p**2 + 15*p + 16. Let h(a) = 25*f(a) + 4*v(a). Factor h(x).
-5*(x - 4)*(x + 1)
Suppose 2*k = 3*o + 1 - 3, -2*k = 3*o - 22. Solve 3*w**2 + 12*w + 34 - 26 - o*w - w**2 = 0.
-2
Let p(m) be the third derivative of -m**6/150 - 8*m**5/75 - 19*m**4/30 - 8*m**3/5 + 15*m**2 - m. Let p(k) = 0. Calculate k.
-4, -3, -1
Solve 3/4*z**4 + 1/2*z**3 - 9/4*z**2 + 1/8*z**5 + 3/2 - 5/8*z = 0.
-4, -3, -1, 1
Let o = 1072 - 1069. Suppose -60*q**4 - o*q**2 - 24*q**5 + 0 + 0*q - 51/2*q**3 = 0. What is q?
-2, -1/4, 0
Let a(t) be the third derivative of t**5/270 - 23*t**4/36 - 70*t**3/27 - 8*t**2 - 16*t. Factor a(b).
2*(b - 70)*(b + 1)/9
Suppose 1 + 153 = -11*u. Let h(d) = -2*d - 25. Let a be h(u). Factor 0*z + 0 + 1/3*z**4 - 1/3*z**2 + 0*z**a.
z**2*(z - 1)*(z + 1)/3
Let i(o) be the second derivative of -36*o**6/5 + 9*o**5/5 + 575*o**4/8 - 24*o**3 + 3*o**2 - 2*o - 6. Determine m so that i(m) = 0.
-2, 1/12, 2
What is p in 28/9*p**3 - 46/9*p**2 - 8/9 - 2/3*p**4 + 32/9*p = 0?
2/3, 1, 2
Let n(p) be the second derivative of -1/168*p**7 - 1/12*p**3 + 0*p**2 - 7/48*p**4 - 16*p + 0 - 1/24*p**6 - 9/80*p**5. Factor n(o).
-o*(o + 1)**3*(o + 2)/4
Suppose -24964*h + 24967*h = 0. Solve 0*k**2 + 3/4*k**3 + h*k + 0 - 1/4*k**4 = 0 for k.
0, 3
Suppose -10/3*f**2 - 2*f**4 + 0 - 2/3*f**5 + 6*f**3 + 0*f = 0. What is f?
-5, 0, 1
Let i = 30069/2 - 15033. What is z in i*z + 3/2*z**2 - 3 = 0?
-2, 1
Suppose -a**2 - 8*a**2 - 3*a**3 + 12*a**3 - 42*a - 12*a**2 - 12*a**2 = 0. What is a?
-1, 0, 14/3
Let m(n) = 3*n**2 - 10*n - 20. Let h be m(10). Let i be 15/h - ((-1)/(-1))/(-4). Find a such that 5/3*a**3 + 0 - a**5 - 2/3*a + i*a**4 - 1/3*a**2 = 0.
-1, -2/3, 0, 1
Let f(a) be the second derivative of -a**5/30 + a**3/3 - 2*a**2/3 - 125*a. Factor f(p).
-2*(p - 1)**2*(p + 2)/3
Let b be -3 + (66/(-88))/((-1)/12). Let l(k) be the second derivative of 0*k**2 - 1/15*k**3 - b*k + 1/30*k**4 + 0. Determine i so that l(i) = 0.
0, 1
Let s(l) = 10*l**2 - 49*l. Let r(c) = 8*c**2 - 50*c. Let x(z) = -3*r(z) + 2*s(z). Solve x(p) = 0.
0, 13
Let d(y) = y**2 - 5*y - 4. Let l be d(6). What is x in -10*x**2 - 13*x**2 - 8*x + 19*x**l + 12 = 0?
-3, 1
Let b(r) = -113*r - 223. Let a be b(-2). Factor 8/3*q**2 + 0 - 2/3*q**5 - 2/3*q + 8/3*q**4 - 4*q**a.
-2*q*(q - 1)**4/3
Suppose 2*i + 4 = 0, 4*b - 8*b - 5*i + 6 = 0. Solve 7*t**b - 4*t**4 - 2*t**4 = 0 for t.
0
Factor -58/7 - 166/7*r**2 + 6/7*r**3 - 230/7*r.
2*(r - 29)*(r + 1)*(3*r + 1)/7
Let v = 3683/14 - 263. Let a(i) be the second derivative of 6*i - 2/7*i**2 + 1/70*i**5 + v*i**4 + 0 - 1/21*i**3 - 1/105*i**6. Suppose a(c) = 0. What is c?
-1, 1, 2
Let k = 872 + -1777/2. Let b = 107/6 + k. Factor 2*g - 2/3 - 2/3*g**5 - 4/3*g**3 + 2*g**4 - b*g**2.
-2*(g - 1)**4*(g + 1)/3
Let -9*s**4 - 6*s**3 + 18 + 8*s + 14*s - 14*s**2 + 18 + 11*s**4 + 8*s = 0. What is s?
-2, -1, 3
Suppose 4*t + 4*o = 0, 3*t = 4*t + 4*o. Suppose 0 = -5*x + 10 - t. Factor -6 + 4 + 0*d**2 - 2*d**x - 2*d + 6.
-2*(d - 1)*(d + 2)
Let u(b) = 7*b**2 + 5*b - 2. Let c be -9 + 9/((-36)/(-16)). Let r(x) = 3*x**2 + 2*x - 1. Let j(k) = c*r(k) + 2*u(k). Factor j(o).
-(o - 1)*(o + 1)
Let f(w) be the second derivative of -w**5/70 + 6*w**4/7 - 108*w**3/7 - 76*w. Solve f(b) = 0 for b.
0, 18
Let o = -46210 + 46213. Factor -4 + 22/3*t + 2/3*t**o - 4*t**2.
2*(t - 3)*(t - 2)*(t - 1)/3
Suppose -16*j = 5*g - 20*j - 12, -8 = -4*j. Suppose -4/3*v**3 + 2/3 + 4/3*v + 0*v**2 - 2/3*v**g = 0. What is v?
-1, 1
Let n(o) be the third derivative of -3*o**5/20 + 19*o**4/24 - o**3/3 + 118*o**2. Factor n(b).
-(b - 2)*(9*b - 1)
Let n be (-1)/(40/(-18))*592/444. Determine f, given that -f**5 + 7/5*f**3 + 3/5*f**2 - 2/5*f + 0 - n*f**4 = 0.
-1, 0, 2/5, 1
Let f(w) = 3*w + 17. Let o be f(-5). Suppose -2*k + p = -5, 2*p + 4 = 2*k - 2. Suppose 3*d**o + 0*d**4 + 2*d**4 - 5*d**2 + 0*d**k = 0. Calculate d.
-1, 0, 1
Let p(x) = -31*x - 9. Let h be p(-3). Let o = 84 - h. Factor o + 4*u**2 + 32/7*u**3 + 8/7*u + 12/7*u**4.
4*u*(u + 1)**2*(3*u + 2)/7
What is d in 1/5*d**2 + 0*d - 16/5 = 0?
-4, 4
Let l(m) be the second derivative of 0*m**4 + 0*m**2 + 0*m**3 + 1/50*m**5 + 0 - 4*m. Let l(w) = 0. Calculate w.
0
Let m(n) be the second derivative of -3/2*n**2 + 1/12*n**4 - 1/3*n**3 + 0 - 19*n. Let m(z) = 0. Calculate z.