 5*m**6/32 + 3*m**5/40 - m**2 + 134*m. Determine g so that t(g) = 0.
-3/7, 0, 2
Let m(s) be the third derivative of -s**8/15120 + s**7/1890 - s**6/540 + 9*s**5/20 - 22*s**2. Let k(c) be the third derivative of m(c). Let k(a) = 0. What is a?
1
Let r be ((-10)/(-30))/((-1)/(-18)) + 0. Let a(j) = -j**3 + 6*j**2 + 4*j - 21. Let m be a(r). Determine v so that 1/3*v - 2/3*v**2 - 1/3*v**m + 2/3 = 0.
-2, -1, 1
Let d(a) be the second derivative of a**4/8 - 5*a**3/2 - 117*a**2/4 - 5*a + 49. Factor d(t).
3*(t - 13)*(t + 3)/2
Let o = 15030/7 + -2147. Let -o*f**2 + 6/7*f - 9/7 = 0. Calculate f.
3
Let j(a) be the second derivative of -4*a**2 + 12*a + 2*a**3 + 0*a**4 + 0 - 1/5*a**5. Factor j(i).
-4*(i - 1)**2*(i + 2)
Let r = 1540 - 10778/7. Factor -12/7*a - 18/7 - r*a**2.
-2*(a + 3)**2/7
Let p be (-6)/8*24/(-6). What is h in -h**5 + 2*h**5 + 15*h**3 - 20*h**p + 9*h**3 - 4*h**4 = 0?
0, 2
Suppose 5*r + 7 = -3*f, r + 10 = 4*f - 2*r. Let o(n) = 12*n. Let u be o(f). Let 0*p**3 - 4*p**4 + 5*p**2 + 0*p**3 - u*p**3 - 13*p**2 = 0. What is p?
-2, -1, 0
Let l(r) = 15*r + 1. Let w be l(-1). Let m = w - -23. Determine c so that 2*c + 6*c + m - 2*c + c**2 = 0.
-3
Let g be (14/24)/(203/232). Find t, given that -5/9*t**4 + 1/3*t**2 + 0 - g*t**3 + 4/9*t = 0.
-1, 0, 4/5
Suppose 0 = 2901*w - 2902*w. Let h(s) be the third derivative of -9*s**2 + w - 91/90*s**5 + 2/9*s**4 - 49/36*s**6 + 0*s + 4/9*s**3. Solve h(b) = 0.
-2/7, 1/5
Let o = 25 - 22. Factor -2*q**2 + 40*q**o - 79*q**3 + 2*q + 2*q**4 + 37*q**3.
2*q*(q - 1)**2*(q + 1)
Let k = -470/3 + 1889/12. Suppose k - 2*v + 5/4*v**2 = 0. What is v?
3/5, 1
Let w(m) be the second derivative of -4/45*m**3 - 1/15*m**2 - 4*m + 2 - 1/30*m**4. Suppose w(i) = 0. What is i?
-1, -1/3
Let b = 26 - 76/3. Let o be -81 + 88 - ((-26)/(-3) - 2). Factor b*z**4 - o + z**3 - z - 1/3*z**2.
(z - 1)*(z + 1)**2*(2*z + 1)/3
Let l(p) be the third derivative of -p**6/1080 + 31*p**5/270 - 61*p**4/216 - 41*p**2. What is g in l(g) = 0?
0, 1, 61
Let -13/3*k**4 - 30*k**2 + 58/3*k**3 + 1/3*k**5 - 9*k + 45 = 0. Calculate k.
-1, 3, 5
Let s(k) be the second derivative of 2/3*k**3 + 0*k**2 + 5/3*k**4 - 12*k + 0 - 11/20*k**5. Let s(l) = 0. What is l?
-2/11, 0, 2
Let m(j) = 4*j**2 + 31*j + 12. Let h be m(-10). Let y = h - 102. What is p in -6/5*p + y - 3/5*p**2 = 0?
-2, 0
Let p be (-4)/18 - (3 - 3) - 64/(-126). Factor -p*o**3 + 0 + 0*o + 0*o**2.
-2*o**3/7
Let f(c) = -c**2 - 7*c - 3. Let p be f(-6). Suppose 5*o - u - 10 = -5*u, 0 = -p*u. Find x such that 2/5*x**o - 2/5*x + 0 = 0.
0, 1
Suppose 0*b - 4/17*b**4 + 4/17*b**2 - 2/17*b**3 + 2/17*b**5 + 0 = 0. What is b?
-1, 0, 1, 2
Let b(a) be the first derivative of -2*a**3/33 - 63*a**2/11 + 260*a/11 + 670. Factor b(r).
-2*(r - 2)*(r + 65)/11
Let b(r) be the first derivative of -1/12*r**3 + 1/16*r**2 - 22 + 0*r + 1/32*r**4. Factor b(k).
k*(k - 1)**2/8
Let u(r) = 2*r**4 - 18*r**2 - 10*r + 3. Let n(q) = -q**4 + 19*q**2 + 10*q - 4. Let i(z) = 3*n(z) + 4*u(z). Factor i(g).
5*g*(g - 2)*(g + 1)**2
Let n be (8/(-24))/(3/(-6)). Factor 1/3*z**3 - 1/3*z**4 + z**2 - n - 1/3*z.
-(z - 2)*(z - 1)*(z + 1)**2/3
Solve -160 - 64*b**4 - 4*b**5 - 104*b - 102*b**3 - 190*b**3 - 568*b**2 - 109*b + 32*b - 315*b = 0.
-10, -2, -1
Let h = -224 - -229. Let u(p) be the first derivative of 4 + 0*p - 3/25*p**h + 4/15*p**3 + 1/30*p**6 + 0*p**4 + 0*p**2. Let u(c) = 0. What is c?
-1, 0, 2
Let l(s) be the second derivative of s**4/3 - 2*s**3/3 - s + 9. Determine x so that l(x) = 0.
0, 1
Let d(v) = -v**2 - 5*v. Let g be d(-3). Factor -12 + t - g*t - 7*t - 3*t**2.
-3*(t + 2)**2
Let n(q) = -2*q + 15. Let p be n(-5). Suppose -5*u + 18 = -4*f + 1, p = 5*f + 3*u. Factor -5*v - 2 - 7/4*v**3 + 13/2*v**f.
-(v - 2)**2*(7*v + 2)/4
Let s be 3/3 + (11 - -3). Let d be 4/(-2) - -3*20/s. Factor 1/4*b**d + 0 + 1/2*b.
b*(b + 2)/4
Let f = -13 + 13. Suppose 2 = o - f. Factor 6*v**3 + 2*v**5 - o*v**4 + 7*v**5 - 3*v**5 - 13*v**4.
3*v**3*(v - 2)*(2*v - 1)
Let x = -11142 + 11146. Let -15/2*m**x - 3/2*m**2 - 51/2*m + 9 + 51/2*m**3 = 0. Calculate m.
-1, 2/5, 1, 3
Let u be ((-218)/(-11445))/((-1)/(-30)). Let -4/7*w**5 - 8/7*w - u*w**4 + 0 + 12/7*w**3 + 4/7*w**2 = 0. Calculate w.
-2, -1, 0, 1
What is s in -1/5*s**2 - 64/5 + 16/5*s = 0?
8
Let g(i) = -i - 3. Let t be g(-6). Suppose -4 = -t*y + 2. Find n, given that n**3 - 3*n + 1 + 3*n**2 + 4*n + y*n = 0.
-1
Let k be 3/(21/(-2)) + (-494)/133. Let h(j) = 13 - 3*j + 0*j - 6*j**2 + 8. Let t(f) = 3*f**2 + f - 10. Let u(z) = k*h(z) - 9*t(z). Factor u(r).
-3*(r - 2)*(r + 1)
Let o(i) = 3*i**3 - 5*i**2 - 19*i - 11. Let r(m) = -2*m**3 + 2*m**2 + 10*m + 6. Let x(l) = 3*o(l) + 5*r(l). Factor x(z).
-(z + 1)**2*(z + 3)
Let i = 6 + -12. Let g = i + 9. What is b in g*b**3 - 2*b**3 - 8 + 12*b - 5*b**3 = 0?
-2, 1
Factor -8/3*t**2 + 4 + 46/3*t.
-2*(t - 6)*(4*t + 1)/3
Let d = 3517 - 3517. Factor -6/13*u**3 + 0 + d*u + 2/13*u**2.
-2*u**2*(3*u - 1)/13
Factor -13*p**2 - 48*p - 45*p**3 - 158*p**2 + 391*p**2 - 67*p**3.
-4*p*(4*p - 1)*(7*p - 12)
Let b = 18760 - 75037/4. Factor 0*s**3 + 0 + 3/2*s - b*s**4 + 9/4*s**2.
-3*s*(s - 2)*(s + 1)**2/4
Let x(m) = -4*m**3 - 4*m**2 + 11*m + 3. Let y(g) = -12*g**3 - 12*g**2 + 34*g + 10. Let i = 44 + -34. Let j(q) = i*x(q) - 3*y(q). What is w in j(w) = 0?
-2, 0, 1
Suppose -5*m**2 - 2 - 13*m - 2 - 197*m + 4 = 0. Calculate m.
-42, 0
Factor 6/7*s**2 + 40/7*s + 24/7.
2*(s + 6)*(3*s + 2)/7
Let w be (-6)/21 + 32/14. Suppose -q = 5*s - 9 - 14, -4*q = -3*s. Solve q*m + m**w + 2 - 3*m + 0*m - 3*m = 0 for m.
1, 2
Let w = 70 + -66. Let y(s) = 2*s**2 - 5*s + 2. Let c be y(4). Let 24*a**w + 6*a**3 + c*a**5 - 2*a + 2*a - 4*a**2 = 0. What is a?
-1, 0, 2/7
Let n(q) = 35*q**2 - 50*q - 15. Let b(y) = 9*y**2 - 13*y - 4. Let s be (270/(-36))/(1/(-2)). Let v(t) = s*b(t) - 4*n(t). Factor v(c).
-5*c*(c - 1)
Let a(d) be the first derivative of -d**3 - 3*d**2/2 + 7. Let p(w) = -6*w**2 - 6*w. Let m(b) = 5*a(b) - 2*p(b). Factor m(s).
-3*s*(s + 1)
Let z(m) be the first derivative of m**5/20 + m**4/16 + 56. Suppose z(s) = 0. What is s?
-1, 0
Suppose 0 = 4*w - 3*g - 8, 3*w - 38 = 3*g - 32. Solve -1/3*i**3 + 0 - 2/3*i**w + 1/3*i**4 + 0*i = 0 for i.
-1, 0, 2
Suppose 0 = -k + 5*t - 5, -t = -3*k + 21 - 8. Suppose u**3 + 2*u**3 + 2*u**2 - k*u**4 + 2*u**3 - 5*u + 3*u**2 = 0. What is u?
-1, 0, 1
What is a in 30*a - 1259*a**3 + 613*a**3 - 225 + 616*a**3 + a**4 + 224*a**2 = 0?
-1, 1, 15
Find o such that -6/19*o**3 + 32/19*o**2 + 2/19*o**5 + 24/19*o - 12/19*o**4 + 0 = 0.
-1, 0, 2, 6
Let o(m) be the third derivative of 45/8*m**4 + 18*m**2 + 45/2*m**3 + 1/24*m**6 + 0*m + 3/4*m**5 + 0. Suppose o(b) = 0. What is b?
-3
Let y(b) = 5*b**2 + 25*b - 90. Let d(s) = -6*s**2 - 27*s + 90. Let n(l) = 2*d(l) + 3*y(l). Determine h, given that n(h) = 0.
-10, 3
Let 26*q**2 - 2 - 78*q**2 + 76*q - 20*q - 2*q**2 = 0. Calculate q.
1/27, 1
Let z be (-7)/1 + 69 + -62. Let t(m) be the second derivative of 0 + z*m**3 + 0*m**2 - 9*m + 1/2*m**4 - 27/20*m**5. Factor t(y).
-3*y**2*(9*y - 2)
Let m(b) = b**2 + 28*b - 288. Let g be m(8). Factor 0*k + 0*k**4 + 0 - 2/9*k**5 + 2/9*k**3 + g*k**2.
-2*k**3*(k - 1)*(k + 1)/9
Factor -161 - 14*h - 6*h + 4*h**2 - 131 + 268.
4*(h - 6)*(h + 1)
Let t(a) be the second derivative of -a**4/6 + 49*a**2 + 4*a + 29. Determine d so that t(d) = 0.
-7, 7
Find j, given that -18/13*j**4 + 0*j + 0 - 32/13*j**2 + 48/13*j**3 + 2/13*j**5 = 0.
0, 1, 4
Find p such that 14/5*p**4 + 4/5*p - 6/5*p**3 - 6/5*p**2 + 0 - 6/5*p**5 = 0.
-2/3, 0, 1
Let a(l) be the third derivative of l**10/302400 + l**9/60480 - l**8/13440 - 2*l**5/15 + 7*l**2. Let h(v) be the third derivative of a(v). Factor h(m).
m**2*(m - 1)*(m + 3)/2
Suppose 12*r - 9*r = 0. Let k(n) be the second derivative of 0 + 0*n**3 - 1/12*n**4 + r*n**2 - 1/20*n**5 - 4*n. Determine l so that k(l) = 0.
-1, 0
Let k(n) = 4*n**2 + 32*n + 45. Suppose -20 = 9*r - 146. Let v(l) = 20*l**2 + 160*l + 226. Let h(g) = r*k(g) - 3*v(g). Let h(f) = 0. Calculate f.
-6, -2
Let l be ((-18)/15)/(564/(-15)). Let n = l - -179/282. Factor 6 + n*r**2 - 4*r.
2*(r - 3)**2/3
Factor -3/2*i**3 + 1 + 3/2*i - 1/2*i**2 - 1/2*i**4.
-(i - 1)*(i + 1)**2*(i + 2)/2
Let q(w) be the third derivative of 67*w**5/510 - w**4/3 + w**3/51 - 2*w**2 - 257. Suppose q(k) = 0. What is k?
1/67, 1
Let b(q) be the first derivative of -q**6/6 + 6*q**5/5 + 7*q**4/4 - 92*q**3/3 + 7