f -q**6/540 + q**5/90 - q**4/54 - 80*q**2. What is f in p(f) = 0?
0, 1, 2
Let d(b) be the third derivative of 0 + 0*b**3 + 0*b + 1/36*b**4 + 1/45*b**5 + 1/144*b**6 + 1/1260*b**7 + b**2. Find o such that d(o) = 0.
-2, -1, 0
Suppose 8*u - 24 = 6*u. Suppose -2*y = 2*y - u. What is r in -r**5 - 5*r**4 - 5*r**3 + r**y + 9*r**4 = 0?
0, 2
Let p(k) be the second derivative of -k**7/12600 + k**6/900 + k**5/50 - 10*k**4/3 - 6*k. Let g(f) be the third derivative of p(f). Factor g(r).
-(r - 6)*(r + 2)/5
Let r(a) be the first derivative of a**4/6 - 4*a**3 + 20*a**2 + 400*a/3 - 86. Factor r(t).
2*(t - 10)**2*(t + 2)/3
What is p in 1/3*p**2 + 22/3 - 13/3*p = 0?
2, 11
Let 2112*h - 2178 + 1/2*h**3 + 131/2*h**2 = 0. What is h?
-66, 1
Let u(g) = -4*g - 42. Let b be u(-10). Let v be (b - 2/4*4)/(-14). Factor 2/7*l**3 + 2/7 - v*l**2 - 2/7*l.
2*(l - 1)**2*(l + 1)/7
Let b(z) be the third derivative of z**8/196 + 16*z**7/735 - 2*z**5/21 - z**4/14 + 4*z**3/21 - 77*z**2 + 2*z. Determine f, given that b(f) = 0.
-2, -1, 1/3, 1
Let w(c) be the second derivative of 1/50*c**5 - 1/105*c**7 + 0*c**6 + 0*c**3 + 0*c**2 + 0 + 11*c + 0*c**4. Find p, given that w(p) = 0.
-1, 0, 1
Let l(k) be the second derivative of 1/18*k**2 + 0 + 12*k + 0*k**3 - 1/108*k**4. Factor l(d).
-(d - 1)*(d + 1)/9
Let o(f) be the first derivative of 0*f**2 - 2/27*f**3 + 0*f + 0*f**4 + 2/45*f**5 + 39. Factor o(l).
2*l**2*(l - 1)*(l + 1)/9
Let l(w) be the first derivative of -8/15*w**3 - 4/5*w + 4 - w**2 - 1/10*w**4. Solve l(p) = 0 for p.
-2, -1
Suppose -9 - 106 = -23*t. Let l be t/(-30)*-6*0. Factor -2/3*p**2 + 5/3*p**4 + p**3 + 0*p + l.
p**2*(p + 1)*(5*p - 2)/3
Let x(j) be the second derivative of j**5/60 - 17*j**4/36 + 40*j**3/9 - 32*j**2/3 - 86*j + 4. Solve x(i) = 0.
1, 8
Factor 0 - 159/7*d - 156/7*d**2 + 3/7*d**3.
3*d*(d - 53)*(d + 1)/7
Solve -2*g - 4/9 - 8/9*g**2 = 0.
-2, -1/4
Let j = 1/358 - -683/11814. Let i(a) be the third derivative of 0 - 7/330*a**5 + a**2 + 0*a - j*a**4 + 4/33*a**3 + 1/132*a**6. Factor i(z).
2*(z - 2)*(z + 1)*(5*z - 2)/11
Determine u, given that -20*u**2 + 5*u + u**3 - 24*u**2 + 46*u**2 - 2*u**3 - 6 = 0.
-2, 1, 3
Let u be ((-157)/1422)/(-6*4/1449). Let z = u - -1/1264. What is j in z*j - 50/3 - 2/3*j**2 = 0?
5
Let i(w) = -w - 1. Let r(m) be the second derivative of -m**4/4 - 23*m**3/2 - 429*m**2/2 + 37*m. Let v(o) = 3*i(o) + r(o). Factor v(n).
-3*(n + 12)**2
Let j be (-12)/90 - 32/(-15). Let w(g) = g**3 - 5*g**2 + 3*g + 7. Let k be w(4). Determine o, given that -64/7*o - 48/7*o**j - 2/7*o**4 - 32/7 - 16/7*o**k = 0.
-2
Let -4/5*i**2 - 2/15 - 8/15*i - 8/15*i**3 - 2/15*i**4 = 0. What is i?
-1
Suppose -18*r + 7*r + 22 = 0. Let p(v) be the second derivative of -3*v + 4*v**3 + 0 + 4/3*v**4 + 9/2*v**r. Find l, given that p(l) = 0.
-3/4
Suppose -30 = -132*k + 448 - 82. Factor 1/8*n**k + 0*n + 0 - 1/8*n**2.
n**2*(n - 1)/8
Solve -2*s + 2/3*s**3 + 0 - 4/3*s**2 = 0 for s.
-1, 0, 3
Suppose -j + 4*j = 12. Factor 4*u - u**4 + 2*u**4 + u**4 + 2*u**2 - 4*u**3 - 4*u**j.
-2*u*(u - 1)*(u + 1)*(u + 2)
Let l be -1 + 4/6 + (-233)/30. Let a = l - -43/5. What is z in -z**2 + 1/2*z**5 - a*z**3 + z**4 + 0 + 0*z = 0?
-2, -1, 0, 1
Let x(v) be the third derivative of -v**5/8 - 61*v**4/24 - 4*v**3/3 + 3*v**2 + 2. Factor x(h).
-(h + 8)*(15*h + 2)/2
Let k(u) = 3*u - 35. Let v be k(13). Let f be ((-48)/15)/4 - -1. Let 2*z**2 + 4/5*z - 1/5*z**3 - f*z**5 - 8/5 - 4/5*z**v = 0. What is z?
-2, 1
Let b(a) be the second derivative of -a**8/168 - 2*a**7/105 + a**5/15 + a**4/12 + 25*a**2/2 + 10*a. Let o(s) be the first derivative of b(s). Factor o(x).
-2*x*(x - 1)*(x + 1)**3
Factor 0 + 0*g - 2/9*g**4 - 20/9*g**2 - 22/9*g**3.
-2*g**2*(g + 1)*(g + 10)/9
Let w(z) be the second derivative of -z**9/11340 + z**7/630 - z**6/270 - 19*z**4/6 + 22*z. Let j(t) be the third derivative of w(t). Factor j(g).
-4*g*(g - 1)**2*(g + 2)/3
Find r, given that 22/3*r**2 + 0 + 34/3*r**3 - 4*r = 0.
-1, 0, 6/17
Let z(b) be the first derivative of 55*b**3/3 - 15*b**2 - 274. Factor z(l).
5*l*(11*l - 6)
Let x = 79 + -2369/30. Let j(g) be the second derivative of 0*g**2 + x*g**6 + 0*g**5 - 1/12*g**4 - 1/84*g**7 + 2*g + 0 + 1/12*g**3. Factor j(w).
-w*(w - 1)**3*(w + 1)/2
Let s(b) = 3*b + 98. Let z be s(-32). Determine p, given that z*p - 5/4*p**3 + 3/4*p**2 - 1 - 1/2*p**4 = 0.
-2, 1/2, 1
Determine z so that 0 + 398*z**2 + 5*z**3 - 214*z**2 + 28*z - 206*z**2 - 8 = 0.
2/5, 2
Let u = 49 + -41. Suppose -5*s = u - 28. Factor -1/2*i + 0*i**2 + i**s + 3/2*i**3 + 0.
i*(i + 1)**2*(2*i - 1)/2
Let t(g) = g**3 + 29*g**2 + 11*g - 45. Let u(c) = 5*c**3 + 115*c**2 + 45*c - 180. Let o(x) = -15*t(x) + 4*u(x). Find p, given that o(p) = 0.
-3, 1
Let w = 684/7 - 676/7. Factor 8/7*a**2 + 0*a + 0 + w*a**4 + 20/7*a**3.
4*a**2*(a + 2)*(2*a + 1)/7
Let -2/9*n**3 - 4/3 + 14/9*n + 0*n**2 = 0. What is n?
-3, 1, 2
Let p = 54 + -50. Factor -w**2 - 2*w**3 + 3*w**2 + 16*w - 6*w - p - 8*w**2 + 2*w**4.
2*(w - 1)**3*(w + 2)
Let b(c) be the third derivative of -c**8/672 + c**6/48 - c**4/12 - 4*c**2 - c. Find s such that b(s) = 0.
-2, -1, 0, 1, 2
Let u(m) = -13*m**2 + 25. Let n(r) = 4*r**2 - r + 1. Let d(p) = 3*n(p) + u(p). Factor d(b).
-(b - 4)*(b + 7)
Let r = 224 + -222. Factor 3/10*a + 0 + 1/10*a**r.
a*(a + 3)/10
Determine t so that -2*t**2 + 8/7 + 6/7*t**4 + 34/7*t**3 - 16/7*t - 18/7*t**5 = 0.
-1, 2/3, 1
Let w(n) = -3*n**3 - 12*n**2 - 15*n - 24. Let x(s) be the first derivative of -s**3/3 - s**2/2 - s + 4. Let g(q) = w(q) - 18*x(q). Factor g(v).
-3*(v - 2)*(v - 1)*(v + 1)
Let d(v) be the third derivative of 2*v**7/105 + v**6/6 + 8*v**5/15 + 2*v**4/3 + 92*v**2 - 2*v. Factor d(t).
4*t*(t + 1)*(t + 2)**2
Find k, given that -1/3*k + 2/3 - k**2 + 1/3*k**3 + 1/3*k**4 = 0.
-2, -1, 1
Let a(i) be the second derivative of i**6/30 + i**5/10 - i**4/12 - i**3/3 + 2*i - 104. Factor a(z).
z*(z - 1)*(z + 1)*(z + 2)
Let u = 47 - -430. Let b be 3/(-1) - u/(-135). Factor 2/5*z**2 - 8/15 - 2/15*z**4 - 4/15*z**3 + b*z.
-2*(z - 1)**2*(z + 2)**2/15
Let h be ((-4)/(-42))/(240/1260). Let s(o) be the third derivative of -h*o**3 - 1/80*o**5 - 13*o**2 - 1/8*o**4 + 0 + 0*o. Factor s(k).
-3*(k + 2)**2/4
Let r be (-16)/(-4) - 2*-1. Let m(o) = -o**3 - 10*o**2 + 24*o + 15. Let l be m(-12). Solve -9*d**2 + 29*d**2 - 10*d**4 - 6*d - r*d + l*d**3 - 5*d**5 - 8*d = 0.
-2, 0, 1
Let c = -16362 - -16362. Factor c - 2/7*f**3 - 32/7*f - 16/7*f**2.
-2*f*(f + 4)**2/7
Let d(q) = q**3 - q - 2. Let x(c) = 3*c**3 - 1. Let a be x(1). Let k be d(a). Let -3 + 29*o**2 - 2*o - 12*o**2 - 16*o**2 + k = 0. Calculate o.
1
Suppose 106/7*a**3 + 110/7*a + 214/7*a**2 + 2/7 = 0. What is a?
-1, -1/53
Let p(b) be the second derivative of b**5/30 - b**4/6 - 7*b**2/2 - 16*b. Let a(v) be the first derivative of p(v). Factor a(o).
2*o*(o - 2)
Let z(o) be the third derivative of -7*o**6/480 - 19*o**5/240 + 17*o**4/48 - o**3/3 + 70*o**2. Solve z(y) = 0.
-4, 2/7, 1
Let h = 1241559/206 - 6027. Let o = h - -875/3502. Solve 0*c**2 - 2/17*c**4 + 2/17 - o*c**3 + 4/17*c = 0 for c.
-1, 1
Let p(r) be the first derivative of 2*r**3/39 + 14*r**2/13 + 98*r/13 - 116. Suppose p(u) = 0. Calculate u.
-7
Factor -k**4 - 3*k - 4*k + 0*k**3 - 2*k + 25*k + 9*k**3 - 24*k**2.
-k*(k - 4)**2*(k - 1)
Let 1/8*u**2 - 1/4*u + 1/8 = 0. Calculate u.
1
Let g(r) = -r + 3. Suppose 0*v - 5*v + 13 = 3*y, -v + 3 = y. Let z be g(y). Factor -2/3*h**3 + 10/3*h**z - 6 - 2*h.
-2*(h - 3)**2*(h + 1)/3
Let a(t) = 4 - t**3 - 44*t**2 + 44*t**2 - 12*t**3 - 4*t**4 - t. Let r(d) = -3*d**4 - 9*d**3 - d + 3. Let w(k) = 5*a(k) - 7*r(k). Factor w(n).
(n - 1)**3*(n + 1)
Let d(v) = v**3 + 16*v**2 + 16*v - 6. Let n(c) = -30*c**2 - 34*c + 13. Let g(w) = 13*d(w) + 6*n(w). Factor g(j).
j*(j + 2)*(13*j + 2)
Let w be 20*((-8)/(-30))/(6/9). Solve -w*r**4 + 20*r**2 - 7*r**4 - 138*r**3 + 163*r**3 - 20*r = 0.
-1, 0, 2/3, 2
Let l(t) = t**3 + 14*t**2 + 23*t - 12. Let n be l(-12). Let y be (n/(-9))/(5 + -3). Determine i so that y + 4/9*i**2 + 2/9*i**3 + 0*i - 2/3*i**4 = 0.
-2/3, 0, 1
Let o be (32/10*-1)/(2/(-10)). Suppose -429*z - 41*z**2 - 363 - 3*z**3 - 14*z**2 + 2*z**2 - o*z**2 = 0. Calculate z.
-11, -1
Let n(w) = -6*w**3 + 4*w**2 - 2*w. Let g(u) = u**4 + 6*u**3 - 3*u**2 + 2*u. Let l(m) = -2*g(m) - 3*n(m). Determine v so that l(v) = 0.
0, 1
Let -8*f**5 + 27*f**3 - 47*f**3 + 12*f**2 + 24*f**3 - 12*f**4 + 4*f = 0.