120*g**2. Suppose q(b) = 0. What is b?
-6, -1, 1
Factor 12*k**3 - 24 + 3/2*k**4 - 12*k + 45/2*k**2.
3*(k - 1)*(k + 1)*(k + 4)**2/2
Let s(c) = -c**3 - 16*c**2 - 59*c - 16. Let w be s(-5). Factor 6/7*r + 2/7*r**2 - 6/7*r**3 - 4/7 + 2/7*r**w.
2*(r - 2)*(r - 1)**2*(r + 1)/7
Suppose 4*n = -2*r - 16, -4*r = -2*n - 3*r - 4. Let g(c) = -c**2 + 7*c. Let s(l) = 4*l**2 - 34*l. Let m(w) = n*s(w) - 14*g(w). Determine f so that m(f) = 0.
-2, 0
Let l(v) = -v**3 + 6*v**2 - 10*v + 3. Let o be l(3). Suppose 2/5*j + 3/5*j**2 + o*j**3 - 1/5*j**4 + 0 = 0. What is j?
-1, 0, 2
Let f be 764/17954 + (-3374)/(-235). What is h in -144/5*h**3 - 32/5*h**4 - 8/5 - 194/5*h**2 - f*h = 0?
-2, -1/4
Let g(u) be the second derivative of -u**5/190 - 10*u**4/57 - 77*u**3/57 + 242*u**2/19 - 29*u. Factor g(j).
-2*(j - 2)*(j + 11)**2/19
Let t(g) = 14*g + g + g**3 - 11 - 9*g**2 - 5*g. Let p be t(8). Let -p*f + 4 + 5*f + f**2 - 5*f = 0. Calculate f.
1, 4
Suppose 24/5*w**3 + 9/5 + 57/5*w**2 + 42/5*w = 0. Calculate w.
-1, -3/8
Let p(d) be the first derivative of d**7/7560 + d**6/3240 + 20*d**3/3 + 2. Let q(n) be the third derivative of p(n). Solve q(g) = 0 for g.
-1, 0
Let y(m) = -9*m**2 - 65*m - 73. Let n(t) = -t**2 - 8*t - 9. Let d(r) = 51*n(r) - 6*y(r). Factor d(f).
3*(f - 7)*(f + 1)
Let o(m) be the first derivative of -m**6/10 - 36*m**5/25 + 6*m**4/5 + 96*m**3/5 - 24*m**2/5 - 576*m/5 + 87. Find y such that o(y) = 0.
-12, -2, 2
Let o(i) = -i**2 + i + 4. Let t(k) = -10*k**2 - 135*k + 60. Let w(d) = 15*o(d) - t(d). Factor w(f).
-5*f*(f - 30)
Let p(w) be the second derivative of -w**4/84 + 5*w**3/3 - 175*w**2/2 + 27*w. Determine b, given that p(b) = 0.
35
Factor -10*a**2 + a**2 + 39*a + 12 + 18.
-3*(a - 5)*(3*a + 2)
Let i(k) be the second derivative of 2*k**7/63 - 19*k**6/45 + 17*k**5/10 - 59*k**4/18 + 31*k**3/9 - 2*k**2 + 2*k - 6. What is z in i(z) = 0?
1/2, 1, 6
Suppose 63*q - 22 = 24*q + 56. Solve 2*j**5 + 0*j + 1/2*j**4 - q*j**3 + 0 - 1/2*j**2 = 0.
-1, -1/4, 0, 1
Determine n, given that -75/2*n**2 + 21/2*n**4 + 0 + 9*n + 18*n**3 = 0.
-3, 0, 2/7, 1
Let v be (-312)/(-182) - (1 - (54/(-7))/(-6)). Find u such that 0 + 0*u + 50/11*u**3 + 28/11*u**4 + 12/11*u**v = 0.
-3/2, -2/7, 0
Let t(m) = 17*m**2 - 639*m - 21136. Let h(z) = 3*z**2 - 128*z - 4227. Let w(p) = 22*h(p) - 4*t(p). Let w(n) = 0. Calculate n.
-65
Factor 1/3*w**3 + 0 + 4/3*w**2 + 4/3*w.
w*(w + 2)**2/3
Let o(u) = 2*u**2 - 19*u + 67. Suppose -2*p + 2*j = 6, 5*p = 3*j - 0 - 17. Let d(x) = 2*x**2 - 20*x + 68. Let r(v) = p*o(v) + 5*d(v). Factor r(l).
2*(l - 6)**2
Suppose -5*w = -8*t + 40, -6*w + 10*w - t = -5. Let w + 9/7*g - 3/7*g**2 = 0. What is g?
0, 3
Factor 1/2*v + 4/3*v**3 + 3*v**2 - 1/3.
(v + 2)*(2*v + 1)*(4*v - 1)/6
Let i = 374 + -371. Solve 3/2*d**3 + 3/2*d**2 - i*d + 0 = 0.
-2, 0, 1
Let u(r) be the second derivative of -400*r**2 - 64/75*r**6 - 10*r + 2 - 326/3*r**4 + 2/105*r**7 + 361/25*r**5 + 920/3*r**3. What is o in u(o) = 0?
1, 10
Let l(y) be the second derivative of -y**5/110 + 17*y**4/22 - 3*y**3 + 49*y**2/11 + 125*y. What is z in l(z) = 0?
1, 49
Let s(n) be the first derivative of -2*n**6/3 + 12*n**5/5 + 11*n**4 - 20*n**3 - 92*n**2 - 96*n + 688. Solve s(d) = 0.
-2, -1, 3, 4
Factor -27*a + 3*a - 3*a**4 - 36*a**2 - 7*a**3 + 3*a**3 - 14*a**3.
-3*a*(a + 2)**3
Suppose 13*u - 20 = 9*u. Suppose -27 + 17 = -u*c. Suppose 1/3*m**3 - m - 2/3 + 0*m**c = 0. What is m?
-1, 2
Suppose 87*w**3 - 84*w**3 - 7*w - 72 + 62*w + 29*w - 30*w**2 = 0. Calculate w.
2, 6
Let g(b) = b**2 - 35*b - 153. Let z be g(39). Solve 0*d**2 - 4/5 + 2/5*d**z - 6/5*d = 0.
-1, 2
Let h(s) be the first derivative of 1/18*s**3 - 11 + s - 7/12*s**2. Solve h(k) = 0 for k.
1, 6
Factor -70 + 5*x + 42*x**2 + 42*x**2 - 30*x**2 + 16*x**2 - 5*x**3.
-5*(x - 14)*(x - 1)*(x + 1)
Let z(t) be the first derivative of -t**8/224 - t**7/280 + 13*t**3/3 + 12. Let r(s) be the third derivative of z(s). Suppose r(o) = 0. Calculate o.
-2/5, 0
Let a(s) = -9*s**5 + 3*s**3 + 6*s**2 - 12*s. Let m(c) = -8*c**5 - c**4 + 4*c**3 + 7*c**2 - 12*c. Let r(p) = 5*a(p) - 6*m(p). What is k in r(k) = 0?
-2, 0, 1
Suppose 0*r - 4*r = -c - 8, 2*c - 4*r = 4. Suppose -2*d = -8*d + c. What is u in -15/2*u**d + 6 - 12*u = 0?
-2, 2/5
Let q = -260 + 8581/33. Let j(k) be the second derivative of -q*k**3 + 0 - k - 2/11*k**2 + 1/66*k**4. Factor j(c).
2*(c - 2)*(c + 1)/11
Let o be ((-217)/372 - 4/(-6))/((-3)/(-12)). Factor 1/6*v**2 + 0 + o*v.
v*(v + 2)/6
Let y(l) be the third derivative of -l**5/20 + 7*l**4/8 - 68*l**2. Factor y(h).
-3*h*(h - 7)
Factor -3/5 - 8/5*l**2 + 11/5*l.
-(l - 1)*(8*l - 3)/5
Let t(f) = f**2 - f - 1. Let y(v) = -7*v. Let w(u) = 7*u + 1. Let i(k) = -3*w(k) - 2*y(k). Let r(a) = i(a) + 2*t(a). What is j in r(j) = 0?
-1/2, 5
Let u(h) be the second derivative of -h**5/10 + 5*h**4/6 + 22*h**3/3 + 16*h**2 - 4*h - 15. Suppose u(m) = 0. Calculate m.
-2, -1, 8
Let i(j) be the third derivative of 0 - 1/16*j**4 + 1/6*j**3 + 0*j - 9*j**2 + 1/120*j**5. Factor i(l).
(l - 2)*(l - 1)/2
Let w(t) be the first derivative of t**6/72 + t**5/24 - 5*t**3 + 10. Let x(q) be the third derivative of w(q). Suppose x(k) = 0. What is k?
-1, 0
Suppose -5 + 17 = 4*t. Let -9*q**3 - 3*q**4 - 2*q**2 + 0*q**4 + t*q**5 + 6*q**3 + 5*q**2 = 0. What is q?
-1, 0, 1
Let x(y) = 169*y - 673. Let k be x(4). Find m, given that 2/15*m**k + 0 + 0*m**2 + 0*m = 0.
0
Let d(t) be the second derivative of 49*t**6/150 - 161*t**5/100 + 43*t**4/60 - t**3/10 - 379*t. Factor d(j).
j*(j - 3)*(7*j - 1)**2/5
Suppose 0 = m - 56 + 46. Let u(n) be the first derivative of 3*n**2 + 7/3*n**4 + 1/9*n**6 + 32/9*n**3 + 4/3*n + m + 4/5*n**5. Factor u(r).
2*(r + 1)**4*(r + 2)/3
Suppose -5 = 5*v, -3*m + 5*v = -5*m + 113. Determine a so that 57*a**3 - m*a**3 + 8*a - 4*a + 2*a**2 = 0.
-1, 0, 2
Suppose -4*w - 194*t + 195*t = -4, -w - t = -6. Suppose 3*f + 36/7 + 3/7*f**w = 0. What is f?
-4, -3
Let r(a) be the second derivative of a**4/42 - 27*a**3/7 + 80*a**2/7 - 138*a - 2. Factor r(d).
2*(d - 80)*(d - 1)/7
Let l(y) be the first derivative of y**8/672 - y**7/420 - y**6/240 + y**5/120 - 25*y**2 - 8. Let f(v) be the second derivative of l(v). Factor f(u).
u**2*(u - 1)**2*(u + 1)/2
Find h such that -h**2 - 40*h**3 - 30*h + 4*h**5 + 38*h + h**2 + 28*h = 0.
-3, -1, 0, 1, 3
Let b(f) be the second derivative of f**5/450 - f**4/90 - f**3/15 - 4*f**2 + 11*f. Let y(s) be the first derivative of b(s). Find r, given that y(r) = 0.
-1, 3
Let b(z) be the first derivative of -4/27*z**3 + 1/36*z**4 + 5/18*z**2 - 11 - 2/9*z. Determine t, given that b(t) = 0.
1, 2
Let x(b) be the second derivative of -b**7/630 - b**6/360 + b**5/360 - 11*b**3/2 + 25*b. Let n(f) be the second derivative of x(f). Find g, given that n(g) = 0.
-1, 0, 1/4
Let j(b) be the first derivative of -5/2*b**2 + 5/8*b**4 + 5/6*b**3 - 19 + 0*b. Factor j(k).
5*k*(k - 1)*(k + 2)/2
Let z(l) = 41*l + 4963. Let v be z(-121). What is n in -14/11*n**v - 4/11*n**3 - 24/11 + 2/11*n**4 + 40/11*n = 0?
-3, 1, 2
Let j(r) be the first derivative of r**3/5 - 81*r**2/5 + 2187*r/5 + 34. Solve j(w) = 0 for w.
27
Factor 23/2*j - 13/2*j**2 + 1/2*j**3 - 11/2.
(j - 11)*(j - 1)**2/2
Factor 7*l + 2 + l**2 + 2*l**2 + 339*l**3 - 347*l**3 - 4*l**4.
-(l - 1)*(l + 2)*(2*l + 1)**2
Let g(l) be the second derivative of 0 + 0*l**2 - 1/126*l**7 + 0*l**3 - 15*l + 0*l**4 - 2/45*l**6 + 0*l**5. Factor g(u).
-u**4*(u + 4)/3
Determine l, given that -4*l**2 + 16/3 + 8/9*l + 2/3*l**3 + 2/9*l**4 = 0.
-6, -1, 2
Let i(l) be the third derivative of -l**6/24 - l**5/3 - 5*l**4/24 + 5*l**3 + l**2 + 156*l. Factor i(r).
-5*(r - 1)*(r + 2)*(r + 3)
Let f be 14/7 + (2 - 0). Suppose 0 = -c - f*u + 22, -5*u + 22 = -3. Factor -4*i + 3*i**2 + 10*i - i**3 - c*i**3.
-3*i*(i - 2)*(i + 1)
Let q(b) = b**4 + 29*b**3 - 73*b**2 + 29*b. Let f(k) = -k**4 - 14*k**3 + 37*k**2 - 14*k. Let p(y) = -7*f(y) - 4*q(y). What is w in p(w) = 0?
0, 1, 2, 3
Let i(k) be the third derivative of -k**5/20 + 7*k**4/12 + 17*k**3/6 - k**2 + 19. Let a(l) = l**2 - 8*l - 9. Let p(z) = -7*a(z) - 4*i(z). Factor p(s).
5*(s - 1)*(s + 1)
Let d(r) be the third derivative of -2/25*r**5 - 256/15*r**3 + 26*r**2 + 0*r - 1/600*r**6 + 0 - 8/5*r**4. Let d(o) = 0. Calculate o.
-8
Let s = -90 + 96. Let d be (-2)/s - (-592)/336. Find i, given that -2*i**3 + 8/7 + 16/7*i + 2/7*i**2 - 2/7*i**5 - d*i**4 = 0.
-2, -1, 1
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