. Let g(o) = 7*r(o) + 2*x(o). Let g(v) = 0. Calculate v.
-2, -1, 0, 1
Let 2/7*s**2 + 18/7*s - 20/7 = 0. Calculate s.
-10, 1
Let d(n) = n**3 - 3*n**2 + 4*n. Let x be d(2). Determine u, given that x*u + 126 - 8*u**2 + 4*u**2 - 118 = 0.
-1, 2
Let m = -170 + 172. Let v(l) be the second derivative of -1/20*l**5 + 0 + 1/6*l**4 + 1/6*l**3 - l**m + 5*l. Solve v(q) = 0.
-1, 1, 2
Let i be 3/(-12) - (-42)/8. Let x = 9 - i. Factor -x*v**3 + 5*v**3 + 3*v**5 + 3*v**2 - 4*v**3 - 3*v**4.
3*v**2*(v - 1)**2*(v + 1)
Let h(k) = -3*k**2 - 11*k + 8. Let o be h(-4). Suppose o*c = 13 + 3. Factor -2/9*m**c + 0 - 2/9*m**2 + 4/9*m**3 + 0*m.
-2*m**2*(m - 1)**2/9
Let p(q) be the third derivative of 5/24*q**4 - 5/9*q**3 - 1/36*q**5 + 0*q + 11*q**2 + 0. What is k in p(k) = 0?
1, 2
Let o = -397 + 401. Let y(c) be the first derivative of -1/6*c**3 - 1/8*c**2 - 9 + 1/2*c + 1/16*c**o. Factor y(n).
(n - 2)*(n - 1)*(n + 1)/4
Let p(z) be the first derivative of z**4 + 38*z**3/21 - 4*z**2/7 - 16*z + 14. Let h(t) be the first derivative of p(t). Find w, given that h(w) = 0.
-1, 2/21
Suppose -3*y**3 + 0*y**2 - 5*y**2 + 2*y**2 = 0. Calculate y.
-1, 0
Let v(p) = 46*p - 80. Let d be v(2). Let k(s) be the third derivative of 0 + 7/78*s**4 - 49/390*s**5 - d*s**2 + 0*s - 1/39*s**3. Find g, given that k(g) = 0.
1/7
Let h(f) be the second derivative of 4*f**5/5 + 13*f**4 - 36*f**3 + 22*f**2 - 93*f. Solve h(w) = 0.
-11, 1/4, 1
Let l(k) = 6*k**3 - 14*k**2 + 22*k - 22. Let c(n) = -n**3 + n**2 + n - 1. Let h(b) = 10*c(b) + 2*l(b). Suppose h(p) = 0. Calculate p.
3
Let q(m) = -4*m**3 + 21*m**2 - 6*m - 16. Let a(t) = -6*t**3 + 32*t**2 - 10*t - 24. Let z(b) = 5*a(b) - 8*q(b). Determine g, given that z(g) = 0.
-1, 1, 4
Let l(p) = -p**2 - 2*p - 1. Let d be l(-1). Let f be (d + -3)/(108/(-18)). Factor 0 + 1/2*n + f*n**2.
n*(n + 1)/2
Let a(m) be the first derivative of 3*m**6 - 39*m**5/5 + 3*m**4/2 + 12*m**3 - 12*m**2 + 3*m + 98. Solve a(d) = 0 for d.
-1, 1/6, 1
Let y be -5 + 5 - -7 - 4. Factor -17*h - 10*h**2 + 122 + y*h - 110.
-2*(h + 2)*(5*h - 3)
Let s(n) be the second derivative of n**8/224 - n**7/35 + n**6/16 - n**5/20 + 5*n**2 - 2*n. Let i(v) be the first derivative of s(v). Factor i(x).
3*x**2*(x - 2)*(x - 1)**2/2
What is g in -42/13 + 42/13*g**2 + 2/13*g - 2/13*g**3 = 0?
-1, 1, 21
Let y(b) = 27*b - 104. Let k be y(4). Suppose 0 = -4*m + k*t, -t = -4*m - 14 + 20. Determine i, given that 0*i + 1/6*i**m + 0 = 0.
0
Let m = 523 + -519. Let d(l) be the first derivative of -8/5*l**3 + 12 - 56/5*l**2 + 11*l**4 + m*l**5 + 32/5*l. Let d(s) = 0. What is s?
-2, -1, 2/5
Find q, given that -1/4*q**2 + 0*q + 1 = 0.
-2, 2
Let v = 2201 - 2196. Let i(q) be the second derivative of -1/42*q**7 + 0*q**2 + 1/15*q**6 - 1/2*q**3 + 2*q - 1/6*q**4 + 0 + 1/5*q**v. Factor i(h).
-h*(h - 3)*(h - 1)*(h + 1)**2
Solve -114*o**5 + 8*o + 12*o**3 + 118*o**5 + 16*o**2 - 16*o**4 - 24*o = 0 for o.
-1, 0, 1, 2
Let x be (-6)/4*60/(-18). Solve -x*g - 11*g + 5*g**2 - g**2 + 16 = 0 for g.
2
Let j = 796 + -793. Let m(i) be the first derivative of 0*i**2 - 2/55*i**5 - 10 - 1/11*i**4 + 0*i**j + 0*i. Factor m(l).
-2*l**3*(l + 2)/11
Let p(k) be the third derivative of k**5/40 + 13*k**4/16 - 12*k**3 - 2*k**2 - 22*k. Solve p(d) = 0.
-16, 3
Let 56/15*a**2 + 16/15*a + 6/5*a**4 + 0 + 4*a**3 = 0. What is a?
-2, -2/3, 0
Suppose -2 = -10*h + 28. Factor -47*k**3 + 36*k**4 - 30*k**3 - 8 + 84*k**2 - 12*k - 23*k**h.
4*(k - 1)**3*(9*k + 2)
Let a be ((-1)/2)/(11/(-22)). Suppose a - 5 = -2*i. Factor -2*x**2 + 4*x**2 + 3*x**2 - i*x**2 - 3.
3*(x - 1)*(x + 1)
Let x(a) be the third derivative of -a**7/1155 - a**6/132 - 7*a**5/330 - a**4/44 - 159*a**2. Find n such that x(n) = 0.
-3, -1, 0
Factor -20*f**2 - 4*f**2 + 5*f**3 - 4*f + 3*f**3 + 24 - f**3 - 3*f**3.
4*(f - 6)*(f - 1)*(f + 1)
Let u be (-4)/(-10) + (-24)/(-800)*-5. Let p(n) be the first derivative of 1/10*n**5 + 1/6*n**3 + 0*n**2 + 0*n - 6 - u*n**4. Find l such that p(l) = 0.
0, 1
Let b(y) = -6*y - 4*y**2 - 3*y + y**3 - 5*y**2 - 2*y**3 - 3. Let k be b(-8). Factor 4/7*u**4 + 0*u**2 + 0*u + 2/7*u**k + 0 + 2/7*u**3.
2*u**3*(u + 1)**2/7
Let g = -149 + 153. Let o be (-6)/5 - -6 - g. Factor -16/5*t**3 - 16/5*t - 24/5*t**2 - o - 4/5*t**4.
-4*(t + 1)**4/5
Suppose -1 = 3*m - 7. Let -2*y**m - 12*y - y + 4*y**2 - y = 0. What is y?
0, 7
Let o(w) be the third derivative of -w**5/12 - 155*w**4/72 + 55*w**3/9 - 5*w**2 - 2*w. Factor o(d).
-5*(d + 11)*(3*d - 2)/3
Suppose 4*t - 5 = 7. Suppose -4*z = u - 12, -2*u + 15 = z + 4*z. Determine c, given that u*c**2 - c**4 - c**t + 0*c**2 + 2*c**4 = 0.
0, 1
Let a(k) be the first derivative of -k**4/34 + 20*k**3/51 - 28*k**2/17 + 48*k/17 - 251. Solve a(b) = 0 for b.
2, 6
Let r(m) = 3*m**4 - 15*m**3 + 8*m**2 - 2*m. Let h(j) = 11*j**4 - 60*j**3 + 31*j**2 - 9*j. Let t(s) = 2*h(s) - 9*r(s). Factor t(g).
-5*g**2*(g - 2)*(g - 1)
Suppose 2*t - 116 = 5*k + 52, -k - t = 28. Let q be k/72 - (-300)/189. Factor -4/7*g + 4/7*g**3 + q*g**2 - 8/7.
4*(g - 1)*(g + 1)*(g + 2)/7
Let w be 672/(-192)*(1498/(-735) + (-1 - -3)). Suppose -8/15*g**2 + 0 + 2/5*g + w*g**3 = 0. What is g?
0, 1, 3
Let d be (-6)/(-10)*(-1 - -2). Factor d*r**2 + 3/5 - 6/5*r.
3*(r - 1)**2/5
Let u = -4459/3 + 1487. Factor -2/3*b + 2/3*b**3 - 2/3 + u*b**2.
2*(b - 1)*(b + 1)**2/3
Factor 2 - 5*h**3 - 5 - 75*h + 35*h**2 + 0*h**3 + 31 + 17.
-5*(h - 3)**2*(h - 1)
Let c(u) = -u**3 + 2*u**2 + 3. Suppose 11 = -5*i + 6. Let a(r) = -1. Let k(o) = i*c(o) - 3*a(o). Find p, given that k(p) = 0.
0, 2
Suppose -5 - 5/3*w**2 + 5/3*w**3 - 25/3*w = 0. What is w?
-1, 3
Let k(y) be the third derivative of -y**6/2700 + y**5/900 - 4*y**3/3 - 2*y**2. Let v(s) be the first derivative of k(s). Factor v(z).
-2*z*(z - 1)/15
Let r(s) be the first derivative of -s**7/105 - 5*s**2 - 10. Let v(p) be the second derivative of r(p). Factor v(t).
-2*t**4
Let c(n) be the third derivative of n**6/30 - n**5/9 - 2*n**4/3 - 95*n**2 - 1. Factor c(r).
4*r*(r - 3)*(3*r + 4)/3
Suppose -3*t = -2*c - 21, -3*t - 5*c = -7*t + 42. Factor 0*k**t + 3/7*k - 3/7*k**5 + 0 - 6/7*k**4 + 6/7*k**2.
-3*k*(k - 1)*(k + 1)**3/7
Let n(g) be the third derivative of -g**6/300 + g**5/50 - g**4/30 - 3*g**2 + 12. Determine s so that n(s) = 0.
0, 1, 2
Let l(c) = -7*c**2 + 458*c - 13465. Let v(h) = -8*h**2 + 456*h - 13468. Let n(k) = 4*l(k) - 3*v(k). Factor n(u).
-4*(u - 58)**2
Suppose 43*m + 21 = 107. Factor 0 + 0*p + 3/5*p**m - 1/5*p**3.
-p**2*(p - 3)/5
Factor -5*d + 6*d - d**3 + 2*d + 16 - 14.
-(d - 2)*(d + 1)**2
Let j(n) be the third derivative of -n**5/12 + 175*n**4/24 + 200*n**2. Factor j(g).
-5*g*(g - 35)
Let m(q) be the second derivative of -q**8/3360 - q**7/1260 + q**6/360 + q**5/60 - q**4/12 + 11*q. Let i(s) be the third derivative of m(s). Factor i(c).
-2*(c - 1)*(c + 1)**2
Suppose 2*j + 3*j**3 + 4*j**5 + 21*j**4 - 5*j**4 + 5*j**3 - 16*j**2 - 14*j = 0. Calculate j.
-3, -1, 0, 1
Let m(n) be the first derivative of -28*n**3 - 81*n**2/2 - 15*n + 20. Factor m(l).
-3*(4*l + 1)*(7*l + 5)
Let w(n) be the third derivative of -n**5/20 + 6*n**4 - 288*n**3 + 4*n**2 - 19*n. Suppose w(o) = 0. What is o?
24
Let l(w) be the second derivative of w**6/6 + w**5 - 5*w**4/12 - 10*w**3/3 - 374*w. Suppose l(u) = 0. What is u?
-4, -1, 0, 1
Let c(y) be the first derivative of 4/3*y**3 + 2/3*y - 3/2*y**2 + 17 - 5/12*y**4. Factor c(l).
-(l - 1)**2*(5*l - 2)/3
Suppose -22 = 2*u - 28. Suppose u*d = -j, 0*d = 3*j - 3*d - 12. Solve -3*k**4 + 3/4*k**5 + 0 + j*k**2 + 9/4*k**3 - 3*k = 0.
-1, 0, 1, 2
Factor 20/3*s**4 - 5*s**2 + 0*s + 0 - 5/3*s**3.
5*s**2*(s - 1)*(4*s + 3)/3
Let c(p) = p**3 - 13*p**2 + 8*p - 22. Let s be c(13). Let i = s - 163/2. Factor 0 + 1/4*l**2 - i*l.
l*(l - 2)/4
Let g(a) be the first derivative of -459*a**5/20 - 45*a**4/2 - 29*a**3/4 - 3*a**2/4 - 320. What is t in g(t) = 0?
-1/3, -2/17, 0
Let w(r) be the second derivative of -45*r**5/4 + 4585*r**4/12 + 1460*r**3/3 + 210*r**2 - 165*r. Find k such that w(k) = 0.
-2/5, -2/9, 21
Let l = 1909/20 + -471/5. Determine s, given that 1/8*s**2 + 25/8 - l*s = 0.
5
Let b(z) = -2*z**4 + 26*z**3 + 17*z**2 - 89*z + 6. Let w(i) = 15*i**4 - 210*i**3 - 135*i**2 + 715*i - 50. Let d(s) = 25*b(s) + 3*w(s). Factor d(v).
-5*v*(v - 4)*(v - 2)*(v + 2)
Let x be (-33)/12*-9 + 27/(-45). Let k = x + -95/4. Factor -1/5*g**2 + 0 + k*g.
-g*(g - 2)/5
Let n(f) = -f**2 + f - 1. Let k