*n**2 + 8 - 12*n + 1/3*n**4 - 28/9*n**o. Suppose h(w) = 0. What is w?
1, 3
Suppose -36*v + 35*v = 5*s + 3, -5*s = 5*v - 5. Let 8/13*f + 2/13*f**v + 8/13 = 0. Calculate f.
-2
Suppose t = -0*t + 1. Suppose l = t + 3. Determine n, given that l*n**2 + 12*n - 12 - 3*n - n + 0*n**2 = 0.
-3, 1
Let j(x) be the third derivative of x**8/896 + 53*x**7/560 + 103*x**6/320 + 51*x**5/160 - 28*x**2 + 11*x. Find b such that j(b) = 0.
-51, -1, 0
Let x(y) be the second derivative of y**4/34 - 4*y**3/51 + y**2/17 + 2*y. Factor x(o).
2*(o - 1)*(3*o - 1)/17
Let b(d) = d**3 - 18*d**2 - 38*d - 37. Let a be b(20). Factor -3/4*c - 3/2 + 3/4*c**a + 3/2*c**2.
3*(c - 1)*(c + 1)*(c + 2)/4
Let q = 72 + -70. Suppose -a = q*c + 6, 5 = -4*a - c + 9. Factor 2/5*k**a - 6/5 - 4/5*k.
2*(k - 3)*(k + 1)/5
Let 11/2 + 6*s - 6*s**3 - 5*s**2 - 1/2*s**4 = 0. Calculate s.
-11, -1, 1
Let w(t) be the first derivative of -9*t + 3/2*t**2 - 1/12*t**3 + 11. Factor w(s).
-(s - 6)**2/4
Let o(g) be the third derivative of -g**6/360 + 7*g**5/60 - 5*g**4/3 + 50*g**3/9 + 91*g**2. Factor o(c).
-(c - 10)**2*(c - 1)/3
Suppose -2*f - 7 = -5*f - 4*w, 15 = 5*f + 5*w. Suppose r = -3*h + 3*r + 7, 4 = 3*h - 5*r. Suppose -7*g**4 - g**h + g**3 + f*g**4 + 2*g**3 = 0. Calculate g.
0, 1
Let v = -14 + 28. Let o = v + -10. Factor -3/4*w**o + 0*w + 0*w**3 - 3/4 + 3/2*w**2.
-3*(w - 1)**2*(w + 1)**2/4
Let c(r) be the third derivative of -r**7/135 - r**6/15 - r**5/5 - 7*r**4/27 - r**3/9 - 74*r**2. Determine i so that c(i) = 0.
-3, -1, -1/7
Let h(p) be the third derivative of -p**8/448 + 11*p**7/280 - 19*p**6/80 + p**5/2 + 13*p**2 - 19*p. Suppose h(n) = 0. Calculate n.
0, 2, 4, 5
Let d = 144 + -1576/11. Factor d*n + 8/11*n**2 + 2/11.
2*(2*n + 1)**2/11
Let z(g) = -9*g**3 + 30*g**2 - 56*g + 16. Let m(l) = -10*l**3 + 30*l**2 - 55*l + 10. Let c(k) = -4*m(k) + 5*z(k). Factor c(h).
-5*(h - 2)**3
Let r be (-7 - 1904/(-252))/(5/12). Factor 0*w**3 + 2/3*w**5 + r*w**4 + 0 - 4/3*w**2 - 2/3*w.
2*w*(w - 1)*(w + 1)**3/3
Let q = -2/23061 + 17939/30748. Suppose q + 1/6*c**3 + 11/12*c**2 + 4/3*c = 0. What is c?
-7/2, -1
Let z(g) be the first derivative of -2*g**3/9 + 17*g**2/3 - 20*g - 7. Find k such that z(k) = 0.
2, 15
Suppose 2*u = 0, 2*v - 8 = 4*u - 4. Factor 205*w**2 - 2*w**3 - 205*w**v + 8*w.
-2*w*(w - 2)*(w + 2)
Determine t, given that -1/6*t**5 - 23/6*t - 17/3*t**2 - 4/3*t**4 - 4*t**3 - 1 = 0.
-3, -2, -1
Suppose -b = 4*r - 11, -3*r + 1 = -2*r + 2*b. Solve -15*t - 7*t**2 + r*t**2 + 24 - 4 - t**2 = 0 for t.
-4, 1
Let t(d) be the second derivative of d**10/136080 - d**9/34020 + d**8/30240 + 2*d**4 + 5*d. Let c(x) be the third derivative of t(x). Factor c(h).
2*h**3*(h - 1)**2/9
Let z(k) be the second derivative of -19*k + 5/3*k**3 + 0 - 6*k**2 - 1/6*k**4. Factor z(j).
-2*(j - 3)*(j - 2)
Let t(p) = 4*p**4 - 37*p**3 + 36*p**2 + 37*p - 40. Let g(j) = 3*j**4 - 25*j**3 + 24*j**2 + 25*j - 27. Let y(l) = -7*g(l) + 5*t(l). Factor y(m).
-(m - 1)**2*(m + 1)*(m + 11)
Let m(r) be the third derivative of r**7/105 + 11*r**6/30 + 181*r**5/30 + 55*r**4 + 300*r**3 - 196*r**2 - 3*r. Let m(t) = 0. Calculate t.
-6, -5
Suppose -3*g = 5*b + 8, 0*g + 6 = -2*g - 4*b. Let k = g - -5. Find a, given that -k*a**2 + 4*a**2 - a - 2 + a**2 = 0.
-1, 2
Determine c, given that 92*c**3 - 4518*c + 6*c**5 - 48*c**4 + 4534*c + 6*c**5 - 8*c**4 - 64*c**2 = 0.
0, 2/3, 1, 2
Suppose 78*f + 39 - 21 - 174 = 0. What is h in -4/5*h**3 + 0*h**f + 2/15*h - 16/15*h**4 - 2/5*h**5 + 0 = 0?
-1, 0, 1/3
Let o = -13/537 - -755/1611. Factor -4/9*l**3 + 4*l**2 + 0 + 4*l - o*l**4.
-4*l*(l - 3)*(l + 1)*(l + 3)/9
Let t(g) be the second derivative of g**6/6 + g**5/4 - 5*g**4/2 - 10*g**3/3 + 20*g**2 + 3*g + 31. Factor t(c).
5*(c - 2)*(c - 1)*(c + 2)**2
Let w(n) be the first derivative of 9*n**3/4 - 3*n**2/4 - 42. What is b in w(b) = 0?
0, 2/9
Let u(h) be the second derivative of h**7/399 + 68*h**6/285 + 578*h**5/95 + 310*h. What is d in u(d) = 0?
-34, 0
Factor 0 - 1/2*s**4 - 13/2*s**3 - 18*s - 24*s**2.
-s*(s + 1)*(s + 6)**2/2
Factor 1/8*d**2 + 1/4*d + 0 - 1/8*d**4 - 1/4*d**3.
-d*(d - 1)*(d + 1)*(d + 2)/8
Let s be 2/(-2)*(-2 - -11). Let u = 39 - s. Factor -u*f - 14*f + 28*f**2 + 14*f - 16.
4*(f - 2)*(7*f + 2)
Let s(b) = 10*b**3 - 7*b**2 - b - 2. Let o(f) = f**3 - 1. Let m(y) = -18*o(y) + 2*s(y). Factor m(a).
2*(a - 7)*(a - 1)*(a + 1)
Factor 213*l**4 - 508*l**3 - 41*l**4 + 492*l**2 + 42442*l - 42590*l - 8.
4*(l - 1)**3*(43*l + 2)
Let r be -2*(9/45 + (-133)/(-10)). Let a(d) = -39*d**3 - 156*d**2 + 195*d. Let m(p) = 3*p**3 + 12*p**2 - 15*p. Let q(g) = r*m(g) - 2*a(g). Factor q(b).
-3*b*(b - 1)*(b + 5)
Factor 16/9*k**2 + 2/9*k - 28/3 + 2/9*k**3.
2*(k - 2)*(k + 3)*(k + 7)/9
Suppose 0 = -310*y + 317*y - 14. Let i(r) be the third derivative of -y*r**2 - 1/525*r**7 + 0*r**3 + 0*r**4 + 0*r + 1/300*r**6 + 1/75*r**5 + 0. Factor i(a).
-2*a**2*(a - 2)*(a + 1)/5
Suppose 0 = -5*h + 15, 4*j + 45*h - 20 = 41*h. Factor 2/5*q**j - 4/5*q + 2/5.
2*(q - 1)**2/5
Let g be (200/(-55))/(-4)*(-6)/(-30). Find d such that -4/11*d**3 + 2/11 - 4/11*d**2 + 2/11*d**4 + g*d**5 + 2/11*d = 0.
-1, 1
Factor 1/6*w**3 - 2*w + 0 + 1/6*w**4 - 4/3*w**2.
w*(w - 3)*(w + 2)**2/6
Let k(b) = 9*b**2 - 60*b + 51. Let o(n) = -n**2 + 1. Let h(c) = -k(c) - 5*o(c). Factor h(q).
-4*(q - 14)*(q - 1)
Factor 1225 + 222*w**3 - 122*w**3 + 83*w**4 + 1820*w - 78*w**4 + 690*w**2.
5*(w + 1)*(w + 5)*(w + 7)**2
Let f(v) be the second derivative of -3*v**5/20 - 9*v**4/4 - 4*v**3 + 8*v + 4. Solve f(n) = 0 for n.
-8, -1, 0
Suppose 0 = -2*k + 21 - 17. Let z(y) be the first derivative of -1 - 2/5*y + 3/5*y**k + 1/10*y**4 - 2/5*y**3. Let z(l) = 0. Calculate l.
1
Let m = -41 + 182. Let z = -689/5 + m. Let -24/5*c - 2/5*c**3 + 12/5*c**2 + z = 0. What is c?
2
Let k(q) be the second derivative of -q**5/90 - 32*q**4/9 - 4096*q**3/9 - 262144*q**2/9 + 76*q - 2. Let k(m) = 0. What is m?
-64
Factor -6 + 2/7*n**2 - 8/7*n.
2*(n - 7)*(n + 3)/7
Let z(j) = -6*j**2 - 24*j + 9. Let g(k) = 3*k**2 + 11*k - 4. Let f(d) = -9*g(d) - 4*z(d). Factor f(a).
-3*a*(a + 1)
Factor 3/4*m + m**2 - 7/4*m**3 + 0.
-m*(m - 1)*(7*m + 3)/4
Solve -8/3*d**2 + 28/3*d - 16/3 - 4/3*d**3 = 0.
-4, 1
Let m(b) be the first derivative of 1/8*b**4 + 1/4*b**2 - 16 + 0*b - 1/3*b**3. Factor m(f).
f*(f - 1)**2/2
Let p(n) be the first derivative of -13*n**6/90 + n**5/3 - n**4/9 - 3*n**2/2 + 24. Let v(a) be the second derivative of p(a). Factor v(j).
-4*j*(j - 1)*(13*j - 2)/3
Let f = -5203 + 5205. Determine u so that -2/5*u + 0 - 2/5*u**f = 0.
-1, 0
Let u(r) be the first derivative of 3*r**4/28 - 8*r**3/7 + 24*r**2/7 + 973. Solve u(o) = 0.
0, 4
Let z(h) be the third derivative of h**6/120 + h**5/20 - h**4/24 - h**3/2 + 9*h**2. Find t such that z(t) = 0.
-3, -1, 1
Suppose -4*q + 36 = -4*l - 20, -5*l + 2*q - 61 = 0. Let u(b) = b**2 + 7*b + 4. Let s(w) = -2*w**2 - 13*w - 7. Let c(v) = l*u(v) - 6*s(v). Factor c(n).
(n - 1)*(n + 2)
Let h(t) be the first derivative of -1/20*t**5 + 1/4*t**4 + 0*t - 1/2*t**2 + 0*t**3 - 5. Let c(g) be the second derivative of h(g). Factor c(i).
-3*i*(i - 2)
Let u(a) be the third derivative of 0*a**4 + 1/1155*a**7 + 0*a**5 + 0 + 0*a**6 - 10*a**2 + 1/1848*a**8 + 0*a + 0*a**3. Let u(l) = 0. What is l?
-1, 0
Factor 0*z + 0*z**3 - 2/3*z**4 + 0 + 2/3*z**5 + 0*z**2.
2*z**4*(z - 1)/3
Let r(p) be the first derivative of 4*p**2 + 4*p - 5 + 1/3*p**4 - 2*p**3. Let m(x) be the first derivative of r(x). Factor m(u).
4*(u - 2)*(u - 1)
Let j = 6763/240 - 169/6. Let p(t) be the third derivative of -2*t**2 + 0 + 1/8*t**4 + 1/40*t**5 + 0*t - j*t**6 + 0*t**3. Find w, given that p(w) = 0.
-1, 0, 2
Suppose 12*d + 35 = 35. Let i(o) be the first derivative of d*o + 2/27*o**3 + 6 + 2/9*o**2. Factor i(h).
2*h*(h + 2)/9
Let w(s) be the first derivative of -s**8/168 + 4*s**7/315 + s**6/180 - s**5/45 - 5*s**2 - 46. Let g(c) be the second derivative of w(c). Factor g(v).
-2*v**2*(v - 1)**2*(3*v + 2)/3
Let d = -27306 - -136536/5. Suppose 1/5*s**2 + 7/5*s + d = 0. Calculate s.
-6, -1
Let t(l) be the third derivative of -l**7/315 + l**6/60 - 6*l**2 - 3*l. Let t(z) = 0. Calculate z.
0, 3
Let l = 17921/12 - 1493. Let x(q) be the first derivative of 0*q + 3 - l*q**3 + 1/4*q**2. Factor x(c).
-c*(5*c - 2)/4
Suppose 5*v + 13 = 5*k - 7, 4*v = -5*k + 20. Determine m, given that 3 + v*m**2 - 23*m + 17*m + 3*m**2 = 0.
1
Let r(f) be