 7. Let -2*k**2 + 11*k**3 - 2*k**2 - 8*k + 4*k**4 - 3*k**s = 0. What is k?
-2, -1, 0, 1
Let y(a) be the second derivative of 41*a + 43/5*a**5 + 112/3*a**3 + 32*a**2 + 22/15*a**6 + 0 + 73/3*a**4 + 2/21*a**7. Solve y(m) = 0 for m.
-4, -1
Let w(l) = -l**3 + 15*l**2 + 15*l + 11. Let g be w(16). Let m(p) = -p - 5. Let i be m(g). Factor -8*u**2 + u**2 + i*u**2 - 3*u + 4*u**2.
-3*u*(u + 1)
Let s(c) = c**2 - 14*c - 5. Let r be s(14). Let z(o) = -4*o - 20. Let i be z(r). Factor i*q - 2/3*q**2 - 4*q**4 + 0 + 5/3*q**5 + 3*q**3.
q**2*(q - 1)**2*(5*q - 2)/3
Let c be 4 + -2 - -1 - (-3 - -1). Let b(w) be the second derivative of 1/15*w**3 + 0*w**2 - w + 3/50*w**c + 0 - 2/15*w**4. Solve b(y) = 0.
0, 1/3, 1
Find g such that 174*g - 279*g**2 - 1287*g**2 - 111*g**3 - 2*g**4 + 1508*g - 3*g**3 = 0.
-29, 0, 1
Let o = -301 - -306. Let r(t) be the third derivative of 10/3*t**3 - 1/24*t**6 + 1/6*t**o + 0*t + 35/24*t**4 + 0 + 4*t**2. Suppose r(d) = 0. What is d?
-1, 4
Let l(m) = -7 + 31 + 4*m**2 - 3*m - 5*m**2 - 12. Let t be l(-5). Suppose -6/5*x + 0 + 9/5*x**t = 0. Calculate x.
0, 2/3
Let l(w) be the second derivative of w**5/450 + w**4/60 + 2*w**3/45 - 7*w**2/2 - 16*w. Let k(a) be the first derivative of l(a). Determine n so that k(n) = 0.
-2, -1
Let c(x) be the third derivative of -x**6/10 - 101*x**5/20 - 121*x**4/8 - 12*x**3 - 304*x**2 - 2. Factor c(h).
-3*(h + 1)*(h + 24)*(4*h + 1)
Let f be (-7)/(336/(-2868)) + -2. Solve f*j**2 - 27*j + 3 - 243/4*j**4 + 27*j**3 = 0 for j.
-1, 2/9, 1
Suppose 0 - 87/5*m + 3/5*m**4 + 177/5*m**2 - 93/5*m**3 = 0. What is m?
0, 1, 29
Let c(q) be the second derivative of -q**4/3 - 4*q**3 - 18*q**2 + 107*q. Factor c(j).
-4*(j + 3)**2
Let w(j) be the first derivative of j**4/4 + 13*j**3/3 + 14*j**2 - 20*j - 9. Let a be w(-10). Factor 0 + a*b - 1/4*b**3 - 1/4*b**2.
-b**2*(b + 1)/4
Let v = 1228/3705 - -7/3705. Factor 0*t**4 + 1/3*t**3 - v*t**5 + 0 + 0*t**2 + 0*t.
-t**3*(t - 1)*(t + 1)/3
Let t = 51/10 - 61/12. Let d(z) be the third derivative of 0*z**3 - t*z**6 + 9*z**2 + 0 - 1/4*z**4 + 2/15*z**5 + 0*z. Let d(s) = 0. Calculate s.
0, 1, 3
Let z = -43 - 22. Let p be -10*(-2 - z/40). Factor p*f + 7*f**2 + 1/2.
(4*f + 1)*(7*f + 2)/4
Determine l, given that -18/7 + 18/7*l + 2/7*l**5 - 2/7*l**4 + 20/7*l**2 - 20/7*l**3 = 0.
-3, -1, 1, 3
Let b be 5/(5/(-2))*-1. Factor -10*q**2 - 24 - 3*q**b - 2*q**2 + 126*q - 60*q.
-3*(q - 4)*(5*q - 2)
Let g be ((-35)/(-28))/(4/16 + 33/8). Determine w so that 0 - g*w**2 + 4/7*w = 0.
0, 2
Let x(g) be the second derivative of -12*g + 0*g**2 + 1/70*g**5 + 0 - 1/21*g**3 + 0*g**4. Factor x(n).
2*n*(n - 1)*(n + 1)/7
Let s(r) = 28*r**2 + 245*r + 31. Let i(p) = -30*p**2 - 244*p - 30. Let o(m) = -3*i(m) - 2*s(m). Factor o(u).
2*(u + 7)*(17*u + 2)
Let m(w) be the first derivative of 0*w**4 - 5 + 0*w + w**2 + 0*w**3 - 1/20*w**5. Let l(i) be the second derivative of m(i). Factor l(q).
-3*q**2
Factor 0*r + 9/2*r**3 + 1/6*r**5 + 0 - 3/2*r**4 - 9/2*r**2.
r**2*(r - 3)**3/6
Let v(z) be the third derivative of -1/3*z**4 + 0*z**3 + 0*z - 10*z**2 + 0 + 1/15*z**5. Factor v(r).
4*r*(r - 2)
Factor 3*j**3 + 5*j - j**3 + 5*j - j**3 + 5*j + 16*j**2.
j*(j + 1)*(j + 15)
Let m(j) be the third derivative of j**7/42 + 13*j**6/12 + 71*j**5/4 + 715*j**4/6 + 1210*j**3/3 + 10*j**2 - 9*j. Suppose m(y) = 0. Calculate y.
-11, -2
Let p = -72 - -103. Suppose k - 4*u + 0 = 16, -4*k + 5*u = -p. Determine b, given that 0*b**2 - 5*b**4 + 8*b**2 + 4*b**5 + 19*b**k + 20*b**3 + 2*b**4 = 0.
-2, -1, 0
Suppose 35 - 43 = -4*r. Suppose -4*p + 13 + 1 = 2*d, 6 = 2*p + r*d. Factor p*n**4 + 32/13*n**2 + 2/13*n - 14/13*n**5 - 68/13*n**3 - 4/13.
-2*(n - 1)**4*(7*n + 2)/13
Let k(f) be the second derivative of -f**7/84 - f**6/10 - f**5/40 + f**4 - 4*f**3/3 - 85*f. Find j, given that k(j) = 0.
-4, 0, 1
Let r = -2389/330 + 80/11. Let l(a) be the second derivative of 1/15*a**3 + 0 + r*a**4 - 1/50*a**5 + 0*a**2 - 7*a - 1/75*a**6. Factor l(u).
-2*u*(u - 1)*(u + 1)**2/5
Let 1/2*i**4 - 1/2*i**2 + 0 - 3/2*i + 5/2*i**3 - i**5 = 0. What is i?
-1, 0, 1, 3/2
Let o be (-81)/(-1)*574/861. Find h, given that -27*h**2 + o*h - 1/2*h**4 - 81/2 + 6*h**3 = 0.
3
Factor 86528/9 - 1384/3*p**2 - 71552/3*p - 20/9*p**3.
-4*(p + 104)**2*(5*p - 2)/9
Let a(x) = x + 2. Let m be a(-2). Let k = 69 - 66. Factor -15/4*y**5 + 0*y**2 + 9/4*y**4 + 0*y + 3/2*y**k + m.
-3*y**3*(y - 1)*(5*y + 2)/4
Let o(a) = 23*a**3 - 458*a**2 + 1620*a - 1576. Let t(y) = -15*y**3 + 305*y**2 - 1080*y + 1050. Let k(j) = -5*o(j) - 8*t(j). Suppose k(w) = 0. Calculate w.
2, 26
Suppose -2*l + 7 - 3 = 0. Suppose -l*h = g - 1, 0 = g - 3*h - 1 - 10. Let 0 + 0*x**2 + 2/9*x**g + 0*x**4 - 4/9*x**3 + 2/9*x = 0. Calculate x.
-1, 0, 1
Let r be -2 - 7/(-1) - 646/136. Determine s so that -1/4*s + r*s**2 + 1/4*s**3 + 0 - 1/4*s**4 = 0.
-1, 0, 1
Let d(t) = 2*t**2 - 14*t + 8. Let w be d(8). Solve 15/2*j**3 + w*j**4 - 3*j**2 + 27/2*j**5 + 0 + 0*j = 0.
-1, 0, 2/9
Let g(m) be the third derivative of -m**6/180 - m**5/90 + m**4/9 + 4*m**3/9 - 66*m**2 - 3*m. Factor g(z).
-2*(z - 2)*(z + 1)*(z + 2)/3
Let i = -3377 - -16887/5. Factor 0 + 4/5*c + i*c**2.
2*c*(c + 2)/5
Let f be 2 - (-2 - (-8 + 4)). Suppose -7*j + f = -14. Find u, given that 739 - 739 + 4*u**3 + 12*u**j = 0.
-3, 0
Factor 15 + 3/2*i**5 - 6*i**4 + 15*i**2 - 12*i**3 + 69/2*i.
3*(i - 5)*(i - 2)*(i + 1)**3/2
Let q(c) be the first derivative of c**3 - c**2 - 5*c - 105. Let u(x) = 0*x + 1 + x + 0. Let o(j) = q(j) + 3*u(j). Let o(w) = 0. What is w?
-1, 2/3
Find r such that -18/7 - 131/7*r**2 + 7*r**4 - 93/7*r - r**3 = 0.
-1, -3/7, 2
Let l be 12/(-21)*(-7)/2. Factor 10*h**l - 14*h**2 + 2*h**2.
-2*h**2
Suppose 0 = -3*y + p + p + 22, 3 = y - 5*p. Suppose -3*w - 2*f = -12, 3*w - y*w - 5*f = -25. Factor -4 - h**2 + 3*h**2 + h**w + h**3.
(h - 1)*(h + 2)**2
Suppose 38 = -y + 5*c, -85 = y + 4*y - 4*c. Let l = -10 - y. Factor -l*b**2 + 35*b - 35*b.
-3*b**2
Suppose 0 = 2*l - 5*o + 13 + 7, 0 = -l - 3*o + 1. Let x be ((-4)/5)/(44/20 + l). Suppose 2/7*r**2 - 4/7 - x*r = 0. What is r?
-1, 2
Factor 0 + 0*s - 6/5*s**2 - s**4 + 13/5*s**3.
-s**2*(s - 2)*(5*s - 3)/5
Let b(r) be the third derivative of 5*r**8/336 - 2*r**7/35 + r**6/30 - 83*r**2 - 3. Factor b(t).
t**3*(t - 2)*(5*t - 2)
Let s(m) = -5*m**3 + 11*m**2 - 31*m + 25. Let u = 0 + -9. Let b(g) = -11*g**3 + 22*g**2 - 61*g + 50. Let x(c) = u*s(c) + 4*b(c). Factor x(p).
(p - 5)**2*(p - 1)
Let o(w) be the second derivative of 0 - 1/24*w**4 - 1/60*w**6 + 0*w**2 + 11*w + 0*w**3 + 1/20*w**5. Factor o(j).
-j**2*(j - 1)**2/2
Suppose 3*w - 7 = v, -42*w + 37 = -39*w + 5*v. Factor 0*n + 4/3*n**2 + 0 - 2/3*n**w - 2/3*n**3.
-2*n**2*(n - 1)*(n + 2)/3
Let f = -180/23 - -1306/161. Factor -4/7 + 4/7*l**2 + f*l - 2/7*l**3.
-2*(l - 2)*(l - 1)*(l + 1)/7
Factor 30*l**3 + 555*l - 27*l**3 + 124 + 30*l + 551 - 87*l**2.
3*(l - 15)**2*(l + 1)
Let d = -4 + 99. Factor 76 - 48*z + 86 + 2*z**2 + 221 - d.
2*(z - 12)**2
Suppose 41*z**3 + 98*z**2 + 2*z**5 + 25*z**3 + 60*z**3 - 346*z**4 + 376*z**4 = 0. Calculate z.
-7, -1, 0
Let p(c) = -c**4 + 14*c**3 - 12*c**2 + 6*c + 6. Let g(a) = -2*a**4 + 29*a**3 - 24*a**2 + 13*a + 13. Let b(z) = 6*g(z) - 13*p(z). Let b(n) = 0. Calculate n.
0, 2, 6
Let t(g) = -2*g + 1. Let y(z) = -30*z**2 - 24*z - 9. Let b(a) = 5*t(a) + y(a). Factor b(f).
-2*(f + 1)*(15*f + 2)
Suppose 79*u + 644 = 802. Factor -4/5*l**3 + 2/15*l**4 + 0 + 6/5*l**u + 0*l.
2*l**2*(l - 3)**2/15
Let v = 12400/273 - 588/13. Let k(g) be the second derivative of 1/7*g**2 + 5/42*g**4 + 0 + g + 1/35*g**5 + v*g**3. Determine a, given that k(a) = 0.
-1, -1/2
Let i(f) = -324*f**4 - 690*f**3 - 636*f**2 - 118*f - 38. Let v(k) = -25*k**4 - 53*k**3 - 49*k**2 - 9*k - 3. Let o(x) = -6*i(x) + 76*v(x). Factor o(q).
4*q*(q + 1)**2*(11*q + 6)
Let y be 7*6/315*39/13. Factor 0 + 6/5*n - y*n**2.
-2*n*(n - 3)/5
Let r = 89/146 - 105/292. Determine l so that -r*l**5 + 0*l**4 + 0*l**2 + 1/4*l**3 + 0 + 0*l = 0.
-1, 0, 1
Let f(z) = 4636*z**3 - 136*z**2 - 11*z. Let a(t) = -2*t**3 + 2*t. Let w(l) = -6*a(l) - f(l). Factor w(g).
-g*(68*g - 1)**2
Let s(q) be the first derivative of 2*q**3/3 + 9*q**2/2 + 3*q - 16. Let o(d) = 2*d**2 + 10*d + 3. Let w(v) = -2*o(v) + 3*s(v). Let w(r) = 0. What is r?
-3, -1/2
Suppose 5*x = -8*x + 169. Suppose -2*i = -5*w + 19, 5*w - x = -i - 0*i. Let -3/4*h**5 + 3/2*h**w + 0*h**4 + 0*h**2 + 0 - 3/4*h 