- 30. Find k such that w(k) = 0.
-1, -2/15, 0
Suppose 0*h = -3*h. Let g(y) be the first derivative of 4 + 1/5*y**2 + h*y - 1/10*y**4 + 1/25*y**5 - 1/15*y**3. Find n such that g(n) = 0.
-1, 0, 1, 2
Let 2/3*q**4 + 0 + 4/3*q**3 + 0*q + 2/3*q**2 = 0. What is q?
-1, 0
Let w(q) be the second derivative of -q**5/20 - 3*q**4/4 - q**3 + 8*q**2 + 14*q + 6. Factor w(t).
-(t - 1)*(t + 2)*(t + 8)
Let a(m) be the first derivative of -1/3*m**6 + 16 + 0*m + 0*m**4 + 0*m**2 + 0*m**3 + 1/5*m**5. Factor a(b).
-b**4*(2*b - 1)
Let d(n) be the first derivative of n**4/40 + n**3/30 - n**2/10 - 33. Solve d(o) = 0.
-2, 0, 1
Let h(z) be the second derivative of -4/3*z**3 - 4*z + 2/15*z**6 + 0 - 1/3*z**4 + 0*z**2 + 2/5*z**5. Factor h(k).
4*k*(k - 1)*(k + 1)*(k + 2)
Factor 1/11*v**2 - 3/11 + 2/11*v.
(v - 1)*(v + 3)/11
Let k(b) be the second derivative of b**5/15 + 2*b**4/3 + 2*b**3 - 4*b**2 - 13*b. Let q(p) be the first derivative of k(p). Factor q(s).
4*(s + 1)*(s + 3)
Let z be 4 + -1*((-104)/40 - -6). Solve -3/5 - z*v**2 - 6/5*v = 0.
-1
Let g(s) = -3*s**4 + 5*s**3 + 8*s**2 - 14*s - 20. Let i(a) = a**4 - a**3 + a + 2. Let c(b) = 2*g(b) + 4*i(b). Let c(r) = 0. What is r?
-2, -1, 2, 4
Let z(b) be the first derivative of -5*b**4/12 - 5*b**3/2 + 10*b + 3. Let h(k) be the first derivative of z(k). Find s such that h(s) = 0.
-3, 0
Let t(z) = -18*z + 148. Let k be t(8). Let y(j) be the first derivative of -3/2*j**k + 2 - j**3 + 0*j + 3/2*j**2. Factor y(v).
-3*v*(v + 1)*(2*v - 1)
Determine o, given that 9/5 + 2/5*o**2 + 9/5*o = 0.
-3, -3/2
Determine n, given that -7 + 65*n - n**2 + n**5 + 47*n**2 + 9 + 23 - 7*n**4 + 2*n**3 - 4*n**3 = 0.
-1, 5
Factor -11/2*f + 13 - 1/2*f**2.
-(f - 2)*(f + 13)/2
Let i = -682/63 + 100/9. Let m = 11419/70 - 1617/10. Find l such that i*l**3 + m*l + 4/7 + 8/7*l**2 = 0.
-2, -1
Let p be ((-6)/4)/((-7)/10). Suppose 7*h = -14*h + 17*h + 8. Factor 0*z + 0 - p*z**5 - 6/7*z**h + 24/7*z**4 - 3/7*z**3.
-3*z**2*(z - 1)**2*(5*z + 2)/7
Let i(s) be the third derivative of 7*s**5/20 + s**4/4 + 3*s**3/2 - 8*s**2. Let l(g) = -g**2 - 1. Let h(m) = -i(m) - 18*l(m). Factor h(c).
-3*(c - 1)*(c + 3)
Let j be (-528)/(-165) - 12/(-15). Let u(n) be the first derivative of -4*n**2 - j*n + 14 - 4/3*n**3. Solve u(m) = 0 for m.
-1
Factor 32 - 7*n**3 - 22*n**2 - 61 - 11*n - 6*n + 27.
-(n + 1)*(n + 2)*(7*n + 1)
Let v(k) be the third derivative of -k**6/210 + 2*k**5/35 + k**4/42 - 4*k**3/7 - 3*k**2 + 44. Factor v(p).
-4*(p - 6)*(p - 1)*(p + 1)/7
Let d(p) = 48*p**3 - 88*p**2 + 46*p - 10. Let l be 1*(-4)/(8/(-10)). Let c(u) = -95*u**3 + 175*u**2 - 91*u + 21. Let v(z) = l*d(z) + 2*c(z). Factor v(s).
2*(s - 1)*(5*s - 2)**2
Suppose -6*u = -10*u. Suppose 0 = 4*n - u*n - 8. Factor -1 + n*i**2 + 7*i - 9*i**2 - 6*i**3 - 13*i - 4*i**2.
-(i + 1)*(2*i + 1)*(3*i + 1)
Suppose 0 = i + 2*i + 3*f, 10 = 5*i + 3*f. Let p be i/2*56/245. Factor 2/7*a - 2/7*a**5 - 4/7*a**2 + p*a**4 + 0*a**3 + 0.
-2*a*(a - 1)**3*(a + 1)/7
Let 79 + 29 - 2*x**2 - 36*x + 6*x**3 - 31*x**2 + 3*x**4 = 0. What is x?
-3, 2
Let s be (-21)/(-6)*((-6)/(-70))/3. Let q(a) be the second derivative of -1/5*a**2 + 0 + s*a**3 + 4*a + 0*a**4 - 1/100*a**5. Factor q(u).
-(u - 1)**2*(u + 2)/5
Let t(c) = -2*c**3 + 5*c**2 - 2*c - 1. Let b be t(3). Let q = b - -23. Factor -q*i - 3*i**4 - 8*i**2 + 4*i**2 + 3*i**3 + 4*i + 7*i**2.
-3*i*(i - 1)**2*(i + 1)
Let t(h) = 2*h**3 - 6*h**2 + 2*h + 6. Let w(y) = 7*y**2 - 3 - 4 - 5*y + 3*y - 3*y**3 + 0. Let g(u) = -5*t(u) - 4*w(u). Let g(j) = 0. Calculate j.
-1, 1
What is t in 3/2*t**2 + 0 - 39/2*t**4 - 27/2*t**3 + 3*t - 15/2*t**5 = 0?
-1, 0, 2/5
Let b(u) = -36*u**3 + 254*u**2 + 238*u - 67. Let f(x) = 108*x**3 - 764*x**2 - 712*x + 200. Let c(l) = -8*b(l) - 3*f(l). What is v in c(v) = 0?
-1, 2/9, 8
Let a = -655 + 655. Let y(s) be the third derivative of a*s + 0 + 3/20*s**5 - 1/2*s**4 - 2*s**3 + 1/70*s**7 + 1/10*s**6 - 4*s**2. Let y(x) = 0. Calculate x.
-2, -1, 1
Let o = 164 - 159. Let w(j) be the third derivative of 0 + 0*j**6 + 1/90*j**o + 0*j**3 - 4*j**2 - 1/315*j**7 + 0*j + 0*j**4. Factor w(m).
-2*m**2*(m - 1)*(m + 1)/3
Let r(f) be the second derivative of -2*f**7/189 + 16*f**6/135 - 128*f**4/27 + 512*f**3/27 + 2*f + 8. Factor r(d).
-4*d*(d - 4)**3*(d + 4)/9
Factor 6/5 + 7*q**2 - 73/5*q.
(q - 2)*(35*q - 3)/5
Let z(j) be the third derivative of 0*j**3 + 0 + 2/105*j**7 - 1/12*j**4 + 14*j**2 + 0*j**6 - 1/15*j**5 + 1/168*j**8 + 0*j. Factor z(c).
2*c*(c - 1)*(c + 1)**3
Let g(j) be the first derivative of j**4/7 - 32*j**3/21 + 10*j**2/7 + 8*j + 358. Suppose g(d) = 0. What is d?
-1, 2, 7
Suppose -3*z + z = 0. Factor 16*i**2 - 1 - 8 + z*i - 28*i + 1.
4*(i - 2)*(4*i + 1)
Let l(c) be the first derivative of 4*c**5/15 + c**4/3 + 100. Factor l(x).
4*x**3*(x + 1)/3
Suppose -2*k = -3*v - 2*v - 14, -5*v = 4*k - 58. Let f be (1 - 2)/((-4)/k). Factor -7*w**2 - 9*w**4 + w + 15*w**f - w**2 + w**2.
-w*(w - 1)*(3*w - 1)**2
Let a = -160/77 - -26/11. Let y = 20/21 - a. Let -2/3 + 4/3*q - y*q**2 = 0. Calculate q.
1
Let y(g) = g**3 - 9*g**2 + 22*g - 7. Let f be y(5). Suppose 5*b - 731 = -2*c - 0*c, 4*c + 423 = 3*b. Factor -u**3 + 4*u**2 - 3*u**f + 153*u - b*u.
-4*u*(u - 2)*(u + 1)
Let l = -153 + 153. Let k(n) be the second derivative of -n + 0*n**2 + 0*n**4 + l*n**3 - 3/20*n**5 - 1/10*n**6 + 0. Determine j, given that k(j) = 0.
-1, 0
Let o(n) be the first derivative of n**5/5 + n**4/3 - 2*n**3/3 - 2*n**2 - 24*n - 29. Let f(h) be the first derivative of o(h). Factor f(c).
4*(c - 1)*(c + 1)**2
Suppose -10 = -5*o, 2*m - 2*o - 16 = -3*m. Factor -r**3 + 12 + 5 + 51*r**2 - 20*r**3 + 3*r**m - 51*r + 1.
3*(r - 3)*(r - 2)*(r - 1)**2
Let g(a) be the third derivative of 5/6*a**5 + 51*a**2 + 1/24*a**6 - 20/3*a**3 + 5/336*a**8 + 0 - 5/6*a**4 - 2/21*a**7 + 0*a. Suppose g(j) = 0. Calculate j.
-1, 2
Let f(l) be the second derivative of 17/12*l**4 - 12*l + 0*l**2 + 0 - 7/10*l**5 + 1/10*l**6 - l**3. Factor f(o).
o*(o - 3)*(o - 1)*(3*o - 2)
Let t(i) = -13*i**3 + 13*i**2 - i - 6. Let l(n) = -4*n**3 + 4*n**2 - 2. Let y(o) = 7*l(o) - 2*t(o). Determine r so that y(r) = 0.
-1, 1
Let f be ((-1354)/15)/((-2)/3). Let k = f - 135. Determine n so that k*n**2 + 0 - 4/5*n = 0.
0, 2
Let c be 2/(((-14)/4)/7). Let s(y) = -8*y**3 + 8*y**2 + 5. Let h(z) = 7*z**3 - 7*z**2 - 4. Let j(b) = c*s(b) - 5*h(b). Let j(o) = 0. Calculate o.
0, 1
Factor -12 + 3/4*f**2 - 18*f + 9/8*f**3.
3*(f - 4)*(f + 4)*(3*f + 2)/8
Suppose 75*r + 96*r - 65*r**4 + 83*r**4 + 318*r**3 - 19*r - 448*r**2 = 0. What is r?
-19, 0, 2/3
Suppose -2*t + 5 = -1. Let d be t/(3/4 + 0). Suppose b**2 + 0*b**d - 2*b**5 - 2*b + 4*b**3 - 9*b**2 + 4 + 6*b**4 - 2*b**4 = 0. What is b?
-1, 1, 2
Factor -99*o**3 - 98*o**2 + 54*o**4 - 261*o - 102 + 3*o**5 + 141*o**3 - 70*o**2.
3*(o - 2)*(o + 1)**3*(o + 17)
Let k(y) be the first derivative of -17 - 4/15*y**3 - 4*y + 12/5*y**2. Let k(l) = 0. What is l?
1, 5
Let b be 247/399 - 1/3. Determine c, given that 0 - 2/7*c - b*c**2 = 0.
-1, 0
Let d be (18/(-12))/(2/148). Let r = d - -781/7. Let -8/7*i + r*i**2 - 12/7 = 0. Calculate i.
-1, 3
Let n(f) be the second derivative of 1/90*f**5 - f**2 + 0 + 5/54*f**4 + 10*f + 1/9*f**3. Let n(a) = 0. Calculate a.
-3, 1
Suppose -31 = 3*x - 16. Let a be (-5)/x*26 - 2. Solve a*s**3 - 4*s**4 + 128*s + 0*s**4 + 8*s**3 - 59 - 96*s**2 - 5 = 0 for s.
2
Suppose 17 + 8 = 5*y. Factor y - 3 - 8*q**3 - 4*q + 0*q**3 - 14*q**2.
-2*(q + 1)**2*(4*q - 1)
Let u(c) be the first derivative of 2*c**5/5 - c**4/2 - 4*c**3 - 50. Factor u(o).
2*o**2*(o - 3)*(o + 2)
Let u(d) be the second derivative of 0*d**2 + 0 + 2/3*d**4 - 8/15*d**6 - 1/5*d**5 + 0*d**3 + 2/7*d**7 + 19*d. Factor u(k).
4*k**2*(k - 1)**2*(3*k + 2)
Let m(o) be the first derivative of -2*o**5/35 - 17*o**4/14 - 10*o**3 - 275*o**2/7 - 500*o/7 - 19. Factor m(g).
-2*(g + 2)*(g + 5)**3/7
Factor -2/9*v**2 - 328/9*v - 13448/9.
-2*(v + 82)**2/9
Let o = -243 + 243. Let w(v) be the second derivative of 1/9*v**4 + 0*v**2 + 0*v**3 + o - 3*v + 1/30*v**5. Let w(p) = 0. What is p?
-2, 0
Let z(s) be the first derivative of 6*s**2 + 14/3*s**3 - 1 - 2*s + 1/5*s**5 + 5/3*s**4. Let j(b) be the first derivative of z(b). Factor j(v).
4*(v + 1)**2*(v + 3)
Let z(q) be the first derivative of 4*q - 2/3*q**3 - q**2 + 3 - 1/6*q**4. Let v(j) be the first derivative of z(j). Factor v(y).
-2*(y + 1)**2
Let o(h) = -h**2 - h +