so that -5*z**3 - 10*z**4 + 3*z**2 + 20*z**x - 5*z**5 - 3*z**2 = 0.
-3, 0, 1
Let b(k) be the second derivative of k**6/165 - 2*k**5/55 + k**4/33 + 4*k**3/33 - 3*k**2/11 - 87*k. Determine m so that b(m) = 0.
-1, 1, 3
Let g(b) = -7*b**3 - 10*b**2 + 34*b + 13. Let j(c) = -41*c**3 - 59*c**2 + 204*c + 71. Let l(d) = 34*g(d) - 6*j(d). Factor l(t).
2*(t - 2)*(t + 4)*(4*t - 1)
Let m(g) = 2*g + 1. Let c be m(1). Let i be (-2 - 0/3)*(0 + -1). Find t such that -7*t**i + 3*t**2 + t + 3*t**2 - 1 - t**c + 2*t**2 = 0.
-1, 1
Let p(w) = -2*w**2 + 65*w + 138. Let h(n) = 5*n**2 - 197*n - 414. Let y(b) = -3*h(b) - 8*p(b). Factor y(v).
(v + 2)*(v + 69)
Let r(m) be the second derivative of -m**4/72 - 4*m**3/9 - 4*m**2 - 2*m + 64. Factor r(c).
-(c + 4)*(c + 12)/6
Let m(u) be the third derivative of 3*u**5/10 + 5*u**4/12 - 4*u**3/3 - 41*u**2. Suppose m(s) = 0. Calculate s.
-1, 4/9
Let 0 - 15/2*u**3 + 1/2*u**4 - 8*u**2 + 0*u = 0. Calculate u.
-1, 0, 16
Suppose -20*c = -17*c - 12. Suppose 3*w + 2 = 3*m - c, -4*w - 4 = -2*m. Factor 0*z + 2/7 - 2/7*z**m.
-2*(z - 1)*(z + 1)/7
Let b(p) = 2*p**3 - 502*p**2 + 45424*p - 1316996. Let x(k) = -2*k**2 - k - 1. Let z(f) = -b(f) - 10*x(f). Factor z(a).
-2*(a - 87)**3
Let q be (-1 + 241)*(-12)/16. Let f = q - -906/5. Let 1/5*u**4 + 0*u + 0 - f*u**3 + 9/5*u**2 = 0. What is u?
0, 3
Suppose -28*v = -27*v. Let r be (2 - (0 - v)) + (-18)/(-45). Factor 18/5*x**4 + 8/5 + r*x**3 - 22/5*x**2 - 8/5*x.
2*(x + 1)**2*(3*x - 2)**2/5
Let i(h) = -4*h**2 + 7*h + 4. Let j(x) = -2*x**2 + 3*x + 2. Let s = 11 + -20. Let m = s + 12. Let y(p) = m*i(p) - 7*j(p). Factor y(l).
2*(l - 1)*(l + 1)
Let 10*x**2 + 15*x**4 - 295*x**5 + 75*x**3 + 15*x**4 + 260*x**5 = 0. What is x?
-1, -1/7, 0, 2
Let d(x) be the second derivative of -x**5/15 + 5*x**4/9 + 4*x**3/3 - 2*x - 34. Factor d(n).
-4*n*(n - 6)*(n + 1)/3
Suppose -4*m - 8 = -4*b, -6*b - 18 = -8*b - 5*m. Let g(a) be the third derivative of 0*a + 1/9*a**3 - 2*a**2 + 1/90*a**5 + 0 - 1/18*a**b. Factor g(f).
2*(f - 1)**2/3
Let l(y) be the second derivative of y**4/3 - 32*y**2 + 36*y + 1. Factor l(i).
4*(i - 4)*(i + 4)
Let k(q) = -3*q**3 + 77*q**2 - 358*q + 542. Let n(x) = 8*x**3 - 232*x**2 + 1073*x - 1627. Let p(v) = 7*k(v) + 2*n(v). Factor p(m).
-5*(m - 6)**2*(m - 3)
Let l be 1*-13 + 17759/903. Factor 8*i**2 + 2/3*i**4 + 2 + 4*i**3 + l*i.
2*(i + 1)**3*(i + 3)/3
Let y be ((-207)/(-120))/((-2)/((-24)/27)). Let r = y - 1/6. Suppose -r*m**3 + 3/5*m + 9/5 - 9/5*m**2 = 0. What is m?
-3, -1, 1
Let t(k) be the second derivative of k**6/20 + 3*k**5/4 + 3*k**4 + 11*k**3/2 + 21*k**2/4 - 88*k. Suppose t(h) = 0. What is h?
-7, -1
Let y(w) = -2*w**2 + 20*w - 1. Let h(q) = -q**2 - q + 1. Let k(j) = 6*h(j) + y(j). Let x(n) = -n**2 + n + 1. Let d(a) = -k(a) + 5*x(a). Factor d(s).
3*s*(s - 3)
Let l(p) be the second derivative of -p**5/80 - 227*p**4/48 - 532*p**3 + 3249*p**2/2 + 118*p. Solve l(m) = 0 for m.
-114, 1
Let u(z) = 3*z**5 + z**4 + 33*z**3 - 41*z**2 - 8*z + 64. Let n(x) = -x**5 - 3*x**3 - 2*x**2 - 1. Let l(y) = -4*n(y) - u(y). Determine q so that l(q) = 0.
-5, -1, 2, 3
Let b be (8/(-10))/((-2)/5). Let k be (4 + -2)/(2/3). Let 7*l + 3 + k*l**b - 3 + 2*l + 6 = 0. What is l?
-2, -1
Let r(p) be the second derivative of p**4/6 + 92*p**3/3 + 2116*p**2 - 77*p. Factor r(y).
2*(y + 46)**2
Let 26 - 273*u + 256*u**5 - 203*u + 1234*u**4 + 2512*u**2 + 2740*u**4 + 2938*u**4 + 6752*u**3 + 893*u = 0. Calculate u.
-26, -1/4
Let x be 33/(-44)*-8 + -3. Let i(b) be the first derivative of -4/3*b**x + 0*b + 8 + 0*b**2 - 4/5*b**5 + 2*b**4. Factor i(z).
-4*z**2*(z - 1)**2
Let t(k) be the first derivative of 2*k**6/3 - 4*k**5/5 - k**4 + 4*k**3/3 + 102. Let t(p) = 0. Calculate p.
-1, 0, 1
Let t(l) be the third derivative of 0 + 1/6*l**4 + 0*l**3 + 3*l**2 + 0*l - 1/15*l**5. Factor t(n).
-4*n*(n - 1)
Let j = 189/190 + -15/38. Let g(i) be the first derivative of -3/20*i**4 - 4 + 3/5*i**3 - j*i**2 + 0*i. Factor g(u).
-3*u*(u - 2)*(u - 1)/5
Let h(s) be the third derivative of -5/36*s**4 + 21*s**2 - 25/18*s**3 - 1/180*s**5 + 0 + 0*s. Suppose h(y) = 0. Calculate y.
-5
Let v(h) be the third derivative of -h**8/588 + 22*h**7/735 + 13*h**6/105 + 2*h**5/105 - 25*h**4/42 - 26*h**3/21 - 220*h**2. Solve v(r) = 0 for r.
-1, 1, 13
Let s(p) = -p**3 - p**2 + p - 4. Let o be s(0). Let l be (-4)/(-40)*o + (-27)/(-30). What is d in -1/4*d**4 + 0*d**2 + l*d - 1/2*d**3 + 1/4 = 0?
-1, 1
Let c(a) be the second derivative of a**5/130 - 43*a**4/78 - 44*a**3/39 - 195*a. Suppose c(g) = 0. What is g?
-1, 0, 44
Let f = 173/418 + 18/209. Factor -1/2*d + 1/4*d**2 - 1/4*d**4 + 0 + f*d**3.
-d*(d - 2)*(d - 1)*(d + 1)/4
Suppose x + 0*x = 3. Suppose 72*r - 2*f - 2 = 73*r, 0 = -r - 5*f - 5. Factor -1/5*p + r + 1/5*p**x + 1/5*p**4 - 1/5*p**2.
p*(p - 1)*(p + 1)**2/5
Let -2/3*v**5 - 8/3*v**4 - 10/3*v + 8/3*v**2 + 0 + 4*v**3 = 0. What is v?
-5, -1, 0, 1
Let u(k) = 2*k**2 - 1. Let m(g) = -4*g**4 + 68*g**3 - 316*g**2 + 560*g - 350. Let y(r) = m(r) + 2*u(r). Factor y(t).
-4*(t - 11)*(t - 2)**3
Let x(o) = -3*o - 3. Let a(i) = i**3 - 2*i - 2. Let j(w) = w**3 - 7*w**2 - 10*w + 19. Let v be j(8). Let k(b) = v*a(b) - 2*x(b). What is y in k(y) = 0?
0
Let f(h) be the third derivative of -625*h**8/336 + 50*h**7/21 + 10*h**6 + 28*h**5/3 + 10*h**4/3 + 2*h**2 - 17*h. What is l in f(l) = 0?
-2/5, 0, 2
Let q(w) be the first derivative of 3*w**4/4 + 2*w**3 + 68. Suppose q(y) = 0. What is y?
-2, 0
Let d(a) be the third derivative of -2*a**7/105 - a**6/10 + 4*a**5/15 - 605*a**2. Determine c, given that d(c) = 0.
-4, 0, 1
Let h(q) = 386*q + 3093. Let v be h(-8). Determine m, given that -m**4 + 0*m - 4/3*m**3 + 0 + 0*m**2 + 1/3*m**v = 0.
-1, 0, 4
Let h(f) be the first derivative of -7*f**5/114 + 11*f**4/57 - 4*f**3/19 + 9*f**2 + 2*f + 38. Let q(c) be the second derivative of h(c). Factor q(l).
-2*(5*l - 2)*(7*l - 6)/19
Suppose 3*n - 6*n**3 + 15*n**3 + 3*n**2 - 6*n**3 - 3 - 6*n**3 = 0. What is n?
-1, 1
Let n(l) = 9*l**4 - 4*l**3 + l**2 - 6. Let t(f) = -8*f**4 + 4*f**3 - f**2 + 5. Let z(a) = -5*n(a) - 6*t(a). Factor z(i).
i**2*(i - 1)*(3*i - 1)
Let x(d) be the second derivative of -d**4/60 - 7*d**3/30 - 3*d**2/5 - 5*d - 5. Factor x(u).
-(u + 1)*(u + 6)/5
Let n(o) be the first derivative of o**4/2 + 8*o**3/5 - 36*o**2/5 - 32*o/5 - 461. Let n(k) = 0. What is k?
-4, -2/5, 2
Let g(i) be the third derivative of -i**7/21 + 13*i**6/60 - i**5/10 - 13*i**4/12 + 8*i**3/3 + 306*i**2. Let g(b) = 0. Calculate b.
-1, 1, 8/5
Suppose 888 = 9*j - 3*j. Factor -317*h**2 + 147*h**5 - 230*h**4 - j*h**4 + 180*h**3 + 293*h**2.
3*h**2*(h - 2)*(7*h - 2)**2
Let q = -26190/187 + 2384/17. Factor 6/11*j + q*j**3 + 2/11 + 6/11*j**2.
2*(j + 1)**3/11
Let n(w) be the first derivative of 5*w**3 - 51*w**2/2 + 18*w + 56. Suppose n(k) = 0. What is k?
2/5, 3
Let s be 10 - 51 - (-2)/(-2). Let v be (s/245)/((-6)/20). Let -11/7*w + 2/7 - v*w**3 + 13/7*w**2 = 0. What is w?
1/4, 1, 2
Let v(a) be the second derivative of -a**7/11 - 8*a**6/165 + 81*a**5/110 - 4*a**4/33 - 20*a**3/11 + 16*a**2/11 - 19*a + 6. Solve v(c) = 0.
-2, -1, 2/7, 1, 4/3
Find i such that -1/3*i**3 + 20*i + 64/3 + 4*i**2 = 0.
-2, 16
Let y = -113 - -115. Let m(d) be the first derivative of 0*d - 2/3*d**3 + 0*d**y + 7. Factor m(k).
-2*k**2
Factor 12/5*i**2 - 16/5 - 4/5*i**4 - 16/5*i + 8/5*i**3.
-4*(i - 2)**2*(i + 1)**2/5
Let h(y) = -5*y - y**3 - 5 + 11*y**2 + y - 5*y**2. Let d be h(5). Factor -2/9*c**2 - 4/9*c + d.
-2*c*(c + 2)/9
Let m(o) = -2*o**3 + o**2 + 8*o + 8. Suppose 3*j + 9 = 6*j. Let k(z) = -10*z**3 + 6*z**2 + 40*z + 40. Let f(a) = j*k(a) - 16*m(a). Factor f(c).
2*(c - 2)*(c + 1)*(c + 2)
Let s(a) be the third derivative of a**8/672 - a**6/60 - a**5/60 + a**4/16 + a**3/6 - a**2 + 46*a. Determine p so that s(p) = 0.
-1, 1, 2
Suppose 0*l - 2*l - i = -12, -6 = -i. Factor -2/5*w**l + 6/5*w - 4/5 + 0*w**2.
-2*(w - 1)**2*(w + 2)/5
Let g(c) be the third derivative of c**5/60 + 23*c**4/24 + 206*c**2. Suppose g(a) = 0. Calculate a.
-23, 0
Factor 1/9*r**3 + 2/3 - 5/9*r - 2/9*r**2.
(r - 3)*(r - 1)*(r + 2)/9
Factor -39/7*k + 9/7 - 9/7*k**3 + 39/7*k**2.
-3*(k - 3)*(k - 1)*(3*k - 1)/7
Let a(l) be the third derivative of l**11/2162160 - l**9/393120 + l**5/12 + 5*l**2. Let r(f) be the third derivative of a(f). Factor r(g).
2*g**3*(g - 1)*(g + 1)/13
Let j(m) = m**3 + m**2 - m - 1. Let w(a) = -a