rivative of -5/8*g**3 + 0 + 1/8*g**4 + 1/56*g**7 + 3/20*g**5 - 8*g - 1/10*g**6 + 3/4*g**r. Factor p(t).
3*(t - 2)*(t - 1)**3*(t + 1)/4
Let i(f) = 36*f**3 - 60*f**2 + 22*f. Let s(n) = -2*n**2 - n + 4. Let h(z) = -i(z) - 2*s(z). Determine j so that h(j) = 0.
-2/9, 1
Let v(a) be the third derivative of -a**6/180 - 23*a**5/90 + 13*a**4/18 + 16*a**3/3 + 616*a**2. Factor v(p).
-2*(p - 2)*(p + 1)*(p + 24)/3
Suppose -3*i - 42 = -240. Let q be 4/8*i/3. Factor 2*u**2 - 9*u**4 + q*u**4 - 4*u**4.
-2*u**2*(u - 1)*(u + 1)
Let n(g) be the third derivative of 0*g + 0 + 10*g**2 + 2/21*g**3 + 1/84*g**4 - 1/420*g**6 - 1/105*g**5. Let n(b) = 0. Calculate b.
-2, -1, 1
Let c(m) = -18*m**3 - 2*m**2 - 2*m - 1. Let k be c(-1). Suppose -3*t = -4*t + 2. Factor -k*x + 24*x**3 - 3 + 48*x**4 + 24*x**2 - 37*x**t - 32*x**2 - 7*x.
3*(x - 1)*(x + 1)*(4*x + 1)**2
What is u in 4/7 - 6/7*u + 2/7*u**2 = 0?
1, 2
Let l(w) be the second derivative of 3*w**5/20 - 2*w**4 + 7*w**3/2 + 264*w - 1. Factor l(y).
3*y*(y - 7)*(y - 1)
Let h(y) be the third derivative of -y**5/30 + y**4 - 20*y**3/3 + 66*y**2. Factor h(x).
-2*(x - 10)*(x - 2)
Let m(b) be the second derivative of b**4/60 - 9*b**2/10 - 255*b. Determine h so that m(h) = 0.
-3, 3
Let l = -2797044/55 + 50868. Let o = -126/11 + l. Factor -9/5 - o*y - 1/5*y**2.
-(y + 3)**2/5
Let j(o) = -15*o**3 - 40*o**2 + 25*o + 36. Let w(t) = -30*t**3 - 79*t**2 + 52*t + 72. Let u(l) = -5*j(l) + 2*w(l). Factor u(c).
3*(c - 1)*(c + 3)*(5*c + 4)
Let x(c) = 120*c**2 + 15300*c + 35. Let h(k) = 7*k**2 + 900*k + 2. Let a(p) = -35*h(p) + 2*x(p). Factor a(s).
-5*s*(s + 180)
Find v such that 35*v**3 + 30*v**4 - 30*v**2 + 5*v**5 + 37514*v - 37554*v + 0*v**5 = 0.
-4, -2, -1, 0, 1
Suppose 0*u - 35 = -2*u - 5*h, 2*u + 4*h = 34. Suppose -2*m + 7*m = u. Factor -2*a**3 + 3*a**2 - a**2 + 4*a**m - 4*a.
2*a*(a - 1)*(a + 2)
Factor 12*a**2 + 9*a**3 - 27*a**4 - 2*a**3 + 28*a**4.
a**2*(a + 3)*(a + 4)
Let f(g) = -6*g**2 + 32*g - 30. Let d(s) = s**2 + s. Let n(u) = -2*d(u) - f(u). Factor n(l).
2*(l - 1)*(2*l - 15)
Let o be (4312/110 + -38)/(4/10). Factor -3/8*t**5 + 3/4*t**o + 3/8 - 3/4*t**2 + 3/8*t**4 - 3/8*t.
-3*(t - 1)**3*(t + 1)**2/8
Suppose -j - 10 = -2*m, 3*j + 22 = 2*m + 4. Find h, given that 2*h**4 + 2*h**m - 128*h**2 + 128*h**2 = 0.
-1, 0
Suppose -m - 7*d + 4*d = -2, 5*m - d = 58. Suppose -m*q + 25*q = 42. Suppose 8/7*j**q + 10/7*j**2 + 2/7*j**4 + 4/7*j + 0 = 0. Calculate j.
-2, -1, 0
Factor 12/5 - 2/5*d - 2/5*d**2.
-2*(d - 2)*(d + 3)/5
Suppose 4*k + 3*n - 308 = 0, 3*n + 83 = -3*k + 314. Let f = k - 75. What is p in 0 + 2/11*p**4 + 2/11*p**f - 4/11*p**3 + 0*p = 0?
0, 1
Let t(p) = 5*p**2 - 194*p - 208. Let v(s) = -10*s**2 + 386*s + 417. Let m(i) = 7*t(i) + 3*v(i). Factor m(z).
5*(z - 41)*(z + 1)
Let s(p) be the second derivative of p**4/6 - 16*p**3 + 576*p**2 - 7*p + 4. Solve s(m) = 0 for m.
24
Let s = 31 + -27. Suppose 5*n = 7*n - s. Solve -6*y**3 - 4/3 + 8*y**n - 2/3*y = 0 for y.
-1/3, 2/3, 1
Let v(i) be the second derivative of 2*i**7/147 + 4*i**6/105 - 8*i**5/35 - 6*i**4/7 - 6*i**3/7 - 20*i + 1. Determine r, given that v(r) = 0.
-3, -1, 0, 3
Let g(z) = -z**3 + 3*z + 1. Let d be g(-2). Suppose d*w - 2 = b, -b + 5*b - 24 = -4*w. Solve 1 + 0*u - u**2 + 0*u**w - u**3 + 0*u + u = 0.
-1, 1
Let g(c) be the third derivative of -c**6/720 - c**5/120 + 7*c**3/2 - 14*c**2. Let s(h) be the first derivative of g(h). Factor s(j).
-j*(j + 2)/2
Determine w so that 2*w**2 - 6*w**4 - 14*w**4 - 32*w**2 + 27*w**3 + 4*w**3 + 24*w**3 = 0.
0, 3/4, 2
Factor 69/7*q + 0 + 1/7*q**2.
q*(q + 69)/7
Let g(o) = -o + 10. Let r be g(13). Let m be 1/5 - -3*r/45. Suppose m*s + 0 - 3/4*s**2 - 3/4*s**3 = 0. What is s?
-1, 0
Let a(f) = 5*f - 2. Let g be a(1). Suppose g*k = 7*k - 24. Factor 1 - 18*d**3 - 21*d - k*d**4 - 21*d**3 - 6*d**4 - 4 - 45*d**2.
-3*(d + 1)**3*(4*d + 1)
Let y = -15638 + 15640. Find n such that -3/2*n**4 + 15/2*n**y - 6 + 6*n + 3/2*n**5 - 15/2*n**3 = 0.
-2, -1, 1, 2
Let s be (62 + -70)/(2*1*-1). Let 0 + 2*h - 10 + s + 2 + 6*h**2 = 0. Calculate h.
-1, 2/3
Let g(q) be the third derivative of q**8/1176 + 11*q**7/735 + q**6/60 - 143*q**5/210 + 2*q**4/3 + 28*q**3/3 - 59*q**2 - 2. Solve g(a) = 0 for a.
-7, -1, 2
Suppose 23*y - 15 = 26*y. Let t(r) = -r**3 - 1. Let j(z) = -z**4 + 6*z**3 + 5. Let u(o) = y*t(o) - j(o). Determine c so that u(c) = 0.
0, 1
Let m(w) be the third derivative of -w**7/1575 + w**6/450 - w**5/450 - w**2 - 36. Factor m(v).
-2*v**2*(v - 1)**2/15
Solve 303/7*b + 9/7*b**2 - 102/7 = 0.
-34, 1/3
Let z(t) be the first derivative of -2/15*t**5 - 5/6*t**4 + 0*t**2 - 2/3*t**3 + 0*t - 7 + 1/9*t**6. Factor z(a).
2*a**2*(a - 3)*(a + 1)**2/3
Let l(v) be the third derivative of v**5/3 - 103*v**4/6 - 28*v**3 + 28*v**2. Let l(w) = 0. Calculate w.
-2/5, 21
Let s(d) be the first derivative of 0*d - 2/3*d**3 - 5 - d**2. Suppose s(u) = 0. Calculate u.
-1, 0
Factor 27/4*p**5 - 69/4*p**3 + 0 + 6*p**2 + 12*p - 9/2*p**4.
3*p*(p + 1)**2*(3*p - 4)**2/4
Let l(h) be the first derivative of 16*h**3 + 4/5*h**5 + 6*h**4 + 16*h**2 - 31 + 0*h. Solve l(v) = 0.
-2, 0
Let f(h) = h**3 + 15*h**2 + 11*h - 9. Let n be f(-14). Let u = n - 24. Let -3 + 4*z**2 + 10*z - 4*z - u + 2*z = 0. Calculate z.
-3, 1
Let y(u) be the second derivative of 2*u + 0 + 1/3*u**2 + 1/18*u**3 - 2/9*u**4 + 1/12*u**5. Determine f so that y(f) = 0.
-2/5, 1
Let p(b) be the third derivative of -25*b**8/336 - b**7/21 + 5*b**6/8 + 4*b**5/3 + 5*b**4/6 + 145*b**2. Determine y, given that p(y) = 0.
-1, -2/5, 0, 2
Let c(b) be the first derivative of b**3/15 + 91*b**2/5 + 8281*b/5 + 188. Factor c(f).
(f + 91)**2/5
Factor -57/4 - 27/2*j + 3/4*j**2.
3*(j - 19)*(j + 1)/4
Let x = 3 - 1. Suppose z = x*z - 2. What is j in -4*j**2 - 3*j**2 + 6*j**z = 0?
0
Let d = -1798/25 - -72. Let s(a) be the first derivative of -d*a**5 + 1 + 0*a + 1/5*a**4 + 0*a**2 + 0*a**3 - 1/15*a**6. Factor s(z).
-2*z**3*(z - 1)*(z + 2)/5
Let m = 148 + -1032/7. Factor -8/7*o - m*o**2 + 12/7.
-4*(o - 1)*(o + 3)/7
Suppose -4*n - 5*i + 21 = -8*i, -5*n - 2*i + 32 = 0. Let c be (20/(-25))/(n/(-5)). Solve -2/3*k**4 - c*k**2 + 0 + 0*k + 4/3*k**3 = 0 for k.
0, 1
Suppose 27*p = 18 + 90. Let z(r) be the third derivative of 0*r**3 - 1/12*r**p + 0 + r**2 - 1/30*r**5 + 0*r. Factor z(n).
-2*n*(n + 1)
Let z be 64/(-80)*45/(-54). Find u such that -z*u**3 + 0*u**2 + 0 + 2/3*u = 0.
-1, 0, 1
Let p(c) be the first derivative of -3*c**6/40 - c**5/2 - c**4 + 12*c**2 + c + 54. Let f(y) be the second derivative of p(y). Factor f(a).
-3*a*(a + 2)*(3*a + 4)
Let j(q) = 4*q**2 - 88*q - 722. Let x(r) = 3*r**2 - 86*r - 722. Let n(a) = -5*j(a) + 6*x(a). Factor n(t).
-2*(t + 19)**2
Let x(b) be the first derivative of -b**8/1176 + b**7/735 + b**6/210 - 27*b**2/2 - 3. Let u(z) be the second derivative of x(z). Let u(i) = 0. What is i?
-1, 0, 2
Factor 8/3*t + 0*t**2 - 4/3*t**4 - 8/3*t**3 + 4/3.
-4*(t - 1)*(t + 1)**3/3
Find d such that 76*d**3 - 19*d**2 - 80*d + 64 - 13*d**2 + 4*d**5 + 162*d**4 - 194*d**4 = 0.
-1, 1, 2, 4
Let h = 236 - 3538/15. Let f(s) be the third derivative of 0*s**4 + 8/105*s**7 + h*s**5 + 3*s**2 - 1/6*s**6 + 0*s**3 - 1/84*s**8 + 0*s + 0. Factor f(q).
-4*q**2*(q - 2)*(q - 1)**2
Let s(g) be the second derivative of g**6/10 + 21*g**5/20 + 7*g**4/2 + 4*g**3 - 14*g - 5. Factor s(c).
3*c*(c + 1)*(c + 2)*(c + 4)
Let x(w) be the first derivative of -2/7*w - 1/14*w**4 - 2/7*w**3 - 5 - 3/7*w**2. Factor x(g).
-2*(g + 1)**3/7
Let w(t) = -5*t**2 - 137*t - 256. Let v(k) = -k**2 - k + 1. Let d(n) = 2*v(n) - w(n). Let d(c) = 0. What is c?
-43, -2
Let v be ((-63)/18 - -4)/35. Let g(t) be the second derivative of -v*t**5 + 2/7*t**2 + 5*t + 2/21*t**4 - 5/21*t**3 + 0. Factor g(x).
-2*(x - 2)*(x - 1)**2/7
Let t(o) be the first derivative of -2*o**3/3 + 6*o**2 + 32*o - 219. Suppose t(v) = 0. Calculate v.
-2, 8
Let u be 1/(2*3/12). Suppose 50 = 5*f + 4*a, -f + 0*f - 19 = -5*a. Solve -l + u*l**3 - 4*l**3 - f*l**3 + 9*l**3 = 0 for l.
-1, 0, 1
Let z(r) be the first derivative of -r**6/6 + 4*r**5/5 - 3*r**4/4 + 605. Factor z(d).
-d**3*(d - 3)*(d - 1)
Let q be (80/(-22))/(-2) - (-24)/132. Factor 8*h**2 + 4*h**3 - 18*h**q + 11*h**2.
h**2*(4*h + 1)
Let n(y) be the second derivative of y**5/5 - 4*y**4 - 26*y**3/3 - 797*y. Solve n(s) = 0.
-1, 0, 13
Let q = -239957/9614 - -549/22. Let u = 2608/3059 - q. Factor -u*i + 0