5). Let g(o) be the first derivative of -8/5*o - 6/5*o**3 + 12/5*o**d + 1/5*o**4 + 1. Factor g(h).
2*(h - 2)**2*(2*h - 1)/5
Factor 2/3*w - 14/3*w**3 - 8/3*w**4 + 0 - 4/3*w**2.
-2*w*(w + 1)**2*(4*w - 1)/3
Let y(l) be the first derivative of -l**6/360 - l**5/15 - 2*l**4/3 - 32*l**3/9 + 2*l**2 + 7. Let k(d) be the second derivative of y(d). Factor k(f).
-(f + 4)**3/3
Suppose -22 = -3*j - 4. Let z(i) be the second derivative of -i - 1/4*i**3 + 1/20*i**j + 3/40*i**5 + 0*i**2 + 0 - 1/8*i**4. Solve z(s) = 0.
-1, 0, 1
Let j(p) be the first derivative of 3/70*p**5 + 1/21*p**3 + 1 + 2*p + 1/14*p**4 + 1/105*p**6 + 0*p**2. Let l(z) be the first derivative of j(z). Factor l(r).
2*r*(r + 1)**3/7
Let d(t) be the second derivative of t**4/18 - t**3/9 - 2*t**2/3 + 11*t. Let d(a) = 0. What is a?
-1, 2
Let r(h) be the second derivative of h**7/10080 - h**6/2880 - h**5/240 + h**4/4 - 2*h. Let v(a) be the third derivative of r(a). Factor v(n).
(n - 2)*(n + 1)/4
Suppose 5*p = 3*p - 2*p. Let v(m) be the first derivative of 0*m**2 + 1 + 1/14*m**4 + p*m - 2/35*m**5 + 2/21*m**3 - 1/21*m**6. Find b such that v(b) = 0.
-1, 0, 1
Factor 4/5 - 8/5*p + 4/5*p**2.
4*(p - 1)**2/5
Let 0 + 0*f - 6/7*f**3 + 6/7*f**2 + 6/7*f**5 - 6/7*f**4 = 0. Calculate f.
-1, 0, 1
Let g(w) = -w**3 - 4*w**2 + 3. Let q be g(-4). Let o(t) be the first derivative of 0*t - 1 + 1/8*t**2 + 5/12*t**q + 1/4*t**4. Determine s so that o(s) = 0.
-1, -1/4, 0
Let x be 2/(-3)*5/(15/(-6)). Factor 2*w + x + 2/3*w**2.
2*(w + 1)*(w + 2)/3
Let p(s) be the second derivative of s**4/4 - 3*s**2/2 + 7*s. Suppose p(d) = 0. Calculate d.
-1, 1
Let h(x) be the third derivative of x**8/60480 + x**7/3780 + x**6/540 - 2*x**5/15 + 6*x**2. Let d(f) be the third derivative of h(f). Factor d(p).
(p + 2)**2/3
Suppose -5*n = -k - 12, -2*n - n - 3*k = -18. Factor 3*b**n - b**3 - b**3.
b**3
Let f(j) be the second derivative of -4*j**7/21 - 2*j**6/3 - 3*j**5/5 + j**4/3 + 2*j**3/3 + 16*j. Find i, given that f(i) = 0.
-1, 0, 1/2
Let o(d) be the second derivative of 0 + 1/10*d**5 + 0*d**4 - 1/2*d**2 + 1/30*d**6 - 1/3*d**3 - 3*d. Let o(i) = 0. Calculate i.
-1, 1
Let u(v) be the first derivative of v**6/120 + v**5/60 + v**2/2 - 3. Let x(f) be the second derivative of u(f). Factor x(o).
o**2*(o + 1)
Let n(f) = -3*f - 14. Let q be n(-7). Let k(s) be the third derivative of 2*s**2 + 0*s**4 + 0 - 1/20*s**6 - 1/105*s**q + 0*s**3 + 0*s - 1/15*s**5. Factor k(w).
-2*w**2*(w + 1)*(w + 2)
Let h(p) be the third derivative of 0 - 1/20*p**6 - 1/2*p**3 - p**2 + 0*p + 0*p**5 + 1/70*p**7 + 1/4*p**4. Factor h(s).
3*(s - 1)**3*(s + 1)
Let s be 26/(-8) - (-3)/12. Let o = 1 - s. Find v such that -3*v**3 + 2*v**3 - 3*v**2 + o*v**2 = 0.
0, 1
Factor -1/12*l**3 + 1/12*l**2 + 0*l + 0 - 1/12*l**4 + 1/12*l**5.
l**2*(l - 1)**2*(l + 1)/12
Let l(x) be the first derivative of -2*x**5/85 + 5*x**4/17 - 16*x**3/17 + 22*x**2/17 - 14*x/17 + 9. Factor l(q).
-2*(q - 7)*(q - 1)**3/17
Let c be 0*(-1 + (-5)/(-10)). What is y in -2/7*y + 0*y**4 + 4/7*y**3 - 2/7*y**5 + 0*y**2 + c = 0?
-1, 0, 1
Factor 40*r + 5*r**2 - 5 - 40*r.
5*(r - 1)*(r + 1)
Let f = -439 + 443. Factor 0*w + 1/3*w**f + 0 - 1/3*w**2 + 0*w**3.
w**2*(w - 1)*(w + 1)/3
Let r = 9 + -4. Let 7*u + r*u + 3*u + 9*u**2 + 6 = 0. Calculate u.
-1, -2/3
Let d(h) be the first derivative of -h**7/3360 + h**5/160 + h**4/48 + 4*h**3/3 - 3. Let z(g) be the third derivative of d(g). Suppose z(s) = 0. Calculate s.
-1, 2
Let t(l) be the first derivative of -l**5/2 + 2*l**4 - 4*l**3/3 - 8*l - 8. Let h(d) be the first derivative of t(d). Find u, given that h(u) = 0.
0, 2/5, 2
Let u(d) be the first derivative of -d**8/336 + d**7/210 + d**6/120 - d**5/60 - 2*d**2 - 6. Let n(t) be the second derivative of u(t). Factor n(o).
-o**2*(o - 1)**2*(o + 1)
Let d be 2/(-4) - (-45)/(-10). Let z = -5 - d. Determine p so that 0*p - 7/3*p**4 + 2/3*p**2 + z + 5/3*p**3 = 0.
-2/7, 0, 1
What is k in -63*k**5 + 128*k**5 + 8*k - 4 - 7*k**3 - 66*k**5 + 5*k**4 - k**2 = 0?
-1, 1, 2
Let d = -20360/17 - -1198. Let l = 39/34 + d. Determine b, given that 0 + b - l*b**2 + 1/2*b**3 = 0.
0, 1, 2
Let b(q) be the third derivative of q**8/560 + q**7/70 + q**6/20 + q**5/10 + q**4/8 - q**3/6 - 4*q**2. Let p(l) be the first derivative of b(l). Factor p(x).
3*(x + 1)**4
Let f(r) be the third derivative of -1/210*r**7 + 1/120*r**6 + 0*r + 0 + 0*r**4 - 1/336*r**8 + 0*r**3 + 3*r**2 + 1/60*r**5. Factor f(z).
-z**2*(z - 1)*(z + 1)**2
Let f(h) be the third derivative of h**6/30 - 14*h**5/15 + 49*h**4/6 + 2*h**2 - 12*h. Solve f(j) = 0.
0, 7
Suppose -1/2*x**3 + 0*x**2 + 0 - 1/3*x**4 + 1/6*x = 0. Calculate x.
-1, 0, 1/2
Let z = 21 - 15. Suppose 5*f - 4*f + z = 4*g, -3*g + 3*f = -9. Let s(m) = m**2 - 1. Let w(b) = -2*b**2 + b + 1. Let i(p) = g*s(p) + w(p). Factor i(t).
-t*(t - 1)
Let v(x) = -3*x**4 - 3*x**3 - 9*x**2 - x. Let i(u) = 7*u**4 + 5*u**3 + 19*u**2 + u. Let k(w) = 2*i(w) + 5*v(w). Factor k(z).
-z*(z + 1)**2*(z + 3)
Let q = -135 - -135. Find z, given that 1/2*z**2 + q*z - 2 = 0.
-2, 2
Let d = 57 - 57. Factor 0*j**2 - 1/2*j**3 + 1/4*j**5 + 1/4*j + 0*j**4 + d.
j*(j - 1)**2*(j + 1)**2/4
Let n(y) be the third derivative of 12*y**7/35 + 7*y**6/5 + 73*y**5/30 + 7*y**4/3 + 4*y**3/3 + 4*y**2. Solve n(j) = 0.
-2/3, -1/2
Suppose 2*z - 4*z = -8. Suppose -c = -z*c. Determine k, given that -2/9*k**4 + c - 16/9*k**2 + 8/9*k + 10/9*k**3 = 0.
0, 1, 2
Suppose -4*v - 2*v = 0. Let b be (2 - -2)*1/22. Factor -b + 4/11*d**3 + v*d**2 + 2/11*d**4 - 4/11*d.
2*(d - 1)*(d + 1)**3/11
Let k(u) be the second derivative of -u**7/168 + u**6/30 - u**5/20 - u**4/24 + 5*u**3/24 - u**2/4 + 50*u. Factor k(d).
-(d - 2)*(d - 1)**3*(d + 1)/4
Let q(h) = -6 - 3 + 11*h - 4*h - h**2 + 5*h. Let m be q(11). Factor 2*r**2 + r + 2*r + m - r**2.
(r + 1)*(r + 2)
Let i(m) be the third derivative of m**11/332640 + m**10/151200 + m**5/12 - 4*m**2. Let z(k) be the third derivative of i(k). Determine n, given that z(n) = 0.
-1, 0
Factor -2/3*p**2 - 8/3 - 8/3*p.
-2*(p + 2)**2/3
Let z(h) = 2*h**2 - h - 1. Let n be z(3). Let w be 0/1 - (-8)/n. Solve w*r**2 - 6/7*r + 2/7 = 0.
1/2, 1
Let h(r) be the third derivative of -r**8/6720 + r**7/630 - r**6/144 + r**5/60 + r**4/8 - r**2. Let a(b) be the second derivative of h(b). Factor a(z).
-(z - 2)*(z - 1)**2
Let p(n) = -n**2 + n - 6. Let x(s) = -s**2 - 6. Let o(r) = -5*p(r) + 6*x(r). Suppose o(d) = 0. Calculate d.
-3, -2
Factor 0*r - 2/17 + 2/17*r**2.
2*(r - 1)*(r + 1)/17
Let h(k) be the second derivative of k**6/1440 - k**5/480 - k**4/48 - k**3/6 + 4*k. Let o(w) be the second derivative of h(w). Factor o(f).
(f - 2)*(f + 1)/4
Let c = 140 - 135. Determine r so that 1/4*r + 5/4*r**4 + 3/4*r**3 - 5/4*r**2 + 0 - r**c = 0.
-1, 0, 1/4, 1
Let j = 33 - 33. Find w, given that 1/2*w**2 + 0*w + j = 0.
0
Let u(h) be the second derivative of h**8/1680 - h**7/1050 + h**2 - 2*h. Let v(q) be the first derivative of u(q). Find d, given that v(d) = 0.
0, 1
Factor 100/7*y**2 - 20/7*y**3 + 0 + 1/7*y**4 + 0*y.
y**2*(y - 10)**2/7
Factor 0*p**2 + 0*p + 0 - 2/13*p**4 + 2/13*p**3.
-2*p**3*(p - 1)/13
Let k(w) be the third derivative of w**8/84 - 8*w**7/105 + w**6/6 - 2*w**5/15 - 22*w**2. Suppose k(f) = 0. Calculate f.
0, 1, 2
Let n(x) be the third derivative of 5*x**8/1008 - x**7/126 - x**6/72 + x**5/36 - 6*x**2. Let n(v) = 0. What is v?
-1, 0, 1
Let w be 1/4 + 1/(-4). Let m be 0 + 4 + 78/(-21). What is r in w + 0*r + 2/7*r**2 - m*r**3 = 0?
0, 1
Let v(y) be the second derivative of y**4/6 + y**3 + 2*y**2 - 2*y. Let v(b) = 0. Calculate b.
-2, -1
Find u, given that -320 + 367 - 4*u**2 - 430 + 160*u - 1217 = 0.
20
Factor 25/4*s**2 - 5/4*s**4 - 15/4*s**3 + 5/4*s**5 - 5/2*s + 0.
5*s*(s - 1)**3*(s + 2)/4
Let n(l) be the third derivative of -l**6/120 + l**5/15 - l**4/12 - l**2. Let j be n(2). Solve -5*r + r**5 - 12*r**2 - j*r**5 + 6*r**4 + 9*r**3 + 2*r - 9*r = 0.
-1, 0, 2
Let h(q) = 21*q**2 + 21*q - 42. Let c(l) be the first derivative of 2*l**3 + 3*l**2 - 12*l - 5. Let a(n) = -18*c(n) + 5*h(n). Factor a(j).
-3*(j - 1)*(j + 2)
Suppose 5*m - 15 = -5*f, 0 = -5*f + 3*m - 4*m + 15. Suppose -4 = p - f*p. Factor h**2 - 2*h**p + 1 + 2*h**2 + 2*h.
(h + 1)**2
Let p(u) be the second derivative of u**5/50 + u**4/15 - u**3/15 - 2*u**2/5 + 5*u. Suppose p(r) = 0. What is r?
-2, -1, 1
Find s, given that -3/2*s**2 + 6*s - 9/2 = 0.
1, 3
