 0). Factor 2*d**3 + 2/3*d**q + 0*d + 2*d**4 + 0 + 2/3*d**2.
2*d**2*(d + 1)**3/3
Let j(r) be the second derivative of -1/6*r**5 - 1/18*r**4 + 1/9*r**3 - 1/15*r**6 + 0*r**2 + 0 - 2*r. Determine i so that j(i) = 0.
-1, 0, 1/3
Factor 0*b - 1/5*b**4 - 1/5*b**3 + 0*b**2 + 0.
-b**3*(b + 1)/5
Let d(i) be the third derivative of 1/15*i**3 + 1/150*i**5 + 2*i**2 - 1/30*i**4 + 0 + 0*i. What is a in d(a) = 0?
1
Let g(l) be the second derivative of 4*l + 1/15*l**4 - 1/15*l**3 - 1/50*l**5 + 0*l**2 + 0. Suppose g(w) = 0. Calculate w.
0, 1
Let u(k) = k**3 - 9*k**2 - 10*k + 11. Let n be u(10). Let r = n - 9. Solve 20*i**r + 2 - 16*i**2 + 4*i + 5*i = 0.
-2, -1/4
Let y(x) be the third derivative of -x**6/360 + x**5/180 + x**4/72 - x**3/18 + 3*x**2. Factor y(w).
-(w - 1)**2*(w + 1)/3
Let w(o) be the second derivative of o**6/180 + o**5/120 - o**4/144 - 9*o**2/2 + 3*o. Let p(r) be the first derivative of w(r). Solve p(z) = 0 for z.
-1, 0, 1/4
Let u = -18 + 21. Factor -7/5*q**2 + 0 + 7/5*q**4 - 2/5*q + 2/5*q**u.
q*(q - 1)*(q + 1)*(7*q + 2)/5
Let x(n) = 4*n. Let s(f) = f**2. Let j(w) = -4*s(w) - 2*x(w). Factor j(h).
-4*h*(h + 2)
Let 29 + 10*d**2 - 29 - 5*d**5 + 15*d**3 = 0. Calculate d.
-1, 0, 2
Let h(l) be the first derivative of 0*l**5 + 0*l**3 - 1/24*l**6 + 0*l**4 + 0*l + 0*l**2 - 5. Factor h(t).
-t**5/4
Let q(j) be the second derivative of -3*j + 0*j**3 + j**2 - 1/6*j**4 + 0. What is u in q(u) = 0?
-1, 1
Factor 3/2*k**3 + 1/2*k**5 + 3/2*k**4 + 0 + 1/2*k**2 + 0*k.
k**2*(k + 1)**3/2
Let 0 + 4/17*k**2 + 0*k - 4/17*k**4 + 2/17*k**3 - 2/17*k**5 = 0. What is k?
-2, -1, 0, 1
Suppose 2*s - 42 = -s. Suppose c = 4*c - 2*x - s, -1 = x. Factor z**2 - 5 + c - 5 + 5.
(z - 1)*(z + 1)
Let r(x) be the third derivative of -x**8/13440 - x**7/1680 - x**6/720 - x**4/8 - x**2. Let u(w) be the second derivative of r(w). Solve u(o) = 0 for o.
-2, -1, 0
Let a(s) be the first derivative of -7*s**4/30 - 2*s**3/15 + 4*s**2/15 - 13. Determine d so that a(d) = 0.
-1, 0, 4/7
Factor 16/3 + 4/3*k**3 - 4/3*k**2 - 16/3*k.
4*(k - 2)*(k - 1)*(k + 2)/3
Factor -2/5*r + 2/15*r**2 + 4/15.
2*(r - 2)*(r - 1)/15
Let z = 152 - 150. Solve 0 - 1/2*a - a**z - 1/2*a**3 = 0 for a.
-1, 0
Let q be -21 + 18 - 22/(-6). Let t be 3*(-1)/((-9)/2). Factor -t*c + 0 - q*c**2.
-2*c*(c + 1)/3
Suppose -2*b - 3 = -l, -9 = 2*b + b + 3*l. Let q be (-32)/(-18) + b/(-9). Factor -1/2*p**3 + 0 + 1/2*p**q + p.
-p*(p - 2)*(p + 1)/2
Let b be (-4)/(-3) + (-6)/(-9). Let n be (-13 - -6 - -6)*2/(-6). Factor -2/3*z + 1/3*z**b + n.
(z - 1)**2/3
Suppose -3*g + 2 = -13. Suppose -5*i + 23 = c + 3*c, -i + 4*c = g. Determine j so that 18*j**i - 26*j**2 - 8/9 + 80/9*j = 0.
2/9, 1
Let p(q) = -16*q**5 - 10*q**4 - 6*q**3 + 21*q**2 + 11. Let r(h) = -3*h**5 - 2*h**4 - h**3 + 4*h**2 + 2. Let v(m) = 2*p(m) - 11*r(m). Factor v(s).
s**2*(s - 1)*(s + 1)*(s + 2)
Let b(d) = 6*d**3 + d + 1. Let t be b(-1). Let u = 8 + t. Find x such that -4/9*x + 2/9 + 2/9*x**u = 0.
1
Let l be (4/(-10))/((-84)/60). Let y(m) be the first derivative of -4/7*m + 1 + l*m**5 + 13/14*m**4 + 6/7*m**3 - 1/7*m**2. Factor y(j).
2*(j + 1)**3*(5*j - 2)/7
Suppose 1 = b - 6. Let k = b + -3. Suppose 0*u**2 + 0*u + k*u - 1 - 3*u**2 = 0. Calculate u.
1/3, 1
Let l(y) be the third derivative of -y**5/12 + 5*y**3/6 - 13*y**2. Factor l(p).
-5*(p - 1)*(p + 1)
Let m be ((-3)/(-158))/(5/(-10)). Let x = 1249/395 - m. What is z in -8/5*z**2 + x*z**3 + 2*z**4 + 0*z + 0 = 0?
-2, 0, 2/5
Let u(k) be the second derivative of -k**7/168 + k**5/80 + 10*k. Factor u(f).
-f**3*(f - 1)*(f + 1)/4
Suppose -26*z + 23*z = 0. Suppose 3/5*l + z + 3*l**2 + 9/5*l**3 - 12/5*l**5 - 3*l**4 = 0. Calculate l.
-1, -1/4, 0, 1
Let z(a) be the first derivative of 2*a**3/9 - 2*a**2 - 8. Solve z(s) = 0.
0, 6
Let x(z) be the third derivative of -3*z**2 + 0*z - 1/84*z**4 + 2/105*z**5 + 0*z**3 + 0. Find w such that x(w) = 0.
0, 1/4
Let d = 73 - 364/5. Let c(b) be the first derivative of -1 + 1/4*b - 3/4*b**3 - d*b**5 + 11/16*b**4 + 1/8*b**2. Solve c(t) = 0 for t.
-1/4, 1
Suppose 15 = -3*v - 2*v. Let d be (v/10)/(30/(-80)). Find g such that d + 6/5*g - 4/5*g**2 = 0.
-1/2, 2
Let z = -133/10 + 29/2. Factor 0*q**2 - 2/5*q**4 + z*q**3 + 0 - 8/5*q.
-2*q*(q - 2)**2*(q + 1)/5
Suppose -4*d + 68 = -3*v, -v - 4*d - d - 48 = 0. Let y = -26 - v. Let 7/3*f**3 + 0 + 3*f**y + 2/3*f = 0. Calculate f.
-1, -2/7, 0
Let f(p) = -23*p - 9*p**2 - 4*p + 4 - 14. Let l(b) = 9*b. Let k(z) = z**2 + 27*z + 1. Let h(j) = 3*k(j) - 8*l(j). Let n(a) = 3*f(a) + 8*h(a). Factor n(w).
-3*(w + 1)*(w + 2)
Factor 0*o**2 + 6/7 + 1/7*o**3 - o.
(o - 2)*(o - 1)*(o + 3)/7
Let y(q) = 2*q**4 - 3*q**3 - 5*q + 5. Let b(x) = 1 - 2*x + 4 + x**4 - x - 2*x**3 - 2. Let g(i) = 5*b(i) - 3*y(i). Suppose g(w) = 0. What is w?
-1, 0
Let x = -76 + 80. Factor 14/5*i**x + 4/5*i + 32/5*i**3 + 22/5*i**2 + 0.
2*i*(i + 1)**2*(7*i + 2)/5
Let q(c) be the second derivative of c**6/165 + c**5/22 + 4*c**4/33 + 4*c**3/33 - 33*c. Suppose q(f) = 0. Calculate f.
-2, -1, 0
Let n(v) be the third derivative of 0 + 0*v**4 + 0*v**3 + 7*v**2 + 0*v + 1/30*v**5. Solve n(t) = 0.
0
Let q(y) = -9*y**4 + 3*y**3 + 48*y**2 - 77*y - 108. Let b(w) = 13*w**4 - 5*w**3 - 72*w**2 + 115*w + 162. Let v(o) = 5*b(o) + 7*q(o). Factor v(k).
2*(k - 3)**2*(k + 1)*(k + 3)
Let d(n) be the third derivative of 0*n + 1/1080*n**6 - 1/72*n**4 + 0*n**5 + n**2 - 1/6*n**3 + 0. Let i(y) be the first derivative of d(y). Factor i(f).
(f - 1)*(f + 1)/3
Let o(k) be the third derivative of -k**8/1008 + k**7/630 + k**6/180 - 11*k**2. Determine v so that o(v) = 0.
-1, 0, 2
Let u(f) be the third derivative of 1/60*f**5 - 1/14*f**8 + 0*f**4 + 0 - 3*f**2 + 13/240*f**6 + 2/105*f**7 + 0*f**3 + 0*f. What is w in u(w) = 0?
-1/4, 0, 2/3
Suppose v + 15 = -0*t + 4*t, -4*t - 3*v + 3 = 0. Determine s, given that 12*s**2 - 7*s + 10*s**3 - 7*s**3 + 25*s + 8 - s**t = 0.
-4, -1
Let l(m) = -m**3 - 2*m**2 + 6*m + 2. Let w be l(-4). Suppose 5*f + 4*b + w = 0, 3*f = -2*f + b + 15. Factor -o**3 + 5*o**f + 2*o - 4*o**2 + 0*o**3.
-o*(o - 2)*(o + 1)
Suppose -2*x - 5*v = -1, 4*v + 5 = 5*x - 14. Let w(o) be the first derivative of -2 - 2/3*o**x + 3*o**2 - 4*o. Factor w(m).
-2*(m - 2)*(m - 1)
Factor 9/7*y**3 - 3/7*y + 0*y**2 + 0 + 6/7*y**4.
3*y*(y + 1)**2*(2*y - 1)/7
Let v be 4/(-11)*88/(-48). Factor 0 + 2/3*s**2 + v*s.
2*s*(s + 1)/3
Suppose 4*b = 7 + 1. Factor -19*q + 0*q**2 + 11*q - 4*q**b - 4.
-4*(q + 1)**2
Let d(o) be the third derivative of -o**7/840 + o**5/80 - o**4/48 - o**2 + 23. Find x such that d(x) = 0.
-2, 0, 1
Let s(d) be the second derivative of -d**6/120 - d**5/60 + d**4/24 + d**3/6 - 7*d**2/2 - 8*d. Let p(z) be the first derivative of s(z). Solve p(w) = 0 for w.
-1, 1
Let b(q) be the third derivative of -q**8/13440 + q**7/2520 - q**6/1440 + q**4/4 + 6*q**2. Let g(j) be the second derivative of b(j). Factor g(t).
-t*(t - 1)**2/2
Let l(g) = -14*g - 16. Let u(n) = -n**2 + 29*n + 31. Let y(h) = 5*l(h) + 2*u(h). Factor y(q).
-2*(q + 3)**2
Let u = 11 - 6. Suppose 3 - f**u - 3*f**5 - 3*f - 6*f**2 + f**5 + 6*f**3 + 3*f**4 = 0. Calculate f.
-1, 1
Factor -u**2 - 36*u + u**5 + 38*u + 0*u**4 - 3*u**3 + 0*u**2 + u**4.
u*(u - 1)**2*(u + 1)*(u + 2)
Let i(j) = 5*j**2 - 10*j - 10. Let p be -6 - 0*(-1)/3. Let d(v) be the first derivative of -v**3/3 + v**2/2 + v + 3. Let t(x) = p*d(x) - i(x). Factor t(k).
(k + 2)**2
Let d(w) be the first derivative of w**4/4 - 2*w**3 + 6*w**2 - 3*w + 2. Let n(j) be the first derivative of d(j). Factor n(x).
3*(x - 2)**2
Let g(i) be the first derivative of 2 + 4/15*i**3 + 1/50*i**5 - 3*i + 0*i**2 - 2/15*i**4. Let j(q) be the first derivative of g(q). Factor j(a).
2*a*(a - 2)**2/5
Factor 0*k**2 + 0*k + 3/8*k**3 + 3/8*k**4 + 0.
3*k**3*(k + 1)/8
Let w(m) = -m**3 - 10*m**2 + 10*m - 13. Let p(q) = -q**2 + q - 1. Let c(f) = 6*p(f) - w(f). Let j be c(-5). Factor -27*u**j + 4*u**2 + 7*u**3 - 4 + 0 + 20*u.
(u - 2)*(u - 1)*(7*u - 2)
Factor 1 - 1/4*u**2 - 3/4*u.
-(u - 1)*(u + 4)/4
Let c(d) be the second derivative of d**7/2940 - d**6/630 + d**5/420 + d**3/3 + 2*d. Let b(r) be the second derivative of c(r). Find y, given that b(y) = 0.
0, 1
Let t = 244 - 239. Determine l, given that -50/7*l**3 + 16/7*l**4 + 0 - 16/7*l**2 + 8/7*l + 6*l**t = 0.
-1, -2/3, 0, 2/7, 1
Let r(l) be the third derivative of -l**8/4032 + l**6/480 + l**5/360 + 16*l**2. Let r(x) = 0. Cal