erivative of -f**7/1120 - f**6/360 + f**5/480 + f**4/48 + 2*f**3/3 + 2*f. Let l(a) be the second derivative of k(a). Factor l(c).
-(c + 1)**2*(3*c - 2)/4
Let v(c) be the third derivative of c**6/210 + c**5/21 + c**4/6 + 2*c**3/7 - 17*c**2. Let v(n) = 0. Calculate n.
-3, -1
Factor -16*y**2 + 10*y**3 + 28*y**2 + 5*y**4 - 10*y - 17*y**2.
5*y*(y - 1)*(y + 1)*(y + 2)
Let z = 523 - 519. Factor -2/5*o**2 + 0*o + 0 - 2/5*o**3 + 2/5*o**z + 2/5*o**5.
2*o**2*(o - 1)*(o + 1)**2/5
Let b(l) be the third derivative of -l**8/840 - l**7/70 - l**6/15 - l**5/6 - l**4/4 - l**3/2 - 2*l**2. Let s(p) be the first derivative of b(p). Factor s(a).
-2*(a + 1)**3*(a + 3)
Suppose 5*l + t - 17 = 0, -4*l + 8 = t - 5. Let y(k) be the third derivative of 0 - 1/180*k**5 - 1/72*k**l + k**2 + 1/360*k**6 + 1/18*k**3 + 0*k. Factor y(s).
(s - 1)**2*(s + 1)/3
Let y = -19/10 + 2. Let f(w) be the second derivative of 0 - 1/75*w**6 - y*w**4 + 0*w**2 - 2*w + 1/15*w**3 + 3/50*w**5. Factor f(i).
-2*i*(i - 1)**3/5
Let c(j) be the first derivative of 2 + j - 1/24*j**4 + 0*j**3 + 1/4*j**2. Let d(n) be the first derivative of c(n). Suppose d(i) = 0. Calculate i.
-1, 1
Let u(k) be the third derivative of -k**6/280 - k**5/140 + 2*k**2. Factor u(s).
-3*s**2*(s + 1)/7
Let k = 11/6 + -1/2. Let d(j) be the first derivative of -1 - 8/3*j + k*j**2 - 2/9*j**3. Suppose d(i) = 0. What is i?
2
Let k(f) be the first derivative of -f**3/3 + 16*f**2 - 256*f + 24. Find p such that k(p) = 0.
16
Let p(k) be the third derivative of -k**7/105 - k**6/60 + k**5/30 + k**4/12 + 7*k**2. Factor p(z).
-2*z*(z - 1)*(z + 1)**2
Let l be 3/24*62 - (-5)/1. Suppose -3/4 + 9/2*o**2 + l*o**3 - 9/8*o + 27/8*o**5 + 45/4*o**4 = 0. Calculate o.
-1, -2/3, 1/3
Let p = 513/652 - 6/163. Factor p*t**2 - 9/4*t + 0.
3*t*(t - 3)/4
Let d(i) be the third derivative of i**8/224 + i**7/140 - i**6/40 + 42*i**2. Factor d(l).
3*l**3*(l - 1)*(l + 2)/2
Let i(j) = j**3 - 9*j**2 + 5*j - 6. Let g be i(9). Let u be (2 - g/15) + 1. Factor -2/5*l**2 + 2/5*l - u*l**3 + 2/5.
-2*(l - 1)*(l + 1)**2/5
Suppose -2*o + 11 = 3. What is c in 20*c - 8*c**2 - 20*c + o*c**3 = 0?
0, 2
Factor 14*g - 1 + 4*g**2 - 19*g + 8*g.
(g + 1)*(4*g - 1)
Let v(d) be the first derivative of 4*d**5/5 - 4*d**3/3 - 8. Suppose v(u) = 0. What is u?
-1, 0, 1
Let i(d) be the second derivative of -3*d**5/25 - 3*d**4/20 + 9*d**3/10 - 3*d**2/5 + 6*d. Factor i(g).
-3*(g - 1)*(g + 2)*(4*g - 1)/5
Suppose 4 = 3*w - 11. Let z(o) be the third derivative of 0 + 1/12*o**3 + 0*o**4 - 1/120*o**w + 0*o - o**2. Find m, given that z(m) = 0.
-1, 1
Let p(x) be the first derivative of x**6 + 27*x**5/10 + 9*x**4/4 + x**3/2 + 3. Let p(j) = 0. What is j?
-1, -1/4, 0
Let i(o) = o**5 - 4*o**4 - o**3 + 4*o**2 + 4*o - 2. Let p(d) = 6*d**5 - 20*d**4 - 4*d**3 + 20*d**2 + 20*d - 11. Let n(k) = -33*i(k) + 6*p(k). Factor n(t).
3*t*(t - 1)*(t + 1)*(t + 2)**2
Let n be 90/4*(-12)/(-15). Factor -n*z**2 + 14*z**3 + 4*z - 21 + 21.
2*z*(z - 1)*(7*z - 2)
Let c(v) be the first derivative of -v**4/26 + 4*v**2/13 - 8. Factor c(d).
-2*d*(d - 2)*(d + 2)/13
Let k be ((-60)/(-70))/(2/14). Let z(m) be the second derivative of 0 + 0*m**4 + 0*m**2 - 2/105*m**7 + 0*m**3 + 2*m - 1/50*m**5 - 1/25*m**k. Factor z(n).
-2*n**3*(n + 1)*(2*n + 1)/5
Let b(k) = 1 - 1 + k + 2 - 1. Let a be b(7). Factor a*h - 2 - 16*h**2 - 3 + 4.
-(4*h - 1)**2
Let z(f) be the second derivative of f**8/210 + f**7/140 - f**6/36 - f**5/20 + f**4/12 + f**3/3 - f. Let x(m) be the second derivative of z(m). Factor x(y).
2*(y - 1)*(y + 1)**2*(4*y - 1)
Factor 8/3*k - 4/3*k**2 - 2/3*k**3 + 16/3.
-2*(k - 2)*(k + 2)**2/3
Suppose b + b - 4 = 0. Factor -1/3*p**b + 0 + 2/3*p - 2/3*p**3 + 1/3*p**4.
p*(p - 2)*(p - 1)*(p + 1)/3
Factor -2*k + 4*k**2 - 2*k**2 + 2 + 2*k**3 - 4.
2*(k - 1)*(k + 1)**2
Let j(r) be the third derivative of r**8/1344 + r**7/120 + 19*r**6/480 + 5*r**5/48 + r**4/6 + r**3/6 + 24*r**2. Determine w, given that j(w) = 0.
-2, -1
Suppose -3*p = 3*b + 12, -4*b - 5*p - 16 = -b. Let g = b + 2. Solve 0*j + 1/3*j**2 + g = 0 for j.
0
Find n, given that -3*n**3 + 0 + 6*n**2 - 4*n + 1/2*n**4 = 0.
0, 2
Let g(a) be the first derivative of 5*a**3/9 + 7*a**2/6 + 2*a/3 + 3. Suppose g(v) = 0. Calculate v.
-1, -2/5
Let h(u) be the third derivative of u**7/840 - u**5/40 - u**4/6 + 5*u**2. Let s(d) be the second derivative of h(d). Factor s(r).
3*(r - 1)*(r + 1)
Suppose -4 - 5 = -3*p + 2*h, -3*p - 3*h + 24 = 0. Factor -2 + p*b**2 - 3*b + b**2 + 7*b + 0*b**2.
2*(b + 1)*(3*b - 1)
Let y be (-12)/117*(-50)/(-8). Let b = -4/13 - y. Factor -b*u**3 + 0*u - 1/3*u**4 + 0 + 0*u**2.
-u**3*(u + 1)/3
Let d(p) be the third derivative of 0*p**4 - 1/60*p**5 + 0*p + 0 + 1/120*p**6 + 0*p**3 + 5*p**2. Factor d(h).
h**2*(h - 1)
Let w(b) = 5*b + 1. Let g be w(1). Let y be ((-36)/g)/(7/(-3)). Determine x, given that 32/7*x**3 + 12/7*x - 4*x**2 - 2/7 + 4/7*x**5 - y*x**4 = 0.
1/2, 1
Let x(r) = 90*r**4 + 250*r**3 + 196*r**2 + 30*r - 6. Let f(l) = 18*l**4 + 50*l**3 + 39*l**2 + 6*l - 1. Let k(n) = 14*f(n) - 3*x(n). Let k(a) = 0. What is a?
-1, 2/9
Let j(b) be the second derivative of -3/100*b**5 + 0 + 5*b - 3/20*b**4 + 0*b**3 + 6/5*b**2. Factor j(s).
-3*(s - 1)*(s + 2)**2/5
Let f(t) be the second derivative of t**7/3360 - t**5/480 - t**3/6 - 4*t. Let z(q) be the second derivative of f(q). Let z(x) = 0. Calculate x.
-1, 0, 1
Let c**4 + c**2 + 4*c**2 + 2*c**2 - 5*c**2 - 3*c**3 = 0. Calculate c.
0, 1, 2
Suppose -p + 4*p - 4*k - 20 = 0, 0 = -4*p - 4*k - 20. Let o be (0/(-24) - 6/(-4))/3. Find f, given that 1/2*f**2 + 0 + o*f**3 + p*f = 0.
-1, 0
Let x(n) be the first derivative of n**5/10 - 5*n**4/8 + 20. Let x(l) = 0. What is l?
0, 5
Let s(q) be the first derivative of -5*q**4/12 - 10*q**3/9 - 5*q**2/6 + 18. Factor s(t).
-5*t*(t + 1)**2/3
Let h(i) be the second derivative of 0 + 1/12*i**4 - 5/12*i**3 - 1/15*i**6 + 1/10*i**5 + 1/2*i**2 + 3*i + 1/84*i**7. Factor h(x).
(x - 2)*(x - 1)**3*(x + 1)/2
Factor 2/5*j**3 + 0*j**2 + 0 - 2/5*j.
2*j*(j - 1)*(j + 1)/5
Find v, given that 2*v + 5*v**2 + 3*v**2 - 6*v**2 = 0.
-1, 0
Factor 5*u**3 - 2*u**4 + 2*u**4 - 9*u**2 + 3*u**4 - 2*u**3 - 3*u + 6.
3*(u - 1)**2*(u + 1)*(u + 2)
Suppose 0 = -8*l + 13*l - 10. Let t(p) be the first derivative of 0*p + 1/21*p**6 + 1 + 4/21*p**3 + 0*p**l + 5/14*p**4 + 8/35*p**5. Solve t(d) = 0 for d.
-2, -1, 0
Let v(k) = -k**5 - k**4 - k**3 - k**2 - k. Let w(r) = 8*r**5 + 56*r**4 + 72*r**3 + 32*r**2 - 4*r. Let d(z) = -12*v(z) + w(z). Factor d(n).
4*n*(n + 1)**3*(5*n + 2)
Let h = -219 + 224. Solve -3*f**2 + h*f**3 + f**5 - 11/3*f**4 + 2/3*f + 0 = 0 for f.
0, 2/3, 1
Let j(n) be the second derivative of 1/6*n**4 + 0 - 5*n + 3/70*n**5 + 0*n**2 + 2/21*n**3. Suppose j(z) = 0. What is z?
-2, -1/3, 0
Factor 5/6*p**2 + 7/6 - 13/6*p + 1/6*p**3.
(p - 1)**2*(p + 7)/6
Factor 2/5*s**2 - 1/5*s**5 + 0 - 2/5*s**4 + 0*s**3 + 1/5*s.
-s*(s - 1)*(s + 1)**3/5
Let x(o) be the second derivative of 0*o**5 - 1/3*o**2 - 1/45*o**6 + 1/9*o**4 + 0 + 0*o**3 + o. Factor x(d).
-2*(d - 1)**2*(d + 1)**2/3
Suppose 2*p = -p + 6. Factor 16/7*a - 32/7 - 2/7*a**p.
-2*(a - 4)**2/7
Suppose -12 - 8 = -4*s. Let y(v) be the second derivative of 1/10*v**s + 0*v**4 + 0*v**3 + 1/15*v**6 + 0 + 0*v**2 - v. What is j in y(j) = 0?
-1, 0
Let q be (9/15)/((-38)/(-20) - 1). Let 2/9*i**3 - 2/9 + 2/3*i - q*i**2 = 0. Calculate i.
1
Suppose 17*z**2 - 15*z**4 + 11*z**4 - 10*z - 20*z**3 - 6*z - 49*z**2 = 0. What is z?
-2, -1, 0
Let u(c) = 230*c**2 + 285*c + 100. Let k(y) = 21*y**2 + 26*y + 9. Let p(z) = 45*k(z) - 4*u(z). Factor p(d).
5*(d + 1)*(5*d + 1)
Suppose 0*l = -2*l + 18. Let w = -6 + l. Let j(m) = -2*m**2 - 7*m - 5. Let x(t) = t**2 + 4*t + 3. Let s(h) = w*j(h) + 5*x(h). Determine n, given that s(n) = 0.
-1, 0
Let f(w) be the third derivative of -w**8/2520 - 2*w**7/1575 + w**6/900 + w**5/225 + 43*w**2. Find r such that f(r) = 0.
-2, -1, 0, 1
Factor 1/2*i + 0 - 1/4*i**2.
-i*(i - 2)/4
Suppose a + 10 = 6*a. Let c(r) = 7*r**2 - 1. Let q be c(1). Determine y, given that -q*y + 8/3*y**a + 4/3 = 0.
1/4, 2
Let t(w) be the third derivative of w**2 + 0*w - 1/60*w**6 + 0 + 1/12*w**4 + 0*w**5 + 0*w**3. Find r such that t(r) = 0.
-1, 0, 1
Factor 0 - 8/11*b + 2/11*b**2.
2*b*(b - 4)/11
Let k = 12 + -12. Let l(w) = -w - 4. Let b be l(-6). Factor 2/3*r**b + k + 2/3*r.
2*r*(r + 1)/3
Let r(s) = s**2 + 5*s. Let x be r(-5