ve of 3*w**7/70 - w**6/10 - w**5/4 + w**4/4 + w**2 + w. Factor i(b).
3*b*(b - 2)*(b + 1)*(3*b - 1)
Suppose 14 = 4*q - 22. Find s such that -8*s**2 + 73*s**3 + 8*s - q*s**3 + 28*s**4 + 52*s**2 = 0.
-1, -2/7, 0
Let h(f) = -f**2 + 10*f. Let t be h(10). Determine d, given that -1/3*d + 1/3*d**3 + t + 0*d**2 = 0.
-1, 0, 1
Let a(k) be the first derivative of -1 + 20/3*k**3 - 16/5*k**5 - k**2 + 5/3*k**6 - 2*k**4 - 4*k. Find t, given that a(t) = 0.
-1, -2/5, 1
Let n(u) be the third derivative of u**5/60 - 5*u**4/24 + u**3 - 27*u**2. What is v in n(v) = 0?
2, 3
Let a(q) be the first derivative of -q**4/6 + 2*q**3/3 - q**2 - 2*q + 7. Let u(s) be the first derivative of a(s). Factor u(n).
-2*(n - 1)**2
Let o(i) = -i**2 + 14*i + 6. Let j be o(14). Find u, given that -7/2*u**5 + 0*u - j*u**4 + u**2 + 0 - 3/2*u**3 = 0.
-1, 0, 2/7
Let s = 12 - 2. Let y(a) = 2*a**2 + a - 3. Let z(c) = 3*c**2 + c - 5. Let p(r) = s*y(r) - 6*z(r). Factor p(t).
2*t*(t + 2)
Let k(o) be the first derivative of o**4/42 - o**3/21 - 4*o - 3. Let a(v) be the first derivative of k(v). Factor a(c).
2*c*(c - 1)/7
Suppose 3*v = -2*q - 0*v + 17, 19 = 2*q + 5*v. Let a(i) = 10*i**2 + 10*i. Let g(p) = -21*p**2 - 20*p + 1. Let t(o) = q*a(o) + 4*g(o). Factor t(s).
-2*(s + 1)*(7*s - 2)
Let w = -30 - -42. Suppose 60*h**2 + 6*h**3 - 2 + 14*h**3 - 14 - 44*h**4 + w*h**5 - 32*h = 0. Calculate h.
-1, -1/3, 1, 2
Let g(x) be the first derivative of 0*x**3 - 4/25*x**5 + 0*x**2 + 5 + 0*x - 1/15*x**6 - 1/10*x**4. Factor g(k).
-2*k**3*(k + 1)**2/5
Let n(u) be the second derivative of u**6/360 + u**5/60 + 2*u**3/3 - 2*u. Let h(s) be the second derivative of n(s). Let h(j) = 0. What is j?
-2, 0
Let s(i) be the second derivative of -i**5/20 + i**4/2 + 7*i**3/6 + 44*i + 1. Factor s(r).
-r*(r - 7)*(r + 1)
Let n = 89/6 + -44/3. Let w(p) be the second derivative of 0*p**2 + n*p**4 + 1/3*p**3 + 2*p + 0. Factor w(l).
2*l*(l + 1)
Let a = -731/3 + 245. Suppose 0*g = -g. Factor -1/3*p - 2*p**3 + 4/3*p**4 - 1/3*p**5 + g + a*p**2.
-p*(p - 1)**4/3
Let o(n) be the first derivative of 8 + 0*n - 8/39*n**3 - 1/26*n**4 - 3/13*n**2. Factor o(h).
-2*h*(h + 1)*(h + 3)/13
Let h = 77/80 + -9/10. Let g(q) be the second derivative of 1/6*q**4 + 0 + 0*q**2 - 1/6*q**3 - h*q**5 + 1/120*q**6 + 3*q. Determine k, given that g(k) = 0.
0, 1, 2
Factor -4*d - 2*d + 4*d**2 + 4 - 4 + 2.
2*(d - 1)*(2*d - 1)
Determine l so that -1/3*l - 1/3*l**2 + 2/3 = 0.
-2, 1
Let u = -17 + 35/2. Let c(y) be the first derivative of 0*y + u*y**4 + 2/5*y**5 - 2 + 0*y**2 + 0*y**3. Let c(t) = 0. Calculate t.
-1, 0
Let k(y) = 3*y - 3. Let f be k(2). Let l(g) be the first derivative of -g**4 + 2*g + 2*g**2 + 0*g**f - 3 - 2/5*g**5. Find u, given that l(u) = 0.
-1, 1
Let w be 315/(-245) + (-1 - 0 - -3). Let z(n) be the first derivative of 8/7*n**3 + w*n**4 + 2 + 6/7*n**2 + 6/35*n**5 + 2/7*n. Factor z(u).
2*(u + 1)**3*(3*u + 1)/7
Let p = 49/4 + -12. Factor -1/2*s**3 + 0*s - 1/4*s**2 - p*s**4 + 0.
-s**2*(s + 1)**2/4
Let l(d) = 3*d**2 - d - 8. Let m(k) = 3*k**2 - 9. Let t be 0 + 1 + -7 + 3. Let f(u) = t*l(u) + 2*m(u). Suppose f(n) = 0. Calculate n.
-1, 2
Suppose 0*c = -3*c + 12. Suppose 0 = -0*b - 2*b + c. Factor -7*w - 3*w**b + 3*w - 11*w**2.
-2*w*(7*w + 2)
Let l(s) be the third derivative of 11/480*s**6 + 3/80*s**5 + 1/210*s**7 + 1/96*s**4 - 1/24*s**3 + 0*s + 0 + 2*s**2. Factor l(b).
(b + 1)**3*(4*b - 1)/4
Let k be 11 - ((-2)/1 - -4). Factor 17*t + 7*t**4 + 7*t + 12*t**3 - 8 - 26*t**2 - k*t**4.
-2*(t - 2)**2*(t - 1)**2
Let o be (9/(-6) + 4)*(-6)/(-5). Find h such that 1/3*h + 2/3*h**2 + 1/3*h**o + 0 = 0.
-1, 0
Let r(y) be the second derivative of 0*y**2 + 0 - 21/40*y**5 + 0*y**3 - 1/4*y**4 - 1/4*y**6 - 4*y. Solve r(s) = 0.
-1, -2/5, 0
Suppose -4*c = 2*o - 16, 2*c - 4 = c + 2*o. Suppose 0 = c*t - 6 - 2. Let t*i**4 + 2/3*i**5 + 2/3*i**2 + 0*i + 0 + 2*i**3 = 0. Calculate i.
-1, 0
Let c = 284 - 282. Let 4/3*l**4 + 0 - 4*l**3 - 20/3*l**c - 8/3*l + 4/3*l**5 = 0. Calculate l.
-1, 0, 2
Let h(g) be the third derivative of g**7/490 - g**6/140 - g**5/140 + g**4/28 + 14*g**2. Factor h(s).
3*s*(s - 2)*(s - 1)*(s + 1)/7
Determine z, given that 48/7 + 3/7*z**2 + 24/7*z = 0.
-4
Let k(t) be the first derivative of -t**5/5 + 5*t**4/6 - 5*t**2/3 + t - 23. Solve k(m) = 0.
-1, 1/3, 1, 3
Let t be 14/4 - (0 - (-1)/2). Let v(q) be the second derivative of -1/3*q**4 + 0*q**t + 0*q**2 + 0 - 3*q + 1/84*q**7 + 3/10*q**5 - 1/10*q**6. Factor v(i).
i**2*(i - 2)**3/2
Let x = -9 - -13. Let r(k) be the second derivative of -1/3*k**3 + 0 - 1/12*k**x - 1/2*k**2 + k. Suppose r(d) = 0. Calculate d.
-1
Let g(f) = -f - 1. Let r be g(-4). Let v = 321/2 - 160. Factor 2*n**r + 3*n + 9/2*n**2 + v.
(n + 1)**2*(4*n + 1)/2
Let i(x) be the first derivative of x**3/5 + x**2/10 - 2*x/5 - 2. Factor i(g).
(g + 1)*(3*g - 2)/5
Let -19*x - 43*x - 32*x - 2*x**3 + 22*x + 24*x**2 = 0. What is x?
0, 6
Suppose 0 = -4*z + 5 + 19. Let r be -7 + z - (-10)/6. Factor 2/3*p - r*p**3 - 1/3 + 1/3*p**4 + 0*p**2.
(p - 1)**3*(p + 1)/3
Let c(g) = 39*g**2 - 78*g + 39. Let y(a) = -3*a**2 + 6*a - 3. Let v(d) = -2*c(d) - 27*y(d). Factor v(r).
3*(r - 1)**2
Let k(o) = -3*o**3 + 6*o**2 + 3*o. Let m(j) = j**3 - j**2 - j. Let g(p) = -k(p) - 6*m(p). Let g(a) = 0. Calculate a.
-1, 0, 1
Factor -3/5*v**3 - 3/5 + 3/5*v**2 + 3/5*v.
-3*(v - 1)**2*(v + 1)/5
Let d(g) be the first derivative of g**4/28 - g**3/7 + 3*g**2/14 + 5*g - 2. Let c(p) be the first derivative of d(p). Factor c(o).
3*(o - 1)**2/7
Let i(d) be the second derivative of -d**4/66 - 10*d**3/33 - 25*d**2/11 + 11*d. Find x, given that i(x) = 0.
-5
Let z(r) be the first derivative of 1/12*r**2 + 1/3*r - 1/18*r**3 - 5. Solve z(t) = 0 for t.
-1, 2
Let i(s) = -3*s - 3. Let r = 0 - 2. Let j be i(r). Suppose 0*l**j + l - 2*l + l**3 = 0. Calculate l.
-1, 0, 1
Let n(b) be the third derivative of -b**9/30240 + b**7/2520 - b**5/240 + b**4/12 - 4*b**2. Let c(a) be the second derivative of n(a). Factor c(m).
-(m - 1)**2*(m + 1)**2/2
Let v = 95 + -92. Factor -2/3*b**2 - 8/3*b + 8/3*b**v + 2/3.
2*(b - 1)*(b + 1)*(4*b - 1)/3
Let w(y) be the second derivative of y**4/12 - y**3/2 + 8*y. Factor w(s).
s*(s - 3)
Let r(v) = v**5 - 2*v**4 + 23*v**3 - 46*v**2 + 40*v - 9. Let f(b) = -b**5 + 3*b**4 - 24*b**3 + 46*b**2 - 39*b + 9. Let s(o) = 7*f(o) + 6*r(o). Factor s(d).
-(d - 3)**2*(d - 1)**3
Factor 2/3*a**2 + 0 - 2/3*a**3 + 0*a.
-2*a**2*(a - 1)/3
Let r(y) be the second derivative of -3*y**5/20 - y**4/4 + y**3/2 + 3*y**2/2 - 16*y. Suppose r(j) = 0. What is j?
-1, 1
Let p(z) = z**3 + 5*z**2 + 5*z - 5. Let q(u) = -8*u**3 - 44*u**2 - 46*u + 46. Let b(y) = 52*p(y) + 6*q(y). Find a such that b(a) = 0.
-2, 1, 2
Let f(a) be the second derivative of -a**5/100 + a**4/60 + a**3/15 - 4*a. Factor f(n).
-n*(n - 2)*(n + 1)/5
Let f(n) be the third derivative of n**5/120 - 5*n**4/48 + 21*n**2. Let f(a) = 0. Calculate a.
0, 5
Let d(b) = b**2 + 24*b + 36. Let t(w) = 3*w**2 + 48*w + 72. Let f(k) = 5*d(k) - 3*t(k). Factor f(p).
-4*(p + 3)**2
Let t = -320 - -968/3. Determine a so that -t*a - 8/3 - 2/3*a**2 = 0.
-2
Factor 0 - 2/3*s**4 + 0*s + 2/3*s**2 - 1/3*s**3 + 1/3*s**5.
s**2*(s - 2)*(s - 1)*(s + 1)/3
Let z = -50 - -52. Factor -6/5*v**z + 2*v + 4/5.
-2*(v - 2)*(3*v + 1)/5
Let i(j) = j + 7. Let n be i(-9). Let m(k) = -k**2 + 1. Let s(b) = -1 - 4*b**2 + 5 + 0 - 2. Let r(y) = n*m(y) + s(y). Factor r(g).
-2*g**2
Factor 0*v**2 + 2*v**4 - 2*v**2 - 4*v**5 + v + 3*v**5.
-v*(v - 1)**3*(v + 1)
Solve -22*b**2 + 3*b**2 + 7*b**2 + 6*b**3 - 3*b**4 + 9*b**2 = 0.
0, 1
Suppose -f + 2*f = 5. Factor -2*c**3 + c + 2*c - 2*c + c**f.
c*(c - 1)**2*(c + 1)**2
Let i(z) be the second derivative of 1/4*z**4 - 6*z + 0 - z**3 + 3/2*z**2. Factor i(j).
3*(j - 1)**2
Let h(g) = -g**2 - 8*g + 8. Let a(n) = -n**2 + 2*n - 3. Let y be a(2). Let b(c) = c**2. Let r(s) = y*b(s) - h(s). What is q in r(q) = 0?
2
Let f be -1*(4 + -3)*0. Let b(l) be the third derivative of 0*l - 3*l**2 + f*l**4 - 1/36*l**3 + 0 + 1/360*l**5. Solve b(s) = 0 for s.
-1, 1
Let r(b) be the first derivative of 2*b**5/55 - 2*b**3/33 - 7. Suppose r(q) = 0. What is q?
-1, 0, 1
Let k(s) be the third derivative of -s**8/560 + 11*s**6/200 - 3*s**5/50 - 7*s**4/10 + 12*s**3/5 - 14*s**2. Solve k(n) = 0 for n.
-3, -2, 1, 2
Let m = -4 + 7. What is w in -3 + 3*w**2 + 6*w**3 - 3*w**m - 15*w**3 + 12*w = 0?
-1, 1/4,