y**2. Factor q(p).
-2*p*(p - 1)**3*(p + 1)/3
Factor 320 + 36*y + 71*y - 27*y + 135*y**2 - 130*y**2.
5*(y + 8)**2
Let o(w) be the third derivative of -w**8/13440 + w**7/5040 + w**6/720 - w**4/12 + 3*w**2. Let d(a) be the second derivative of o(a). Solve d(h) = 0.
-1, 0, 2
Let b = -18 - -18. Let 0*t**3 + 0*t + 0 + 1/2*t**4 - 1/2*t**5 + b*t**2 = 0. Calculate t.
0, 1
Suppose -w + 55 = -3*q - 2*w, 2*q - w = -45. Let y be 8*(4 - (-76)/q). Factor 14/5*b**4 + 10*b**2 + y - 2/5*b**5 - 32/5*b - 38/5*b**3.
-2*(b - 2)**2*(b - 1)**3/5
Let p(o) be the first derivative of o**6/180 + o**5/10 + 3*o**4/4 - 4*o**3/3 - 7. Let r(q) be the third derivative of p(q). Find m, given that r(m) = 0.
-3
Let u(h) = -h**3 + 9*h**2 - h + 12. Let v be u(9). Find i, given that 7/3*i - 2/3 - 7/3*i**v + 2/3*i**2 = 0.
-1, 2/7, 1
Find i such that 5*i - 3*i**2 - 2*i**2 + 2*i - 2*i = 0.
0, 1
Let k = -24963/117884 - -1/4534. Let x = k + 6/13. Factor 0 + 1/4*c**3 - x*c**2 - 1/4*c + 1/4*c**4.
c*(c - 1)*(c + 1)**2/4
Let z(a) be the third derivative of -a**8/13440 + a**6/480 - a**5/120 + a**4/24 + 3*a**2. Let f(k) be the second derivative of z(k). What is b in f(b) = 0?
-2, 1
Let r(g) be the first derivative of g**6/360 + g**5/120 - g**4/12 - 2*g**3 + 6. Let h(s) be the third derivative of r(s). Factor h(f).
(f - 1)*(f + 2)
Let g(t) = -17*t**2 + 21*t + 16. Let x(l) = -26*l**2 + 32*l + 24. Let d(n) = -8*g(n) + 5*x(n). Find a, given that d(a) = 0.
-2/3, 2
Suppose -o - 64 + 70 = 0. Let z(i) be the first derivative of o*i**2 - 4 + 18*i + 2/3*i**3. Factor z(g).
2*(g + 3)**2
Find m such that -3/2*m + 1/2*m**3 + 1 + 0*m**2 = 0.
-2, 1
Let k(c) = -c - 1. Let n(x) = -2*x**2 - 2*x + 2. Let a(u) = 2*k(u) + n(u). Factor a(b).
-2*b*(b + 2)
Let n be 26/42 + (-50)/175. Factor -n*k**3 - 1/3*k**2 + 1/3 + 1/3*k.
-(k - 1)*(k + 1)**2/3
Suppose 3*x = 2*u + 9, -2*u - 15 = -5*x + u. Suppose -5*v**2 + 0*v - v**x - 2*v**3 + 4*v - 2*v = 0. Calculate v.
-2, 0, 1/3
Let l = -1 + 3. Suppose -2*q = l*q - 4. Factor 0 + k + q + k**2 + k.
(k + 1)**2
Suppose -2*g - 2*g = -12. Suppose 0 = -4*b + g*n + 23, -5*b - n + 3*n = -20. Determine k so that -b*k**5 + 2*k**2 - 6*k + 4*k + 2*k**3 + 2*k - 2*k**4 = 0.
-1, 0, 1
Suppose 0 = -d - 9*d - 4*d. Factor d*h + 0*h**2 + 0 + 1/2*h**3.
h**3/2
Let r(d) = -d - 5. Let l be r(-6). Let x(c) = c**2 - c - 1. Let h(n) = 2*n**3 - 6*n**2 + 10*n + 10. Let s(z) = l*h(z) + 10*x(z). Factor s(y).
2*y**2*(y + 2)
Let n(x) be the third derivative of -1/210*x**7 - 1/24*x**6 - 1/6*x**4 + x**2 + 0*x + 0*x**3 + 0 - 2/15*x**5. Factor n(b).
-b*(b + 1)*(b + 2)**2
Let b(z) be the second derivative of -z**6/10 + 3*z**5/4 - 3*z**4/2 - 2*z**3 + 12*z**2 - 27*z. Let b(d) = 0. What is d?
-1, 2
Let q(p) = 0*p**2 + 4*p**2 + 8*p - 5*p**2 - 12. Let k be q(6). Let k + 12/5*m**3 - 24/5*m**2 - 2/5*m**4 + 16/5*m = 0. Calculate m.
0, 2
Let u(y) be the third derivative of y**8/336 - y**6/40 - y**5/30 + 6*y**2. Determine n, given that u(n) = 0.
-1, 0, 2
Suppose 2*r - i - 5 + 1 = 0, 3*r = 2*i + 5. Factor 5*j**2 + r*j + 3*j**3 - j**2 - 4 - j - 5*j**3.
-2*(j - 2)*(j - 1)*(j + 1)
Let d(g) be the second derivative of -4/75*g**6 + 0 + 0*g**3 - 1/15*g**4 - 1/105*g**7 + 0*g**2 - 3*g - 1/10*g**5. Suppose d(x) = 0. Calculate x.
-2, -1, 0
Suppose -5*x - 4*t - 6 = 0, -18 = x + 3*t + 2*t. Suppose 0 = z - 3*l - l - 18, 5*z + l = 6. Factor -3*w**2 + w**4 - 2*w**4 + w**z + w**2 - x*w**3.
-w**2*(w + 1)**2
Let a = -29 - -29. Factor a + c**3 - 1/2*c**4 + 0*c - 1/2*c**2.
-c**2*(c - 1)**2/2
Let s = -15 - -23. Let y(l) be the third derivative of -1/6*l**5 + 9/112*l**s + 9/70*l**7 + l**2 + 7/24*l**4 - 3/20*l**6 - 1/6*l**3 + 0 + 0*l. Factor y(h).
(h + 1)**2*(3*h - 1)**3
Let z(f) be the second derivative of -3/100*f**5 + 1/50*f**6 + 1/60*f**4 + 0 + 2*f + 0*f**3 + 0*f**2 - 1/210*f**7. What is g in z(g) = 0?
0, 1
Let j(z) = -z**3 + 2*z**2 + 2*z + 5. Let d(g) = g**2 + g. Let r(f) = -5*d(f) + j(f). Let w(i) be the first derivative of r(i). Factor w(b).
-3*(b + 1)**2
Factor 3/5*d**3 - 4/5*d + 0*d**2 - 1/5*d**4 + 0.
-d*(d - 2)**2*(d + 1)/5
Suppose 3*c - 3 = -2*d, 5*d + 3*c + 0*c - 21 = 0. Suppose 5*z - d = 2*z. Solve 0*m**z + m + 1/2 - m**3 - 1/2*m**4 = 0.
-1, 1
Suppose 5*v = 3*u + 2*u, 0 = 3*v + u + 4. Let z(p) = -3*p**2 + 2*p + 13. Let s(y) = y**2 + y - 1. Let d(x) = v*z(x) - 4*s(x). Suppose d(m) = 0. Calculate m.
-3
Let c(u) be the third derivative of -u**6/300 + u**5/30 - 2*u**4/15 + 4*u**3/15 - 13*u**2. Determine k, given that c(k) = 0.
1, 2
Suppose -6 = t - 4*t. Factor 4*u - t*u - 4*u + 2 + u**3 - 2*u**2 + u**3.
2*(u - 1)**2*(u + 1)
Let h be 1 - (-18)/20*16/24. Factor 0 - 2/5*w**3 - h*w**2 - 8/5*w.
-2*w*(w + 2)**2/5
Suppose -5*z - 45 = -f, 9*z = -f + 4*z - 5. Let h = f - 58/3. Suppose 0 + 0*n - h*n**3 + 0*n**2 = 0. What is n?
0
Suppose 15*b = 7*b + 6*b. Factor 14/9*x**5 + 2*x**4 + 0*x**2 + 4/9*x**3 + 0*x + b.
2*x**3*(x + 1)*(7*x + 2)/9
Suppose -14*w = -18*w. Find g, given that -2/7*g**2 - 2/7*g**3 + w + 4/7*g = 0.
-2, 0, 1
Suppose -2*t - t = -12. Solve 0*h**2 - 2*h**2 - t*h + 2*h = 0 for h.
-1, 0
Factor 2/7*m**3 - 4/7*m**2 + 4/7 - 2/7*m.
2*(m - 2)*(m - 1)*(m + 1)/7
Let d(c) be the second derivative of c**4/3 + 2*c**3 + 4*c**2 + 33*c. Factor d(h).
4*(h + 1)*(h + 2)
Let l(w) be the second derivative of -w**7/3360 + w**3/2 + 5*w. Let c(a) be the second derivative of l(a). Suppose c(h) = 0. What is h?
0
Let r(o) = o**3 - 9*o**2 + o - 6. Let a be r(9). Suppose 12 = a*f + f. Factor 12*n**2 - 10*n**2 + 2 - n - f*n.
2*(n - 1)**2
Suppose -5*a + 17 = -8. Suppose -8 - 2 = -a*g. Find h such that 1/2*h + 1/2 - 1/2*h**3 - 1/2*h**g = 0.
-1, 1
Let i(f) be the second derivative of -f**4/30 + 4*f**2/5 - 7*f - 2. Factor i(q).
-2*(q - 2)*(q + 2)/5
Solve -24*d - 40/9*d**3 - 4/9*d**4 - 16*d**2 - 12 = 0.
-3, -1
Let q = 83 + -745/9. Factor -2/9*r**3 - 2/9*r**2 + 0 + q*r + 2/9*r**4.
2*r*(r - 1)**2*(r + 1)/9
Let m(b) = -b**2 + 53*b - 238. Let x be m(5). Find k, given that 2/3*k**3 + 2/3*k**5 + 0 + 2*k**4 - 4/3*k - 2*k**x = 0.
-2, -1, 0, 1
Let x(w) = w**3 - 5*w**2 - 2*w + 4. Let n be x(5). Let j = n - -8. Find p, given that -p + p - 3 + 1 + 2*p**j = 0.
-1, 1
Let u(x) = 23*x**5 + 9*x**4 - 3*x**3. Let b(w) = -8*w**5 - 3*w**4 + w**3. Let t(c) = 11*b(c) + 4*u(c). Factor t(z).
z**3*(z + 1)*(4*z - 1)
Solve 0 + 3/2*v**2 - 3/2*v = 0.
0, 1
Suppose -t = 1 - 4. Factor -3*m**5 - 3*m**2 + 0*m**4 + 4*m**t - m**3 + 3*m**4.
-3*m**2*(m - 1)**2*(m + 1)
Let n(w) be the third derivative of -w**5/24 - 5*w**4/24 + 5*w**3/4 - 13*w**2. Find r such that n(r) = 0.
-3, 1
Factor 5/4*n**2 + 1/2*n + 0 + 3/4*n**3.
n*(n + 1)*(3*n + 2)/4
Suppose -2*a + 5*o + 1 = -5*a, 5*a - 35 = -o. Let d(u) = u**3 - 8*u**2 + u - 6. Let r be d(a). Find n such that -6*n + 7*n**2 - 3*n**2 - r + 4*n**2 = 0.
-1/4, 1
Let i(m) = -2*m**3 + 2*m**2 + 13*m + 6. Let n(h) = 2*h**3 - 2*h**2 - 12*h - 6. Let v(z) = -2*i(z) - 3*n(z). Suppose v(w) = 0. Calculate w.
-1, 3
Let d(g) = 8*g**2 - 2*g + 3. Let t(n) = 1. Let j(a) = 2*d(a) - 6*t(a). Find p such that j(p) = 0.
0, 1/4
Let d = 26 + -17. Factor -2*u**2 + 3*u - d - u + 13.
-2*(u - 2)*(u + 1)
Solve -r**4 + 4*r**3 + 3*r**2 - r**4 - 5*r**2 = 0.
0, 1
Let w be 4/22 + 136/220. Let x be (12/(-50))/(12/(-20)). Find h such that 2/5*h - 4/5*h**3 + 2/5*h**5 + x*h**4 - w*h**2 + 2/5 = 0.
-1, 1
Suppose 0 = -k + 5*r - 25, 0*r - 25 = -2*k - 5*r. Determine h so that -4/5*h**2 + 2/5*h**3 + k*h + 0 = 0.
0, 2
Let k(s) be the second derivative of 0*s**5 + 0*s**4 + 0*s**2 + 0 + 0*s**3 + s + 1/60*s**6. Solve k(m) = 0 for m.
0
Factor -3/4*r**5 + 21/4*r + 3/2 + 6*r**2 - 3/2*r**4 + 3/2*r**3.
-3*(r - 2)*(r + 1)**4/4
Let y(j) be the second derivative of 9*j**4/16 + 29*j**3/8 + 9*j**2/4 + 13*j. Factor y(f).
3*(f + 3)*(9*f + 2)/4
Let y(v) be the second derivative of v**7/280 - v**5/40 + v**3/6 + 2*v. Let r(a) be the second derivative of y(a). Solve r(i) = 0.
-1, 0, 1
Let n(r) be the first derivative of -r**6/57 + 12*r**5/95 - 11*r**4/38 + 4*r**3/57 + 12*r**2/19 - 16*r/19 - 2. Determine v, given that n(v) = 0.
-1, 1, 2
Suppose 22*z**3 + 10*z**2 + 5*z**2 - 3*z**5 + 6*z - 3*z**4 - 13*z**3 = 0. What is z?
-1, 0, 2
Let m(d) be the second derivative of -d**5/100 - d**4/12 + 13*d**3/30 - 7*d**2/10 + 5*d. Let m(g) = 0. What is g?
-7, 1
Let r = -115 - -347/3. What is f in -r*f**2 - 6 + 4*f = 0?
3
Let r be (1 - -2)*(-4)/(-3)