alculate w.
-1, 0, 2/3, 1
Find j such that 316*j**3 - 674*j**3 + 16 + 54*j**2 - 36*j - 14*j + 2*j**4 + 336*j**3 = 0.
1, 8
Let b(a) = a**3 + 6*a**2 + 4*a + 2. Let h be b(-4). Suppose r + 2*r = h. Find f, given that -16*f**4 + 17*f**4 + 9*f**2 + 4*f + r*f**3 - 4*f = 0.
-3, 0
Let w(f) be the second derivative of -25*f**7/3 - 11*f**6/3 + 99*f**5/5 + 32*f**4/3 - 32*f**3/3 + 234*f. Let w(c) = 0. Calculate c.
-4/5, 0, 2/7, 1
Suppose 23 = -c + 27. Let o be (6 - 72/15)*10/c. Find x, given that 1/2 + 1/2*x**4 + 0*x**o + 0*x - x**2 = 0.
-1, 1
Let c(w) be the first derivative of 21*w**5/80 + 5*w**4/16 - w**3/4 - 11*w + 12. Let o(d) be the first derivative of c(d). Factor o(n).
3*n*(n + 1)*(7*n - 2)/4
Let y(c) = -c**2 - c + 1. Let b(o) = 5*o**2 - o - 1. Suppose -2 = -5*g + 3*g. Let i(p) = g*b(p) + 3*y(p). Suppose i(r) = 0. What is r?
1
Let q = -216 + 210. Let n be (-11)/((-33)/q) + (-44)/(-18). Factor -n + 2/9*j**3 + 10/9*j - 8/9*j**2.
2*(j - 2)*(j - 1)**2/9
Suppose -79*n - 6 = -81*n. Let k(l) be the third derivative of 1/42*l**3 + 1/420*l**5 + 0*l + 0 + n*l**2 + 1/84*l**4. Suppose k(p) = 0. What is p?
-1
Factor 32/11*k + 16/11 + 1/11*k**4 + 8/11*k**3 + 24/11*k**2.
(k + 2)**4/11
Let k be (-2)/(-9) - 789*(-2)/(-54). Let g = k - -32. Factor 3*m**2 + 0*m**g - 3*m**4 + 0 + 3/2*m - 3/2*m**5.
-3*m*(m - 1)*(m + 1)**3/2
Let f = 146 - 218. Let w = f + 145/2. Factor 0 - u - 5/2*u**2 + w*u**4 - 3/2*u**3 + 1/2*u**5.
u*(u - 2)*(u + 1)**3/2
Let r = 28 - 24. Suppose -r*b - 20 = -9*b. Factor -4*d**b + 4*d - d + 5*d**2 - 1 + 3*d**3 - 2*d - 4*d.
-(d - 1)**2*(d + 1)*(4*d + 1)
Let v(q) be the first derivative of -8*q**3 - 1/10*q**5 - 22 + 0*q - 16*q**2 - 3/2*q**4. Let v(c) = 0. What is c?
-4, 0
Let j(h) = 3*h**5 - 4*h**4 - 2*h**3 + 6*h**2 - h + 2. Let p(k) = -21*k**5 + 27*k**4 + 15*k**3 - 42*k**2 + 6*k - 15. Let y(t) = 15*j(t) + 2*p(t). Factor y(a).
3*a*(a - 1)**3*(a + 1)
Let l(q) be the second derivative of q**6/6 - q**5/2 + 5*q**4/12 + 950*q. Find b such that l(b) = 0.
0, 1
Let u(z) = 13*z**2 + 4. Let k be u(-3). Determine h so that -117*h**2 + 7*h**4 + 8*h + k*h**2 + h**4 - 20*h**3 = 0.
-1/2, 0, 1, 2
Factor 5/2*y - 1/2*y**2 + 3.
-(y - 6)*(y + 1)/2
Let x(l) be the third derivative of 1/70*l**5 - 2/21*l**3 + 0 - 5/84*l**4 + 0*l + 3*l**2. Factor x(j).
2*(j - 2)*(3*j + 1)/7
Suppose 0 = -46*q + 113 - 113. Find k, given that -8/7*k**4 + 10/7*k**3 - 4/7*k**2 + 0 + 2/7*k**5 + q*k = 0.
0, 1, 2
Let l = 53/11 - 95/22. Factor -1/6*w**2 + 2/3 + l*w.
-(w - 4)*(w + 1)/6
Suppose 0*u - 60 = 3*u. Let r be ((-30)/u)/(1/2). Factor 2*d**2 - 3*d**3 + d + d**4 + d**2 + 2*d**r - 4*d**2.
d*(d - 1)**2*(d + 1)
Suppose -5*r = -3018 - 6112. Factor -r*m + 1826*m + 3*m**2.
3*m**2
Let u be 4/(5/((-10)/(-4))). Let q(w) = 2 + 3 - 4*w + 5*w + 3*w**2 - u*w. Let g(h) = -3*h**2 - 6. Let s(x) = -5*g(x) - 6*q(x). Let s(t) = 0. What is t?
0, 2
Let d = -37 + 39. Factor -4*a**4 - a**3 + 4*a**d + a**3.
-4*a**2*(a - 1)*(a + 1)
Let x(o) be the first derivative of 7 + o + 1/2*o**2. Let j(h) = -2*h**2 + 19*h - 29. Let b(m) = -2*j(m) + 6*x(m). Factor b(s).
4*(s - 4)**2
Let p(r) be the first derivative of 3*r**4/20 + r**3/5 - 3*r**2/5 - 39. Factor p(j).
3*j*(j - 1)*(j + 2)/5
Suppose 0 = -4*v - 2*u + 9 + 15, -5*v = 4*u - 24. Suppose -x - n + 2*n + 2 = 0, v = 4*x + 3*n. Factor 3*a**3 - a**2 + 3*a**x - a**4 - 3*a**4 + 5*a**4.
a**2*(a + 1)*(a + 2)
Let q(x) be the second derivative of -x**5/5 - 4*x**4/3 - 8*x**3/3 + 4*x + 8. Find a, given that q(a) = 0.
-2, 0
Let v(d) = -8*d**2 - 10*d - 2. Suppose -3*f = -4*f. Suppose -j = -f*j - 2. Let u(r) = -7*r**2 - 9*r - 2. Let o(q) = j*v(q) - 3*u(q). Let o(t) = 0. Calculate t.
-1, -2/5
Let j(s) be the first derivative of -10 + 0*s + 0*s**2 - 2/3*s**3. Find a such that j(a) = 0.
0
Let d(c) = 4*c**3 - 7*c**2 + 33*c - 39. Let p(s) = 7*s**3 - 15*s**2 + 66*s - 77. Let r(m) = 10*d(m) - 6*p(m). Suppose r(f) = 0. What is f?
3, 4
Factor -33075/2 - 315*a - 3/2*a**2.
-3*(a + 105)**2/2
Suppose -3*x + 12 = -33. What is g in 5*g**4 - x + 0*g + g + 10*g**2 + 20*g**3 - 21*g = 0?
-3, -1, 1
Factor 9*i**2 - 4 - 5*i**2 + 7*i**3 - 3*i**3 - 36*i - 32.
4*(i - 3)*(i + 1)*(i + 3)
Factor 27*s - 5*s**2 - s**2 - 47*s + 4*s**2.
-2*s*(s + 10)
Let x(k) be the second derivative of k**5/15 - k**4/3 + 2*k**3/3 + 5*k**2/2 - 7*k. Let j(f) be the first derivative of x(f). Find r such that j(r) = 0.
1
Suppose -3*c - 3 = 2*h - 21, -4*c = 3*h - 25. Let p(f) be the second derivative of 7*f - 7/15*f**3 - 2/5*f**2 + 1/15*f**c + 7/50*f**5 + 0. Factor p(s).
2*(s - 1)*(s + 1)*(7*s + 2)/5
Let s(i) be the third derivative of -4*i**5/75 - 19*i**4/10 - 106*i**3/15 + i**2 - 20. Factor s(n).
-4*(n + 1)*(4*n + 53)/5
Let y be (-694)/14 - (2 + 72/(-28)). Let x be 1 + -2 - (-2 + (-7)/y). Factor -2/7*c**2 + 0*c + 2/7*c**5 + 0 + 6/7*c**3 - x*c**4.
2*c**2*(c - 1)**3/7
Let q be -3 + (-16)/5*35/(-14). Suppose 0 = -5*f + q, -4*c - f + 1 = -6*c. Factor 0*g**2 + c*g**4 + 2/7*g**5 + 0*g + 0 - 2/7*g**3.
2*g**3*(g - 1)*(g + 1)/7
Factor -105/2*t - 207/4 - 3/4*t**2.
-3*(t + 1)*(t + 69)/4
Suppose 5*h + 4*f - 17 = 0, 0 = -2*h - 0*h - 5*f. Suppose -4*v + 0*r = 4*r - 24, 3*v = h*r + 2. Solve 2*z - 2*z**2 - 2*z**2 + 4*z**v - z - z**3 + 0*z = 0 for z.
-1, 0, 1/4, 1
Let y = -57/98 + 102/49. Let j(t) = 2*t - 4. Let i be j(3). Factor -27/8*x**i + y*x**3 + 9/4*x - 3/8.
3*(x - 1)**2*(4*x - 1)/8
Let b be 10*6/140 - (-1)/14. Find n, given that 0 + 1/2*n**4 + b*n**3 - 1/2*n**2 - 1/2*n = 0.
-1, 0, 1
Let c(s) = s**2 - 3*s - 3. Let x be (-1)/((39/(-18))/(-13)). Let n(t) = -4*t - 9*t + 8*t - 34 - 27*t + 12*t**2. Let f(r) = x*n(r) + 68*c(r). Factor f(b).
-4*b*(b + 3)
Let x = -6 - -12. Suppose 0 = 28*u - 18*u. Factor x*v**3 - 6*v + 2*v**4 - 2*v**4 + u + 2*v**2 + 2*v**4 - 4.
2*(v - 1)*(v + 1)**2*(v + 2)
Determine y so that -20/7*y**3 + 6/7*y**5 - 4/7 - 2/7*y - 4/7*y**4 + 24/7*y**2 = 0.
-2, -1/3, 1
Suppose -4 = 2*r + 2*r. Let o be (r*(-24)/63)/((-9)/(-21)). Factor -8/9 + 2/9*f**3 + 2/9*f**2 - o*f.
2*(f - 2)*(f + 1)*(f + 2)/9
Let w(b) be the third derivative of 0*b - 13 + 1/70*b**5 - 6/7*b**3 + b**2 + 5/28*b**4. Find h, given that w(h) = 0.
-6, 1
Suppose 169/2*n - 219/2*n**2 + 83/2*n**3 - 19 + 5/2*n**4 = 0. What is n?
-19, 2/5, 1
Let q(n) be the second derivative of 125/2*n**3 + 1/4*n**5 - 25/4*n**4 - 625/2*n**2 + 0 - 11*n. What is a in q(a) = 0?
5
Let o be 120/48*((-5548)/(-1330) - (1 + 3)). Factor 1/7*b**3 - 5/7 - o*b**2 - 9/7*b.
(b - 5)*(b + 1)**2/7
Determine t, given that -8*t**3 + 4 - 40/9*t**4 + 4/9*t**2 + 74/9*t - 2/9*t**5 = 0.
-18, -1, 1
Factor 3*j**4 - 2 + 40*j**2 - 40*j**4 - 10*j + 2*j**4 - 10*j**3 - 3 + 20*j**5.
5*(j - 1)**3*(j + 1)*(4*j + 1)
Let s = -7 + 9. Factor -6*g**3 + 4*g**s + 6*g**2 - 4*g**2 - 2*g**5 + 6*g**4 - 4*g**2.
-2*g**2*(g - 1)**3
Suppose 2*n + 1 = 3*x - 3, 3*n - 2*x = -11. Let k be (-1)/3*(-14 - n). Factor -k*h - 21*h**2 + 6 + 10*h**2 + 8*h**2.
-3*(h - 1)*(h + 2)
Suppose -11 = r - 3*n, -r - n - 8 = -1. Let d = 10 + r. Suppose -y - d*y - y**2 + 3*y - y = 0. Calculate y.
-1, 0
Factor -534 + 3*y**3 + 534.
3*y**3
Let t(q) be the first derivative of 4 + 24*q - 3/4*q**4 + 6*q**3 - 18*q**2. Let t(i) = 0. What is i?
2
Let x be (-75)/30*8/(-10). Solve -f - f + x*f + 4*f**2 - 4*f - f**3 = 0.
0, 2
Let v be 264/15 - (-2)/5. Suppose 0 = -3*j - 2*j + p + 22, -5*j - p + v = 0. Factor -4*z**3 - 15 + 2*z**j + 15.
2*z**3*(z - 2)
Let q(t) be the first derivative of t**4 + 148*t**3/3 + 720*t**2 + 1296*t + 345. Factor q(v).
4*(v + 1)*(v + 18)**2
Let l(z) = -8*z - 9. Let m be l(-6). Let t = -34 + m. Factor -12 + 2*r**3 + 2*r**4 + 2*r**4 + 2*r**t + 12.
2*r**3*(r + 1)**2
Suppose 0 = -7*d + 2 + 12. Find k such that 12/7*k + 0 + 4/7*k**d = 0.
-3, 0
Let h be (2/4*-18)/(-56). Let y = 865/504 - h. What is u in -8/9*u - 20/9*u**2 + 2/3 + 8/9*u**3 + y*u**4 = 0?
-1, 3/7, 1
Let n be (7 - -4 - 10)*(-2 - -4). Factor -5/6*q**n + 1/6*q**4 - 1/2*q**3 + 0 - 1/3*q + 1/6*q**5.
q*(q - 2)*(q + 1)**3/6
Factor 3036/5*r + 1452/5 + 1587/5*r**2.
3*(23*r + 22)**2/5
Let r be ((-6)/(-4))/((-2)/4). Let u be r/((-9)/(-6))*11/(-77). Let 6/7*d**5 + 0*d**2 + 0*d + 0 + u*d**3 - 8/7*d**4 = 0. Calculate d.
0, 1/3, 1
Suppose -4*r + 28 = 5*c + 3, 2*c = 4*r + 10. Factor 0*g**2 + r + 0*g + 2/9*g**3.
2*g**3/9
Let k(s) be the third derivative of s**6/40 - s**5/30 - s**4/8 + s**3/3 - 126*s**2. Factor k(v).
(v -