*3. Factor n(p).
3*(p - 2)*(p - 1)*(p + 1)
Let g(d) = -d**2 + 3*d - 5. Let b(a) = a**2 + a - 1. Let p(w) = -3*b(w) - g(w). Factor p(c).
-2*(c - 1)*(c + 4)
Let m(a) be the first derivative of -2*a**3 - 3*a**4 - 1/2*a**6 + 0*a - 2*a**5 - 1/2*a**2 - 3. Factor m(d).
-d*(d + 1)**3*(3*d + 1)
Let b(u) be the second derivative of 18*u**2 + 0 - 4*u**3 + 7*u + 1/3*u**4. Let b(m) = 0. What is m?
3
Let r(b) = 5*b**2 + 4*b - 19. Let f(y) = -14*y**2 - 12*y + 56. Let p(v) = -3*f(v) - 8*r(v). Factor p(h).
2*(h - 2)*(h + 4)
Suppose 16 = 51*c - 47*c. Let d(s) be the second derivative of s + 1/24*s**c + 0 + 1/3*s**3 + s**2. Determine j, given that d(j) = 0.
-2
Let g(k) = 13*k**3 + 0*k - k - 12*k**3 + 2*k. Let u(c) = 6*c**4 - 20*c**3 + 16*c**2 + 10*c. Let a(n) = -2*g(n) + u(n). Find x such that a(x) = 0.
-1/3, 0, 2
Let l = -2 - -2. Factor -2*y + l*y**3 - y**3 + y**5 + 2*y.
y**3*(y - 1)*(y + 1)
Suppose 5*y + 5*f = 15, 4*y - 5*f - 3 - 9 = 0. Let d = 2 + 0. Factor 4/3*x**d + 4/3*x + 1/3*x**y + 0.
x*(x + 2)**2/3
Let o(t) be the third derivative of t**9/38880 + t**8/7560 + t**7/7560 - t**6/1620 - t**5/60 - t**2. Let g(y) be the third derivative of o(y). Factor g(z).
2*(z + 1)**2*(7*z - 2)/9
Suppose j = 4*j. Suppose 2 = -j*p + p. Factor -a + 3/2*a**p + 0 - 1/2*a**3.
-a*(a - 2)*(a - 1)/2
Let h(i) be the third derivative of 2*i**7/105 - i**6/30 + 35*i**2. What is p in h(p) = 0?
0, 1
Let k(f) = f**3 + f**2 + f - 1. Let c be k(1). Solve -3*l + 10*l**c - 10*l**2 + l**5 - 2*l**3 + 4*l = 0.
-1, 0, 1
Let f = -19/3 + 233/6. Let n = f - 32. Determine v, given that -2*v**2 - n*v**3 - 1 - 5/2*v = 0.
-2, -1
Suppose -4*q + 10 = -38. Let k be 3/q*(-1 + 2). Factor -1/4*s**2 + k*s - 1/4*s**3 + 0 + 1/4*s**4.
s*(s - 1)**2*(s + 1)/4
Let z(a) = 27*a**3 + 46*a**2 - 10*a - 2. Let h(u) = -27*u**3 - 45*u**2 + 9*u + 3. Let d(v) = -2*h(v) - 3*z(v). Suppose d(k) = 0. Calculate k.
-2, 0, 2/9
Suppose -4*o = 2*j + 43 - 37, 2*o - 3 = -3*j. Factor -1/2*z**2 + z + 0 - z**j + 1/2*z**4.
z*(z - 2)*(z - 1)*(z + 1)/2
Let j be 0/(2 - (-2 - -2)). Suppose -c + 5 = 4*r, 4*c = 2*c - 6. Factor j + 2/3*w**4 - 2/3*w**3 + 0*w**r + 0*w.
2*w**3*(w - 1)/3
Let w be 44/(-12) - (1 + -3). Let z = -4/3 - w. Determine h so that z*h**3 - 1/3*h**4 - 1/3*h + 0 + 1/3*h**2 = 0.
-1, 0, 1
Factor -3/7*z**3 + 0 + 0*z**4 + 3/7*z**5 + 0*z**2 + 0*z.
3*z**3*(z - 1)*(z + 1)/7
Let y(v) = 4*v**4 - 7*v**3 + 5*v - 5. Let f(q) = -6*q**4 + 11*q**3 - 8*q + 8. Let p(x) = -5*f(x) - 8*y(x). Factor p(n).
-n**3*(2*n - 1)
Let m(q) be the third derivative of -1/30*q**5 + 2/15*q**4 - 3*q**2 - 4/15*q**3 + 1/300*q**6 + 0 + 0*q. Factor m(s).
2*(s - 2)**2*(s - 1)/5
Let v(r) be the third derivative of r**6/600 - r**5/100 + 2*r**3/15 - 7*r**2. Factor v(h).
(h - 2)**2*(h + 1)/5
Factor 2/7*b**2 + 0 + 4/7*b.
2*b*(b + 2)/7
Suppose 0 = 3*n - d - 22, -2*n + 4*d = -0*n - 28. Let -7*x**4 - n*x**3 + 2*x**4 + 2*x**4 + 3*x**2 + 12*x**5 - 6*x**3 = 0. Calculate x.
-1, 0, 1/4, 1
Let r(j) = -12*j**2 - 52*j - 8. Let s(y) = 4*y**2 + 17*y + 3. Let c(o) = -3*r(o) - 8*s(o). Solve c(t) = 0 for t.
-5, 0
Suppose 2*n = 3 + 5. Let c(m) = 3*m**3 - 2*m**4 - 4 - 5*m**4 - 5*m**2 - 4*m + 4*m**4 + m**5. Let g(t) = t**2 + t + 1. Let b(v) = n*g(v) + c(v). Factor b(r).
r**2*(r - 1)**3
Find c, given that 4/5*c - 4/5*c**3 + 14/5*c**4 - 14/5*c**2 + 0 = 0.
-1, 0, 2/7, 1
Suppose 0 = -36*o + 20 + 88. Factor 2/3*c**5 + 0 - 4/3*c**2 + 4/3*c**4 + 0*c**o - 2/3*c.
2*c*(c - 1)*(c + 1)**3/3
Let i(h) be the second derivative of -h**4/21 + h**3/42 + 3*h**2/14 - 6*h. Let i(v) = 0. Calculate v.
-3/4, 1
Suppose 6 = t - 0*t. Suppose 3*i = t*i. Find w such that 0 + 2/9*w**2 + i*w = 0.
0
Let m(y) be the second derivative of 0 - 4/39*y**4 + 1/39*y**6 - 4/39*y**3 - 5*y + 7/130*y**5 + 0*y**2. Determine o, given that m(o) = 0.
-2, -2/5, 0, 1
Let y(t) be the third derivative of -t**6/48 - 3*t**5/8 - 5*t**4/6 + 11*t**2. Factor y(q).
-5*q*(q + 1)*(q + 8)/2
Let -2/5*r - 4/5 + 4/5*r**2 + 2/5*r**3 = 0. What is r?
-2, -1, 1
Let x(p) be the first derivative of -p**4/22 - 4*p**3/33 + 1. Factor x(q).
-2*q**2*(q + 2)/11
Let a be (-175)/75 + 1*3. Let l = 7 - 20/3. Let -a*d + 1/3 + l*d**2 = 0. Calculate d.
1
Let s(x) = -2*x**5 + x**4 - x**3 + 5*x**2 - 3*x - 3. Let j(r) = 12*r**5 - 5*r**4 + 5*r**3 - 29*r**2 + 17*r + 17. Let u(g) = -6*j(g) - 34*s(g). Factor u(c).
-4*c**2*(c - 1)*(c + 1)**2
Let m = -19 + 33. Suppose 3*p = -3*r + 15, r + 8*p - 4*p - m = 0. Factor 0*f**4 - 2*f + 3*f**3 - f**3 - 2*f**4 + r*f**2.
-2*f*(f - 1)**2*(f + 1)
Let a(v) = -4*v**2 + 4*v - 7. Let h(n) = -n**2 - 1. Suppose 3 - 8 = -5*p. Let r(g) = p*a(g) - 3*h(g). Factor r(d).
-(d - 2)**2
Let f = -2/21 - -3/7. Factor 2/3*w**2 - 2/3 + f*w - 1/3*w**3.
-(w - 2)*(w - 1)*(w + 1)/3
Let p(n) = n + 12. Let v be p(-9). Suppose 0 = -t + 3*t - 32. What is g in -1 - 8*g**2 + 3*g - 16*g**2 + t*g**v + 6*g = 0?
1/4, 1
Let u(d) be the first derivative of 3 - 2/3*d**2 + 1/9*d**3 + 4/3*d. Let u(p) = 0. Calculate p.
2
Let r(d) be the second derivative of -2*d**7/7 + 8*d**6/15 + 4*d**5/5 - 9*d. Factor r(i).
-4*i**3*(i - 2)*(3*i + 2)
Solve -6*x**3 + x**5 - 6*x + 9*x + 2*x**5 = 0 for x.
-1, 0, 1
Let h(l) = 3*l - 18. Let k be (-11)/33*(-18 - 0). Let n be h(k). Determine x so that -3/4*x**2 + 0 + 3/4*x**3 + n*x = 0.
0, 1
Let q(f) be the first derivative of 0*f**2 + 0*f + 1/16*f**4 + 3 + 1/20*f**5 - 1/6*f**3. Solve q(y) = 0.
-2, 0, 1
Let n(v) = 14*v**4 + 38*v**3 + 27*v**2 + 5*v - 1. Let j(g) = -42*g**4 - 114*g**3 - 80*g**2 - 16*g + 2. Let s(k) = -3*j(k) - 10*n(k). Factor s(x).
-2*(x + 1)**3*(7*x - 2)
Suppose -2*a = -4*a + 200. Suppose -a = -m - 3*m. Factor 98*x**4 + 47*x**2 + 48*x**2 + m*x**2 + 252*x**3 + 16*x.
2*x*(x + 2)*(7*x + 2)**2
Let g be (-9 + -4 + 11)/(1/(-2)). Factor 0*s**3 - 3/5*s**5 + 0*s + 3/5*s**g + 0 + 0*s**2.
-3*s**4*(s - 1)/5
Suppose -18 = -28*l + 66. Find w such that 3/5*w**l + 0 - 6/5*w**2 + 3/5*w = 0.
0, 1
Let p be ((-18)/(-15))/(-3)*-15. Let b be 0/(p + (1 - 3)). Suppose -2/3*g + 5/3*g**2 + b = 0. Calculate g.
0, 2/5
Let b(g) be the second derivative of 1/3*g**2 + 0 - 1/18*g**4 - 3*g + 0*g**3. Determine j so that b(j) = 0.
-1, 1
Factor 2/9*b**5 + 44/9*b**2 + 2/3 + 14/9*b**4 + 26/9*b + 4*b**3.
2*(b + 1)**4*(b + 3)/9
Solve 29/9*r**2 - 3*r**4 - 4*r**5 + 37/9*r**3 - 1/9*r - 2/9 = 0.
-1, -2/3, -1/3, 1/4, 1
Let l = 30/11 - 21/44. Find m, given that -1/2*m - l*m**2 + 0 = 0.
-2/9, 0
Let x(j) be the first derivative of 0*j + 4/35*j**5 - 5/14*j**4 + 8/21*j**3 - 1/7*j**2 + 1. Factor x(f).
2*f*(f - 1)**2*(2*f - 1)/7
Suppose -14*g = -16*g. Let f(u) be the second derivative of 1/30*u**4 + 2/5*u**2 - 1/5*u**3 + g - 2*u. Solve f(c) = 0.
1, 2
Let b = 25 + -9. Let c = 16 - b. Factor -4/7*w - 2/7*w**2 + c.
-2*w*(w + 2)/7
Factor 2/3*t**2 + 0 + 10/3*t.
2*t*(t + 5)/3
Let c(n) be the third derivative of -7*n**5/150 - n**4/12 + 2*n**3/15 - n**2. Let c(v) = 0. Calculate v.
-1, 2/7
Let y(g) be the first derivative of -g**6/6 + 2*g**5/5 + 2. Let y(o) = 0. What is o?
0, 2
Let v(p) be the third derivative of p**8/60480 + p**7/15120 - p**6/1080 - p**5/30 + 4*p**2. Let y(t) be the third derivative of v(t). Factor y(j).
(j - 1)*(j + 2)/3
Let f be 1 - (-1 + (-224)/49 + 6). Let n(c) = c**2 + 6*c + 7. Let d be n(-5). Suppose -6/7*z - 2*z**3 - f + 24/7*z**d = 0. Calculate z.
-2/7, 1
Let k be (-3)/(-7) - (5 - (-955)/(-140)). Solve k*j + 0 - 3*j**2 = 0.
0, 3/4
Let d = -204253 + 2244777/11. Let g = -182 - d. Determine k, given that 2/11*k - g + 2/11*k**2 = 0.
-2, 1
Suppose 2*p + j + 6 = 14, 5*j - 22 = -4*p. Factor -8*f + p*f**3 - 8*f**4 + 4*f**4 + 5*f**3 + 4.
-4*(f - 1)**3*(f + 1)
Let p(f) be the second derivative of -81*f**7/70 - 63*f**6/25 + 51*f**5/25 - 2*f**4/5 + 21*f. Factor p(v).
-3*v**2*(v + 2)*(9*v - 2)**2/5
Let n be 2/108 - (1 + -1). Let p(h) be the second derivative of -1/135*h**6 + 1/45*h**5 + 0 + 0*h**3 - n*h**4 - 2*h + 0*h**2. Determine b, given that p(b) = 0.
0, 1
Let s = -272 - -274. Find q such that -10/11*q - 4/11*q**s - 4/11 = 0.
-2, -1/2
Suppose 12 = -3*f, 0*w - 21 = -w + 5*f. Determine a, given that 0 + 3 - w - 3*a - a + 2*a**2 = 0.
1
Let l = -10/301 + 1234/903. Factor -l*w**2 + 0 - 4/3*w.
-4*w*(w + 1)/3
Suppose -3*n - 2 = t + 9, -3*t + 4*n = -6. Let y be t*(-3)/(-14) - -1. Factor y - 2/7*i - 2/7*i**2.
-2*(i - 1)*(i + 2)/7
Suppose -4 - 16 = -p + 5*u, -p - 5*u = 20. Let d be p - 1 - 