4). Factor -3*r - 4*r + 5*r**3 - z*r**2 + 0*r + g + 2*r + 5*r**4.
5*(r - 1)**2*(r + 1)*(r + 2)
Let y(o) = -3*o**3 + 2*o**2 - o. Let r(x) = 34*x**3 - 4*x**2 - 74*x. Let p(q) = r(q) + 10*y(q). Factor p(s).
4*s*(s - 3)*(s + 7)
Let i = 118 - 1302/11. Let l = i + 56/33. Find c, given that -l*c - 1/3*c**2 - 4/3 = 0.
-2
Suppose 75*n + 60*n = -7*n + 284. Factor 8/5 + 2/5*y**n - 2*y.
2*(y - 4)*(y - 1)/5
Let u be (18 - 23) + (0 - -9). Let s(k) be the second derivative of 1/78*k**4 + 0 + 2/39*k**3 + u*k + 1/13*k**2. Factor s(x).
2*(x + 1)**2/13
Let d(c) be the first derivative of -2/9*c**3 - 2 - 2/3*c**2 - 2/3*c. Solve d(t) = 0.
-1
Let h(j) be the second derivative of -1/30*j**3 + 0 + 6*j - 1/10*j**2 + 1/30*j**4. Let h(r) = 0. What is r?
-1/2, 1
Let q be 1/(-11)*5*(-1200)/(9 - -15). Factor q - 212/11*x**3 + 34/11*x**4 + 580/11*x**2 - 650/11*x - 2/11*x**5.
-2*(x - 5)**3*(x - 1)**2/11
Let f(i) be the second derivative of 0 + 1/4*i**4 - 47*i - i**3 + 3/2*i**2. Let f(n) = 0. What is n?
1
Let c = -59 - -64. Suppose -9*l = c*l - 28. Suppose -6 - 4*d - 2/3*d**l = 0. What is d?
-3
Suppose -3*r + 2 = -7. Let s(w) = -8*w**3 + 7*w**2 + 8*w - 10. Let k(z) = -19 + 23*z + 22*z**2 - z**3 - 11 - 22*z**3. Let y(m) = r*k(m) - 8*s(m). Factor y(a).
-5*(a - 2)*(a - 1)*(a + 1)
Let g(d) be the second derivative of -d**7/840 - d**6/120 + d**4/6 - 24*d. Let r(p) be the third derivative of g(p). Factor r(s).
-3*s*(s + 2)
Suppose -162*r = -173*r + 22. Let d(p) be the first derivative of 2/5*p**r + 4/5*p + 1/15*p**3 - 2. Solve d(u) = 0 for u.
-2
Let b(s) = s + 3. Let c be b(-2). Factor -j**2 + 5*j - 15 - c + 3*j.
-(j - 4)**2
Suppose -12*l - 2*l**2 + 24*l**3 + 6*l**4 - 254*l**5 - 250*l**5 + 496*l**5 = 0. What is l?
-1, 0, 3/4, 2
Let w be 12/3 - (2 + -1). Factor -3*h**3 + 18*h**2 + 13*h**2 - w*h - 25*h**2.
-3*h*(h - 1)**2
Determine v so that v**4 - 47*v**3 + 16*v**2 - 17*v**2 + 46*v**3 + v**5 = 0.
-1, 0, 1
Let o(w) = -35*w**2 + 1270*w - 76910. Let c(h) = 2*h**2 - 2*h + 2. Let r(s) = -15*c(s) - o(s). Suppose r(v) = 0. Calculate v.
124
Let t(o) be the second derivative of -7*o + 0 - 1/24*o**4 + 1/120*o**6 + 0*o**5 + 1/8*o**2 + 0*o**3. Factor t(j).
(j - 1)**2*(j + 1)**2/4
Let g be (-2)/((-15)/(585/52)). Solve 4*q**2 - 3/2*q**3 - g*q + 0 - q**4 = 0.
-3, 0, 1/2, 1
Let x(w) be the third derivative of 0*w**5 + 1/60*w**6 + 0 + 0*w - 1/12*w**4 - 4*w**2 + 0*w**3. Factor x(o).
2*o*(o - 1)*(o + 1)
Let r(h) = -13*h**4 + 9*h**3 + 132*h**2 - 100*h - 120. Let n(v) = -v**4 - 2*v**3 - v**2. Let w(q) = -2*n(q) - r(q). Factor w(m).
5*(m - 2)**2*(m + 3)*(3*m + 2)
Factor -3*t**3 + 0 - 24/5*t**2 - 3/5*t**4 - 12/5*t.
-3*t*(t + 1)*(t + 2)**2/5
Suppose -d - 4 = 2*t, -5*d = 5*t - 2*t + 20. Factor t + 10/7*a**2 + 4/7*a + 2/7*a**4 + 8/7*a**3.
2*a*(a + 1)**2*(a + 2)/7
Let s(f) = f**3 - 4*f**2 + 3*f + 2. Let p be s(3). Factor -8*b - 25 + 0*b + p*b - b**2 - 4*b.
-(b + 5)**2
Suppose -94 - 11 - 216*f - 119*f - 65*f**2 + 55 = 0. Calculate f.
-5, -2/13
Let p(t) = -t**4 + 2*t**2 - t - 2. Let x(g) = -4*g**4 + 20*g**3 + 12*g**2 - 6*g - 12. Let h(v) = -6*p(v) + x(v). Solve h(m) = 0.
-10, 0
Let k = 17 + -15. Factor -5*b**2 + 25*b**2 - 15*b**k + 10*b.
5*b*(b + 2)
Let y = 73 + -71. Let n be (44/(-462))/(y + (-18)/7). Solve -n*u**2 - 1/3*u + 0 = 0.
-2, 0
Factor -29*a**2 + 145*a**3 + 135*a - 244*a**2 + 5 - 14*a**2 + 2*a**2.
5*(a - 1)**2*(29*a + 1)
Let a = 204 + -204. Let z(f) be the third derivative of 3/8*f**4 - 3/20*f**5 - 1/2*f**3 + a*f + 0 + 5*f**2 + 1/40*f**6. Suppose z(g) = 0. What is g?
1
Let u(j) = -58*j**2 + 64*j**3 + j - 44*j**3 + 9*j + 16. Let i(o) = -20*o**3 + 57*o**2 - 11*o - 16. Let f(z) = 6*i(z) + 5*u(z). Determine g so that f(g) = 0.
-2/5, 1, 2
Suppose 27*t - 22*t**2 - 79*t - 18 - 2*t + 16*t - 2*t**3 = 0. What is t?
-9, -1
Let x(s) be the first derivative of 4/7*s**2 - 44 - 2/105*s**5 + 1/7*s**4 - 26/63*s**3 - 8/21*s. Suppose x(v) = 0. Calculate v.
1, 2
Suppose -14*j = 20*j - 45*j. Let x(r) be the first derivative of 0*r**3 + j*r - 1 + 0*r**2 - 1/6*r**4. Factor x(m).
-2*m**3/3
Let v = 24 - 18. Let -13*p + 4*p + p**3 + 14*p - v*p**2 = 0. Calculate p.
0, 1, 5
Suppose 4*a + 2 = p, -3*a - 8 = -9*p + 5*p. Factor -51*c**p + 17 - 59 - 27*c + 48*c**2.
-3*(c + 2)*(c + 7)
Factor -5*w**2 + w**2 - 246*w - 1272 + 0*w**2 - 3771 + w**2.
-3*(w + 41)**2
Let c(x) be the third derivative of x**6/480 + x**5/30 + x**4/6 - 39*x**2 + 2. Factor c(y).
y*(y + 4)**2/4
Let u be 1 + 5 + 25/((-16800)/4018). Let t(x) be the second derivative of 0*x**2 + 4*x + 1/80*x**5 + 0 + 0*x**3 - u*x**4. Let t(c) = 0. What is c?
0, 1
Let y be (-67 - -72)/((-20)/(-12)). Find j such that -14/9*j - 4/9*j**2 + 2/9*j**y - 8/9 = 0.
-1, 4
Let l(n) be the first derivative of n**8/5880 - n**7/1470 + n**6/1260 + 7*n**3/3 - 11. Let y(i) be the third derivative of l(i). Factor y(c).
2*c**2*(c - 1)**2/7
Let v(l) be the first derivative of 8 + 6*l + 2*l**2 + 2/9*l**3. Factor v(z).
2*(z + 3)**2/3
Let k(a) be the second derivative of a**6/6 + 3*a**5/2 + 65*a**4/12 + 10*a**3 + 10*a**2 - 107*a. What is y in k(y) = 0?
-2, -1
Let l(m) = 2*m**2 + 200*m + 2003. Let d(n) = 3*n**2 + 200*n + 2002. Let f(u) = 3*d(u) - 2*l(u). Factor f(a).
5*(a + 20)**2
Let a(r) be the second derivative of -r**8/60480 + r**7/7560 - r**6/3240 - 5*r**4/4 + 2*r. Let p(k) be the third derivative of a(k). Factor p(q).
-q*(q - 2)*(q - 1)/9
Let y be (1 + 1010/(-30))/((-8)/6). Let f(n) be the first derivative of -36/5*n**2 + 16/5*n - 28/5*n**3 + y*n**4 + 6. Determine j so that f(j) = 0.
-2/5, 2/7
Let u(a) be the third derivative of a**5/300 + 3*a**4/2 + 270*a**3 + a**2 + 33. Let u(k) = 0. Calculate k.
-90
Let j = 362/25 + -71/5. Let i = 271/75 - j. What is k in -14/3*k - i*k**2 - 2 - 2/3*k**3 = 0?
-3, -1
Suppose 0 = 4*a - 8, 5*y + 17 = -5*a + 152. Factor 25*d + y*d**4 + 5 + 49*d**3 - 4*d**5 + 9*d**5 + 7*d**2 + d**3 + 43*d**2.
5*(d + 1)**5
Let i(r) = -2*r**3 - 18*r**2 - r + 15. Let j(h) = -5*h**3 - 37*h**2 - 2*h + 30. Let o(v) = -14*i(v) + 6*j(v). Let o(s) = 0. What is s?
-1, 1, 15
Let j = -10810/13 - -832. Solve -j*m + 6/13*m**3 - 4/13 + 2/13*m**4 + 2/13*m**2 = 0.
-2, -1, 1
Let y = 25 + -31. Let d be (-5)/2*y/5. Solve -1 + 17*f**d + 12*f**2 - 21*f**3 - 15 = 0.
-1, 2
Let j(l) be the third derivative of -l**7/630 + 13*l**5/180 + l**4/6 - 196*l**2. Factor j(r).
-r*(r - 4)*(r + 1)*(r + 3)/3
Let w(x) be the third derivative of -x**8/560 - x**7/280 + x**6/120 + x**5/40 - 5*x**3/6 + 6*x**2. Let j(c) be the first derivative of w(c). Factor j(h).
-3*h*(h - 1)*(h + 1)**2
Determine v so that 1/6*v**2 + 7/6*v + 5/3 = 0.
-5, -2
Suppose -2*g - 25 = 5*r, -5*g + 3*r + 8 = -7. Suppose -4*i - 2*i + 12 = g. Determine k so that 1/3*k**4 + 0 - k**3 - 1/3*k + k**i = 0.
0, 1
Let t(p) be the third derivative of p**5/10 + 2*p**4/3 - p**3 - p**2 - 34. What is h in t(h) = 0?
-3, 1/3
Let y(i) be the first derivative of -2/5*i**5 + 2/3*i**3 - 6 + 2/5*i**2 + 0*i - 1/5*i**4. Find z such that y(z) = 0.
-1, -2/5, 0, 1
Let b be 83/4 - (-1818)/(-101). Find f, given that -b*f**4 + 7/2*f**2 + 3/4*f**5 - 5/4*f - 3/4 + 1/2*f**3 = 0.
-1, -1/3, 1, 3
Let a(b) = 60*b**2 - 40*b + 12. Let w(s) = -4*s**2. Let y(h) = a(h) + 8*w(h). Find f, given that y(f) = 0.
3/7, 1
Let f(d) = d**3 - 2*d**2 - 14*d - 3. Let j be f(5). Let l(t) be the first derivative of t**4 - 4/3*t**3 + 4/5*t**5 - 2/3*t**6 - 6 + 0*t**j + 0*t. Factor l(x).
-4*x**2*(x - 1)**2*(x + 1)
Let t(q) = -q**2 - 46*q + 15. Let d(r) = -2*r**2. Let l(g) = -2*d(g) + t(g). Factor l(j).
(j - 15)*(3*j - 1)
Let x(a) be the third derivative of -a**5/240 - a**4/96 + a**3/12 + 4*a**2 + 50. Factor x(n).
-(n - 1)*(n + 2)/4
Let h be (-15)/6*(72/15 - 6). Find u, given that 5/3*u**h + 1/6*u**5 + 1/6 + 5/6*u + 5/3*u**2 + 5/6*u**4 = 0.
-1
Let u = 14881/20 - 743. Let c(b) be the first derivative of -21/10*b**2 + u*b**4 - 6/5*b - 1 + 2/5*b**3. Factor c(a).
3*(a - 1)*(a + 1)*(7*a + 2)/5
Determine m, given that 72/11 + 74/11*m**2 + 8/11*m**3 + 136/11*m - 2/11*m**4 = 0.
-2, -1, 9
Solve 128/7*o**2 + 30/7*o**5 - 32/7*o + 0 - 32/7*o**4 - 16*o**3 = 0 for o.
-2, 0, 2/5, 2/3, 2
Let j be (-6 - -4)/40*-9. Let b(a) be the third derivative of 0 + 0*a - 6*a**2 - j*a**5 + 1/16*a**6 + 2*a**3 + 3/4*a**4. Factor b(d).
3*(d - 2)**2*(5*d + 2)/2
Let w(j) be the third derivative of -j**6/1800 + 7*j**5/150 - 49*j**4/30 + 17*j**3/6 -