a. Factor c*l - l**2 - 2*l + 5 - 4.
-(l - 1)*(l + 1)
Suppose -8 = -4*z - 4*c, -5*c = -c. Let l(f) be the first derivative of 8 - 7*f**3 + 0*f + 9/2*f**z. Determine t, given that l(t) = 0.
0, 3/7
Suppose -2*q = 4*p + 20, -5*q = -2*q - 2*p - 2. Let w be (-28)/(-21) - (1 + 2/q). Factor -2/3*r**4 - 2/3 + 4/3*r**2 + 2/3*r**5 + 2/3*r - w*r**3.
2*(r - 1)**3*(r + 1)**2/3
Suppose 32*p - 23 + 2*p**2 + 3 + 50 = 0. Calculate p.
-15, -1
Let g = -2/23663 - -331320/449597. Factor 2/19*d**2 - 16/19 + g*d.
2*(d - 1)*(d + 8)/19
Suppose 0 = k - 2 + 1. Let t(b) = 77*b**2 - 34*b - 1. Let c = -106 - -111. Let d(p) = -p**2 - p - 1. Let w(r) = c*d(r) + k*t(r). Suppose w(i) = 0. Calculate i.
-1/8, 2/3
Let g(a) be the third derivative of -1/52*a**4 - 1/390*a**5 + 0 + 0*a - 2/39*a**3 + a**2. Let g(o) = 0. Calculate o.
-2, -1
Let g be 1*4 - (-10 - -5). Suppose -3*q**5 + q**4 - 102*q + 90*q + g*q**3 + 5*q**4 - 12*q**2 = 0. What is q?
-1, 0, 2
Factor 5*q**3 + 82 - 278*q**2 - 85*q + 18 + 257*q**2 + q**4.
(q - 4)*(q - 1)*(q + 5)**2
Let r(q) be the third derivative of 2*q**7/105 - 2*q**6/15 - q**5/5 + 7*q**4/3 - 16*q**3/3 - 13*q**2. Suppose r(b) = 0. What is b?
-2, 1, 4
Let x(h) be the first derivative of 6 + 0*h**2 + 1/2*h**4 + 0*h + 4/3*h**3 - 4/5*h**5 - 1/3*h**6. Find l, given that x(l) = 0.
-2, -1, 0, 1
Let a(r) be the third derivative of -3*r**8/560 - 13*r**7/350 - r**6/15 + 2*r**5/25 + 2*r**4/5 + 8*r**3/15 + 6*r**2 - 10. Determine g so that a(g) = 0.
-2, -2/3, 1
Factor -t**4 + 16400*t + 410*t**3 - 1037 - 4*t**4 - 6963 - 8805*t**2.
-5*(t - 40)**2*(t - 1)**2
Let b be 1/1 + 13/((-26)/16). Let r(a) = 5*a**3 - 35*a**2 + 68*a - 45. Let i(k) = -5*k**3 + 35*k**2 - 69*k + 45. Let f(n) = b*i(n) - 6*r(n). Factor f(d).
5*(d - 3)**2*(d - 1)
Let n(m) be the third derivative of 0 + 21*m**2 - 1/525*m**7 + 1/75*m**5 + 0*m - 1/15*m**3 + 0*m**4 + 0*m**6. Suppose n(o) = 0. What is o?
-1, 1
Let s(q) be the third derivative of q**8/1176 + 4*q**7/245 + 17*q**6/140 + 44*q**5/105 + 4*q**4/7 - 28*q**2. Let s(m) = 0. Calculate m.
-4, -3, -1, 0
Let z be 681/171 - (-1770)/(-5605). Find t such that 2*t - 23/3*t**2 + 28/3*t**3 + 0 - z*t**4 = 0.
0, 6/11, 1
Let m(a) be the third derivative of -a**7/840 + a**6/360 + 7*a**3/3 - 2*a**2 - 16. Let k(g) be the first derivative of m(g). Determine i so that k(i) = 0.
0, 1
Let f be 35/35*1/(0 + -1). Let z be (14/(-126))/(f/4). Factor -2/3*g - z - 2/9*g**2.
-2*(g + 1)*(g + 2)/9
Let x(r) be the second derivative of r**4/3 - 22*r**3 - 120*r. Factor x(n).
4*n*(n - 33)
Let v(o) be the third derivative of -o**8/2800 + 3*o**7/1400 - 2*o**3 - 11*o**2. Let z(d) be the first derivative of v(d). Factor z(r).
-3*r**3*(r - 3)/5
Let j(c) be the second derivative of c**4/54 - 194*c**3/27 + 9409*c**2/9 + 88*c + 1. Determine x, given that j(x) = 0.
97
Let d(g) be the third derivative of -g**7/1260 + g**6/144 - g**5/40 + 7*g**4/144 - g**3/18 - 19*g**2. Solve d(j) = 0.
1, 2
Suppose 0 = -3*a + 6, -8*b + 94 = -3*b - 3*a. Let z be (-15)/b*(-6 - -2). Factor 2/5*p**z + 2/5*p**2 - 2*p + 6/5.
2*(p - 1)**2*(p + 3)/5
Let f(b) be the first derivative of 3*b**5 - 10*b**4 - 12 - 26*b**3 - 31*b + 6*b - 4*b**5 - 40*b**2 - 4*b**3. Factor f(s).
-5*(s + 1)**3*(s + 5)
Let c be (-1)/(-4) - 270/(-72). Suppose -v = -4, c*v - 11 = 5*b - 5. Suppose 2/3*k**4 - 2/3*k + 0 - 2*k**3 + b*k**2 = 0. Calculate k.
0, 1
Let u = -51 - -53. What is i in 5*i**4 - i**4 - 2*i**4 - 2*i**2 + 0*i**3 + 2*i**3 - u*i = 0?
-1, 0, 1
Let m = 5682/35581 - 16/2737. Let -6/13*j + m*j**2 + 4/13 = 0. What is j?
1, 2
Let l(o) be the third derivative of -o**5/540 - 7*o**4/216 - o**3/9 - 139*o**2 + 2*o. Find m, given that l(m) = 0.
-6, -1
Let q(y) be the second derivative of 5*y**4/12 + 25*y**3/3 + 40*y**2 - 68*y + 1. Suppose q(x) = 0. What is x?
-8, -2
Let y(k) be the second derivative of k**7/168 + k**6/40 + 3*k**5/80 + k**4/48 + 656*k. Factor y(c).
c**2*(c + 1)**3/4
Let w = 21 + -18. Suppose -2*p + 19 = w*c, 3*p + 0 = 4*c - 14. Suppose -1/3*y**3 - 8/3*y + 4/3 + 5/3*y**p = 0. Calculate y.
1, 2
Let m = 2538 + -2533. Determine d so that 43/3*d**4 - 3*d**m + 15*d**2 - 4/3*d - 71/3*d**3 - 4/3 = 0.
-2/9, 1, 2
Suppose 3*g - 58 = 5. Factor 13 - 92*p + 7*p**2 + g*p**2 + 11.
4*(p - 3)*(7*p - 2)
Let r(y) be the first derivative of 9 + 0*y - 2/63*y**3 - 4/21*y**2. Determine f so that r(f) = 0.
-4, 0
Let m(u) be the first derivative of 0*u + 0*u**4 + 1/4*u**3 + 1/4*u**2 - 6 - 1/20*u**5. Factor m(v).
-v*(v - 2)*(v + 1)**2/4
Let g(n) = n**2 - 11*n + 8. Let y(p) be the second derivative of p**4 - 24*p**3 + 105*p**2/2 - 13*p. Let t(d) = -27*g(d) + 2*y(d). Factor t(c).
-3*(c - 2)*(c - 1)
Let s(y) be the second derivative of 1/9*y**3 + 1/36*y**4 - 1/2*y**2 + 0 - 49*y. Factor s(r).
(r - 1)*(r + 3)/3
Let x(z) be the first derivative of -3 - 15/8*z**2 - 5*z + 5/12*z**3. Let x(o) = 0. Calculate o.
-1, 4
Factor -73/4*p**2 + 3/2 + 21/2*p**3 - 25/4*p.
(p - 2)*(6*p - 1)*(7*p + 3)/4
Let y(s) be the second derivative of 2*s**6/15 - s**5 + 8*s**4/3 - 8*s**3/3 + 24*s - 4. Factor y(g).
4*g*(g - 2)**2*(g - 1)
Let t(d) = 5*d**2 - 122*d + 129. Let k(v) = -45*v**2 + 1100*v - 1160. Let o(l) = 4*k(l) + 35*t(l). Suppose o(p) = 0. Calculate p.
1, 25
Suppose 2/5*s**3 + 24/5*s**2 + 0 + 8*s = 0. Calculate s.
-10, -2, 0
Let z(y) be the third derivative of -y**6/300 - 4*y**5/75 - 13*y**4/60 - 2*y**3/5 - 131*y**2 - 2. Solve z(r) = 0.
-6, -1
Let n(h) = -h**3 + h**2 - 1. Let v(c) = 15*c**4 + 8*c**3 + 9 + 2*c - 7*c - 6 - 18*c**2. Let g(l) = 3*n(l) + v(l). Factor g(z).
5*z*(z - 1)*(z + 1)*(3*z + 1)
Let f = -13 - -18. Let y = f - 3. Factor -7*w**3 + 2*w**y + w**3 + w**5 - 33*w**4 + 39*w**4 - 3*w**5.
-2*w**2*(w - 1)**3
Let z(w) = 2*w**4 - 16*w**3 + 2*w**2 + 6*w - 4. Let v(h) = 2*h**3. Let a(t) = 10*v(t) + 2*z(t). Factor a(q).
4*(q - 2)*(q - 1)**2*(q + 1)
Let -8*p + 191/3*p**2 - 16/3 + 34*p**3 + 4*p**5 - 85/3*p**4 = 0. Calculate p.
-1, -1/4, 1/3, 4
Let -80/7*i - 2*i**5 + 24/7 + 18/7*i**4 - 6*i**2 + 94/7*i**3 = 0. Calculate i.
-2, -1, 2/7, 1, 3
Let w(b) be the second derivative of -1/2*b**3 - 9/8*b**2 + 1/8*b**4 + 1/40*b**6 + 3/20*b**5 + 0 + 2*b. Factor w(z).
3*(z - 1)*(z + 1)**2*(z + 3)/4
Let h(m) = m**2 + m. Let o(v) = v**3 - 2*v - 5. Let s(p) = -h(p) - o(p). Let x(t) be the first derivative of s(t). Factor x(j).
-(j + 1)*(3*j - 1)
Suppose -y + 1 = z - 7, -4*y = -2*z - 32. Let g(j) be the first derivative of 2/3*j**3 + 2 - y*j + 0*j**2. Determine l, given that g(l) = 0.
-2, 2
Let k(l) be the first derivative of 5*l**8/672 - l**7/42 + l**6/48 - 8*l**2 - 9. Let u(b) be the second derivative of k(b). Find g, given that u(g) = 0.
0, 1
Let r(o) be the third derivative of o**5/360 - o**4/16 + 2*o**3/9 + o**2 + 2. Solve r(i) = 0.
1, 8
Let d(q) = 5*q**2 + 2*q + 1. Let p be d(-1). Factor 144*k + 7*k**p - 144*k + 4*k**5 + 2*k**3 - k**2.
k**2*(k + 1)**2*(4*k - 1)
Let v = -5231/60 + 349/4. Let u(q) be the second derivative of -v*q**6 - 5/6*q**4 + 0*q**2 + 0 - 2/3*q**3 + 5*q - 2/5*q**5. Solve u(m) = 0 for m.
-2, -1, 0
Let y(i) be the second derivative of 2/9*i**3 - 2/9*i**4 + 18*i + 0 + 1/20*i**5 + 0*i**2. Find a, given that y(a) = 0.
0, 2/3, 2
Let i(w) be the first derivative of -3*w**4/32 - 111*w**3/8 - 12321*w**2/16 - 151959*w/8 + 141. Factor i(y).
-3*(y + 37)**3/8
Let s be (4/(-4))/(-2) - (-2856)/(-18). Let i = -158 - s. Determine q, given that -1/2*q**2 + 1/6*q**3 - i + 1/2*q = 0.
1
Suppose -57*b + 8 = 8. Factor b - 1/3*c**4 - 1/3*c - c**2 - c**3.
-c*(c + 1)**3/3
Let g(n) be the second derivative of -n**6/120 - 23*n**5/80 + n**4/16 + 71*n**3/24 + 23*n**2/4 - 2*n + 23. Solve g(b) = 0 for b.
-23, -1, 2
Let t(x) be the second derivative of -x**7/1890 + 13*x**4/12 + 16*x. Let v(i) be the third derivative of t(i). Find g, given that v(g) = 0.
0
Let r(a) be the third derivative of 0*a**4 + 1/330*a**5 + 0*a**3 + 1/660*a**6 + 0*a + 0 - 12*a**2. Factor r(k).
2*k**2*(k + 1)/11
Let t(n) = -35*n**4 - 50*n**3 - 15*n**2 - 30. Let k(c) = 3*c**3 - 32 + 33 + c**4 - 2*c**3 + 0*c**4. Let j(g) = 30*k(g) + t(g). Solve j(d) = 0.
-3, -1, 0
Let b be (12/10)/(4/10). Suppose 7*g + 12*g**2 - b*g - 4 - 4*g**3 - 4 - 4*g**4 = 0. Calculate g.
-2, -1, 1
Let o(h) = -h**2. Let a(x) = 35*x**2 + 65*x - 25. Let l(b) = -a(b) - 5*o(b). Let f(i) = -5*i**2 - 11*i + 4. Let w(c) = -35*f(c) + 6*l(c). Solve w(t) = 0.
-2, 1
Factor