, 1
Let w(t) be the first derivative of t**6/2 - 6*t**5 + 117*t**4/4 - 74*t**3 + 102*t**2 - 72*t + 55. Factor w(m).
3*(m - 3)*(m - 2)**3*(m - 1)
Let y = 467/3 - 153. Let q(n) be the first derivative of -y*n - 2/3*n**4 + 2 + 8/15*n**5 - 14/3*n**2 + 2/9*n**6 - 32/9*n**3. Find v, given that q(v) = 0.
-1, 2
Let t be 2306/22 + (-3)/(-66)*4. Let c be 203/t + (-6)/10 - 1. Factor -c + 1/3*q**2 + 1/6*q - 1/6*q**3.
-(q - 2)*(q - 1)*(q + 1)/6
Suppose q = -q - 6. Let g be 1 - -2 - (q + 4). Suppose 3*d + 4*d**3 + 3*d**2 + d**4 - d + 2*d**g = 0. What is d?
-2, -1, 0
Let r(w) be the first derivative of -2*w**5/5 - 9*w**4/8 - w**3/3 + 315. Determine q, given that r(q) = 0.
-2, -1/4, 0
Let p(k) = -90*k**3 - 340*k**2 - 285*k + 75. Let t(v) = -35 + 57*v - 34*v - 3 + 45*v**3 + 170*v**2 + 119*v. Let n(s) = -2*p(s) - 5*t(s). Factor n(f).
-5*(f + 2)**2*(9*f - 2)
Let i(g) be the third derivative of g**6/1080 - 7*g**5/540 + g**4/36 + 155*g**2. Factor i(l).
l*(l - 6)*(l - 1)/9
Factor 612*c**2 - 937*c**3 - c**5 + 5000 - 7900*c + 4591*c**2 - 845*c**2 + 0*c**5 + 69*c**4 - 13*c**4.
-(c - 25)**2*(c - 2)**3
Factor -2/3*d**2 - 12*d + 0.
-2*d*(d + 18)/3
Suppose -7*f = -3*f - 80. Determine n so that -692 + 5*n + 692 + 30*n**3 + 5*n**5 - f*n**2 - 20*n**4 = 0.
0, 1
Let q(k) be the third derivative of -1/27*k**5 + 0*k**3 + 1/18*k**4 + 2/945*k**7 + 0 + 1/270*k**6 + 10*k**2 + 0*k. Factor q(w).
4*w*(w - 1)**2*(w + 3)/9
Let u = -3203 - -22423/7. Factor 1/7*o + 0 - u*o**2 + 1/7*o**3.
o*(o - 1)**2/7
Let d be 1/(0 + 1/6). Let l(n) be the first derivative of -1 - 4/9*n**3 + 1/3*n**4 + 2/5*n**5 - n**2 - 2/3*n + 1/9*n**d. Find u such that l(u) = 0.
-1, 1
Let r = 122 + -122. Let k(i) be the second derivative of -11*i + 0*i**5 + 0 + r*i**4 + 0*i**2 + 1/60*i**6 + 0*i**3. Factor k(m).
m**4/2
Let o = -4 + 19. Let t be ((-10)/o)/(12/(-9)). Factor 2 + 3*q**3 + t*q**4 + 6*q + 13/2*q**2.
(q + 1)**2*(q + 2)**2/2
Let f(w) be the third derivative of -4/3*w**3 + 1/30*w**5 - 1/3*w**4 - 13*w**2 + 1/60*w**6 + 0*w + 0. Suppose f(a) = 0. What is a?
-2, -1, 2
Let j(f) be the first derivative of -f**4/16 - 5*f**3/6 + 17*f**2/8 + 33*f/2 + 862. Factor j(y).
-(y - 3)*(y + 2)*(y + 11)/4
Let d(b) be the second derivative of -b**9/35280 - b**8/15680 - 2*b**4/3 + 9*b. Let k(u) be the third derivative of d(u). Factor k(t).
-3*t**3*(t + 1)/7
Let q(a) be the first derivative of -a**4/4 - 4*a**3 + a**2/2 + 12*a - 24. Factor q(t).
-(t - 1)*(t + 1)*(t + 12)
Let v(b) be the first derivative of b**6/40 + b**5/4 + b**4 + 2*b**3 - 13*b**2 - 6. Let h(c) be the second derivative of v(c). Factor h(a).
3*(a + 1)*(a + 2)**2
Let q(v) = -2*v**4 + 16*v**2 - 6. Let u(k) = 2*k**4 - k**3 - 18*k**2 + k + 6. Let w(b) = -5*q(b) - 4*u(b). Factor w(o).
2*(o - 1)**2*(o + 1)*(o + 3)
Let u = -903876/7 + 129379. Let t = -253 + u. What is n in 0 - t*n**3 - 2/7*n - 8/7*n**2 = 0?
-1, -1/3, 0
Let c(d) = -13*d - 32. Let o be c(-4). Let s be o/30 - 13/24. Factor s*i**4 + 0*i + 0 + 0*i**3 + 0*i**2 + 1/8*i**5.
i**4*(i + 1)/8
Let t be -2 - (-25)/(-15)*-3. Let -3*l + 6*l**2 - 6*l**t - 3/5*l**5 + 3/5 + 3*l**4 = 0. What is l?
1
Let m(q) = q**2 + 3*q - 16. Let i be m(-6). Factor -d - i*d**3 + 4*d + 2*d**2 + d.
-2*d*(d - 2)*(d + 1)
What is i in -51*i + 3/4*i**2 + 867 = 0?
34
Let j(a) be the second derivative of a**5/15 - 35*a**4/3 + 2450*a**3/3 - 85750*a**2/3 + 56*a. Factor j(m).
4*(m - 35)**3/3
Let y(s) = -4*s**3 + 8*s**2 + 4*s - 2. Let k(z) = z**2 + 4*z**3 + z - 5*z**3 - 2 + 2. Let i be 1 + (7 - (4 - 2)). Let t(b) = i*k(b) - y(b). Factor t(u).
-2*(u - 1)*(u + 1)**2
Let y be (-932)/(-40) - ((-154)/(-55) + -2). Let d(r) be the first derivative of -10*r - 20/3*r**3 - 14 + y*r**2. Factor d(u).
-5*(u - 2)*(4*u - 1)
Let s(z) be the first derivative of -z**6/39 - 2*z**5/13 - 4*z**4/13 - 8*z**3/39 + 116. Factor s(n).
-2*n**2*(n + 1)*(n + 2)**2/13
Factor 7*d**2 + 72 - 42*d**3 + 45*d + 45*d**3 + 5*d**2 - 132*d.
3*(d - 3)*(d - 1)*(d + 8)
Let y(h) = -8*h**3 + 392*h**2 - 3*h + 151. Let i be y(49). Suppose 6/7*f**i + 8/7*f**2 - 16/7*f**3 + 0 + 0*f = 0. What is f?
0, 2/3, 2
Suppose -6 = 3*w, 4*b - 9 - 1 = -w. Let i(v) be the first derivative of 1/12*v**2 + 0*v - 7 - 1/18*v**b. Factor i(f).
-f*(f - 1)/6
Let k(l) be the third derivative of l**5/420 - 3*l**4/56 - 11*l**3/21 + 4*l**2 - 9*l. Factor k(d).
(d - 11)*(d + 2)/7
Let n = -18 + 21. Factor 11 - 13*c**4 - 11 + 68*c**4 + 10*c**n.
5*c**3*(11*c + 2)
Let o(w) be the second derivative of 2*w - 1/3*w**2 + 1/45*w**6 - 1/15*w**5 + 0 + 2/9*w**3 + 0*w**4. Factor o(t).
2*(t - 1)**3*(t + 1)/3
Let l(o) = -5. Let a(f) = 1. Let q(w) = 9*a(w) + 2*l(w). Let h(z) = 2*z**4 - 6*z**3 + 6*z**2 - 2*z + 10. Let g(x) = -h(x) - 10*q(x). Factor g(p).
-2*p*(p - 1)**3
Determine t, given that 6*t - 45 - 1/5*t**2 = 0.
15
Let k(h) = 9*h - 149. Let s be k(16). Let i be (-18)/(-6) + (25/2)/s. Determine d so that i*d + 0 - d**2 + 1/2*d**3 = 0.
0, 1
Let g = 11414 + -22827/2. Solve -g*r**2 - 49/2 - 7*r = 0.
-7
Let g(w) be the first derivative of w**6/18 + 2*w**5/15 - w**4/4 + 206. Solve g(a) = 0 for a.
-3, 0, 1
Suppose 16*n = 3*s + 40*n + 192, -5*s + 40 = -5*n. Factor 0*j**2 + 0 + 0*j + 0*j**3 + s*j**4 - 5/3*j**5.
-5*j**5/3
Let r(w) be the second derivative of w**5/20 + w**3/2 + 2*w**2 + 14*w. Let q be r(0). Determine a so that 0 + 18*a**3 - 81/2*a**q + 0*a - 2*a**2 = 0.
0, 2/9
Let h be 0/(1 + 0/9). Let m(c) be the second derivative of 3/28*c**4 + h*c**2 + 1/21*c**3 - c + 0. Factor m(f).
f*(9*f + 2)/7
Let p = -325 + 329. Let v(c) be the first derivative of 8/3*c**3 + 3/2*c**2 + 3/4*c**p + 6 - 2*c. Factor v(o).
(o + 1)*(o + 2)*(3*o - 1)
Let j(c) be the first derivative of -17*c**4/4 + 23*c**3/2 - 9*c**2 + c/2 - 177. Solve j(m) = 0 for m.
1/34, 1
Find c, given that 0*c**2 - 44/3*c**3 + 8*c**4 + 0 - 1/3*c**5 + 0*c = 0.
0, 2, 22
Let h(n) be the third derivative of -1/40*n**5 + 0*n + 0 - 1/40*n**6 - 1/140*n**7 + 0*n**3 + 0*n**4 - 21*n**2. Determine o, given that h(o) = 0.
-1, 0
Let v = -16 - -116. Let k be (-6)/4*(-40)/v. Factor 3/5*a**2 - 3/5*a**3 - k + 3/5*a.
-3*(a - 1)**2*(a + 1)/5
Let i(s) be the first derivative of 1/9*s**3 - 5/12*s**4 + 2/15*s**5 - 8 + 1/3*s**2 + 0*s. Factor i(v).
v*(v - 2)*(v - 1)*(2*v + 1)/3
Suppose 4*y - 2*s - 54 = 0, -3*y + 0*y - s + 33 = 0. Determine z so that 11*z**5 + 2*z**5 - 21*z**3 + 12*z**2 - 4*z**5 - y*z**4 + 12*z = 0.
-1, -2/3, 0, 1, 2
Let p = -2 + 2. Suppose -3*d - d + 36 = p. Factor 18*n + 10*n - n**3 - 4*n**5 + 4 + d*n**3 - 8*n**4 + 32*n**2 + 4.
-4*(n - 2)*(n + 1)**4
Let m(n) be the first derivative of n**3/15 - 13*n**2/10 - 67. Factor m(j).
j*(j - 13)/5
Suppose -14*i + 8 = -10*i - 2*j, 4 = 2*i + 5*j. Let h(g) be the first derivative of -4 + 4/15*g**3 + 16/5*g - 3/5*g**4 + 16/5*g**i. Factor h(p).
-4*(p - 2)*(p + 1)*(3*p + 2)/5
Let p be ((-12)/(-21))/(4 + (-88)/28). Factor 4/3 - 2/3*r**2 + p*r.
-2*(r - 2)*(r + 1)/3
Let l = -244824/5 + 48966. Factor 0*b + 0 - 9/5*b**3 + l*b**2 + 3/5*b**4.
3*b**2*(b - 2)*(b - 1)/5
Let u(q) = 2*q**3 - 39*q**2 + 18*q + 21. Let d be u(19). Factor -50 + 6*g**2 - 4*g**d + g**2 - 15*g + 2*g**2.
5*(g - 5)*(g + 2)
Suppose 0 = 4*y - 0*y - 16, 2*d - 3*y + 8 = 0. Find z, given that -4*z - 9*z**4 - 2*z**4 + z**4 + 2*z**3 - 2*z**d + 14*z**3 = 0.
-2/5, 0, 1
Let b(r) be the first derivative of 2/3*r**6 - 7 + 6*r**2 - 4*r**4 - 8/3*r**3 + 8*r + 0*r**5. Let b(m) = 0. What is m?
-1, 1, 2
Let y be (56/12 - 5)*-3. Suppose y + 10 + 2*g**2 + 6*g - 1 - 6 = 0. Calculate g.
-2, -1
Solve 20*d - 6*d**4 - 4*d - 5*d**4 + 64*d**2 + 55*d**4 - 124*d**3 = 0 for d.
-2/11, 0, 1, 2
Suppose -2*w + 4 - 2 = 5*b, 1 = 3*b + w. Suppose 4*t = -b*t - 2*t. Determine g, given that 5/3*g**2 - 2/3*g + t = 0.
0, 2/5
Suppose -7*z = -1964 + 1950. Factor 0 - 1/2*m**4 + 1/2*m**3 + 1/2*m**z - 1/2*m.
-m*(m - 1)**2*(m + 1)/2
Let y(f) be the third derivative of -5*f**8/1512 + 254*f**7/945 - 119*f**6/15 + 11849*f**5/135 + 4913*f**4/108 - 114*f**2 + 3*f. Find k such that y(k) = 0.
-1/5, 0, 17
Let m = -68758 + 2750171/40. Let f = m + 49/8. Solve 2/5 - 8/5*o**3 + 18/5*o**2 - f*o = 0 for o.
1/4, 1
Suppose 4*i = -0*i + 3*f + 15, -4*i = f + 5. Let g(u) be the first derivative of i*u + 1 - 3/5*u**2 + 1/5*u**3. Solve g(a) = 0.
0, 2
Let w(z) be the third derivative of -z**6/120 - 3*z**5/40 + z**4/2 - 11*z**3/6 - z**2. Let o(j) be the first derivative of w