4. Suppose q(p) = 0. What is p?
1, 6
Let d(q) = -27*q - 483. Let k be d(-18). Let z(t) be the third derivative of 2/75*t**5 - t**2 + 0 - 4/15*t**k + 0*t + 1/30*t**4 - 1/150*t**6. Factor z(u).
-4*(u - 2)*(u - 1)*(u + 1)/5
Suppose m = 2*u - 157, -5*m - 222 + 4 = -3*u. Let d = 81 - u. Determine v so that d*v - 2/5*v**5 + 6/5*v**4 + 0 + 2/5*v**2 - 6/5*v**3 = 0.
0, 1
Let a(f) = f**4 + 2*f**3 - f**2 - f. Let b(j) = -61*j**4 + 174*j**3 - 75*j**2 - 57*j. Let q(s) = 3*a(s) - b(s). Suppose q(d) = 0. Calculate d.
-3/8, 0, 3/2
Let r(f) = f**4 - f**3 + f**2 + f. Let k(t) = 3*t**4 + 3*t**3 + 5*t**2 - 3*t - 4. Let n(l) = k(l) - 2*r(l). Factor n(p).
(p - 1)*(p + 1)**2*(p + 4)
Let y(i) be the third derivative of 0 - 1/15*i**5 - i**4 + 0*i - 6*i**3 + 18*i**2. Let y(d) = 0. What is d?
-3
Let t(p) be the second derivative of -p**6/15 - p**5/5 + 7*p**4/6 + 20*p**3/3 + 12*p**2 + 403*p. Factor t(x).
-2*(x - 3)*(x + 1)*(x + 2)**2
Let o(i) be the third derivative of -i**9/18900 - i**8/2800 + i**7/3150 + i**6/300 - 7*i**4/24 - 5*i**2. Let c(d) be the second derivative of o(d). Factor c(u).
-4*u*(u - 1)*(u + 1)*(u + 3)/5
Let u(r) be the first derivative of -r**4/2 - 8*r**3/3 + 5*r**2 + 232. What is c in u(c) = 0?
-5, 0, 1
Suppose -5*z + 24 = -3*z. Let o(r) = r**2 - 11*r - 9. Let y be o(z). Factor -13 + m**3 - y*m + 37 - 6*m**2 + 15*m - 4*m**3.
-3*(m - 2)*(m + 2)**2
Let 1 + 998*y - 21 - 1152*y - 30*y**2 = 0. Calculate y.
-5, -2/15
Let o = 2/1525 - -3028/16775. What is s in -o + 4/11*s**3 + 4/11*s**2 - 2/11*s - 2/11*s**4 - 2/11*s**5 = 0?
-1, 1
Let q(w) = -w**3 - w**2 + 2*w - 1. Let u(y) = 29*y**3 - 81*y**2 - 78*y + 44. Let l(s) = 4*q(s) + u(s). What is t in l(t) = 0?
-1, 2/5, 4
Let w(k) = -3*k**5 - 33*k**4 + 6*k**3 + 60*k**2 - 3*k - 33. Let q(t) = -t**4 - 1. Let f(v) = -3*q(v) + w(v). Suppose f(j) = 0. What is j?
-10, -1, 1
Let w(u) be the third derivative of 5*u**8/336 + u**7/6 - 3*u**6/8 - 115*u**5/12 - 125*u**4/6 - 636*u**2. Suppose w(q) = 0. Calculate q.
-5, -1, 0, 4
Let r(i) be the second derivative of -27*i + 1/140*i**5 + 0*i**2 - 2/21*i**3 + 1/28*i**4 + 0. Determine t so that r(t) = 0.
-4, 0, 1
Let p be (-10)/6*((-60)/(-25) + -6). Factor p*u**2 + 1 + 30*u**2 - 26*u + 38*u.
(6*u + 1)**2
Let s be (-252)/(-70) + (6/4)/(87/(-116)). Determine u so that 0 - 12/5*u**2 - s*u - 4/5*u**3 = 0.
-2, -1, 0
Let d(n) = -13*n**2 - 102*n - 252. Let r(f) = -7*f**2 - 51*f - 126. Let c(x) = 4*d(x) - 7*r(x). Factor c(t).
-3*(t + 3)*(t + 14)
Determine k, given that 1/5*k**2 + 2/5*k - 8/5 = 0.
-4, 2
Let h = 3/124 - -965/1116. Let i(w) be the first derivative of h*w**3 + 0*w**2 + w**6 + 1 + 0*w - 4/3*w**4 - 2/5*w**5. Solve i(z) = 0.
-1, 0, 2/3
Let y be ((-42)/9 + -2)*144/(-30). Find x such that x - 84*x**2 + y + 86*x**2 + 15*x = 0.
-4
Let j(w) be the second derivative of w**7/12600 - w**6/900 + w**5/200 + 3*w**4/4 + 3*w. Let l(s) be the third derivative of j(s). Suppose l(y) = 0. What is y?
1, 3
Factor -33*c - 32*c + 84*c**2 - 3*c**3 - 10*c - 162.
-3*(c - 27)*(c - 2)*(c + 1)
Let a(d) be the first derivative of -d**3/7 + 69*d**2/14 + 321. Factor a(r).
-3*r*(r - 23)/7
Suppose 0 = 4*m - 7*m + 9. Find n such that 0*n**5 + n**4 + 3*n**2 + 1 + 2*n**m - 5*n**2 - n - n**5 = 0.
-1, 1
Let l(q) be the first derivative of -1/4*q**4 + 5*q**2 - 8/3*q**3 - 8 - 10*q. Let i(d) = -5*d**3 - 33*d**2 + 39*d - 41. Let r(v) = 2*i(v) - 9*l(v). Factor r(n).
-(n - 2)**3
Let p(b) be the first derivative of -b**6/240 + b**5/30 - b**4/16 + 2*b**2 + 2. Let z(g) be the second derivative of p(g). Factor z(x).
-x*(x - 3)*(x - 1)/2
Suppose -42 = k + 3*d + 57, k = -2*d - 95. Let l = k - -351/4. Suppose l*v**2 - 3/4 - 1/4*v + 1/4*v**3 = 0. Calculate v.
-3, -1, 1
Let t(h) be the first derivative of -h**5/5 + 7*h**4/2 - 53*h**3/3 + 38*h**2 - 36*h + 114. Let t(r) = 0. What is r?
1, 2, 9
Suppose 780 = -50*h + 44*h. Let f = 406/3 + h. Factor 3 + 22*o - 88/3*o**3 + f*o**4 + 97/3*o**2.
(o - 3)**2*(4*o + 1)**2/3
Let d(g) be the third derivative of g**6/40 - g**5/4 - 13*g**4/8 - 7*g**3/2 - 152*g**2. What is p in d(p) = 0?
-1, 7
Let s = 96 - 91. Let u be 6*(-5)/(-50)*s. Suppose -40/7*d**u - 8*d**2 - 4/7 - 26/7*d = 0. What is d?
-1/2, -2/5
Let m(y) be the first derivative of 28*y**3/15 - y**2/5 + 158. Solve m(p) = 0 for p.
0, 1/14
Let r(t) = t**3 + 2*t**2 - 7*t + 8. Let z be r(2). What is q in -74 + z + 25*q**2 + 27*q**2 - 56*q**2 - 32*q = 0?
-4
Let j be (-17)/9 + -3 + 1. Let s = j + 403/99. Factor 0 - 2/11*w - 6/11*w**2 - s*w**4 - 6/11*w**3.
-2*w*(w + 1)**3/11
Let p = -32 + 26. Let o be 1/(-10)*72/p. What is t in -4/5*t**2 + 14/5*t - o = 0?
1/2, 3
Let o(g) be the first derivative of -g**6/3060 + g**5/1020 + 14*g**3/3 + 14. Let a(n) be the third derivative of o(n). Let a(q) = 0. Calculate q.
0, 1
Suppose 32 = 31*m - 92. Factor 2/3*f**5 + 20*f**3 - 6 - 6*f**m - 92/3*f**2 + 22*f.
2*(f - 3)**2*(f - 1)**3/3
Let y(z) be the third derivative of 15*z**2 - 5/6*z**3 + 0*z + 0 - 1/4*z**4 - 1/60*z**5. Factor y(s).
-(s + 1)*(s + 5)
Let j(g) be the third derivative of g**6/60 + 2*g**5/15 - g**4/12 - 4*g**3/3 - 3*g**2 + 4*g. Factor j(y).
2*(y - 1)*(y + 1)*(y + 4)
Find x such that 8*x - 151*x**3 + 14*x**2 + 161*x**3 + 2*x**4 + 2*x**2 = 0.
-2, -1, 0
Let b(j) = j**4 - j**2 - j - 1. Let g(m) = -7*m**4 + 8*m**3 + 13*m**2 + m + 3. Let o(k) = -18*b(k) - 2*g(k). Factor o(q).
-4*(q - 1)*(q + 1)**2*(q + 3)
Let t(w) be the third derivative of 1/270*w**5 + 1/540*w**6 - 4*w**2 - 4/27*w**3 + 0 - 1/27*w**4 + 0*w. Let t(s) = 0. What is s?
-2, -1, 2
Let y(h) be the second derivative of 3*h**5/140 - h**4/14 - h**3/14 + 3*h**2/7 - 3*h - 11. What is o in y(o) = 0?
-1, 1, 2
Let i be (-27)/(-2)*(-3 + 10 + -5). Solve 6*l - 26*l**3 + i*l**3 - 1 - 3*l**2 - 3*l = 0 for l.
1
Suppose x + 23 = -5*h, 0 = x - 0*x - 3*h + 31. Let r = 65/2 + x. Factor 1/2*n**4 - 5/2*n**3 + r*n**2 - 7/2*n + 1.
(n - 2)*(n - 1)**3/2
Suppose 11 = 28*v - 45. Let c be (-12)/(-15) - 0/4. Suppose -6/5*n + c - v*n**2 = 0. Calculate n.
-1, 2/5
Let c be ((-56)/12)/14 + 4/6. Let l(i) be the second derivative of -c*i**3 + 6*i + 0 - 1/2*i**2 - 1/12*i**4. Let l(d) = 0. What is d?
-1
Let z = -355 - -555. Let a = z + -200. Factor a*v**2 + 0*v - 2/9*v**4 + 2/9*v**5 + 0*v**3 + 0.
2*v**4*(v - 1)/9
Let i(s) be the first derivative of 2/55*s**5 - 5/11*s**4 + 72/11*s + 74/33*s**3 - 60/11*s**2 + 9. Suppose i(j) = 0. What is j?
2, 3
Let k(l) = -3*l - 9. Let w be k(-3). What is a in 0*a + w*a + a**2 - 4*a + 5*a = 0?
-1, 0
Factor -132*r + 464*r**2 + 2178 - 229*r**2 - 233*r**2.
2*(r - 33)**2
Let d(k) be the first derivative of 1/30*k**6 + k**2 + 5 - 1/4*k**4 + 1/20*k**5 + 2*k - 1/6*k**3. Let f(q) be the first derivative of d(q). Factor f(p).
(p - 1)**2*(p + 1)*(p + 2)
Determine c so that -18/5*c + 0 - 1/5*c**3 + 19/5*c**2 = 0.
0, 1, 18
Factor 25/8 - 49/8*i + 1/8*i**3 + 23/8*i**2.
(i - 1)**2*(i + 25)/8
Factor 0 + 3/2*c**3 + 0*c + 3/2*c**5 + 0*c**2 + 3*c**4.
3*c**3*(c + 1)**2/2
Let u(o) = -1. Let d = 1501 - 1504. Let i(r) = -3*r**2 - 3 + 2*r**2 - 2*r + 6. Let b(x) = d*i(x) - 12*u(x). Find m, given that b(m) = 0.
-1
Let l be (1 + -5)*-11*5/110. Let o(r) be the first derivative of -2/21*r**3 - 1/14*r**l + 1/28*r**4 + 9 + 2/7*r. Factor o(y).
(y - 2)*(y - 1)*(y + 1)/7
Determine u, given that -16*u + 19*u + 5*u**3 - 5*u**2 + 2*u**2 - 5*u**2 = 0.
0, 3/5, 1
Suppose 2/3*f**2 + 0 + 32/3*f = 0. Calculate f.
-16, 0
Suppose 3*d + 3 = -4*c, 5 = 2*d + c + 2. Let g = d - -7. Factor -g*n - 16 - 3*n - n**2 + 5*n.
-(n + 4)**2
Let l(c) be the second derivative of -c**5/80 + 23*c**4/8 - 529*c**3/2 + 12167*c**2 + 56*c. Factor l(n).
-(n - 46)**3/4
Let r(x) be the first derivative of 1/6*x**6 + 3/5*x**5 + 0*x**2 + 0*x - 4/3*x**3 + 13 + 0*x**4. Find k such that r(k) = 0.
-2, 0, 1
Let s(n) = n**3 - 3*n**2 + 6*n - 3. Let d be s(5). Let g be (-17)/(-21) + (-11)/d. What is r in 0*r**3 - g*r**4 + 0 + 0*r + 2/3*r**2 = 0?
-1, 0, 1
Let q(k) = -k**2 + 6*k - 5. Let y be q(2). Let n(d) be the second derivative of 0 + 0*d**2 + y*d - 1/30*d**4 + 1/15*d**3. Factor n(m).
-2*m*(m - 1)/5
Let p be ((-33)/(-6))/((-126)/(-48)). Let 10/21*w**3 + 8/3*w - p*w**2 - 16/21 = 0. Calculate w.
2/5, 2
Let a(r) be the first derivative of -15/2*r**2 + 22 + 15/2*r**4 - 5/2*r**6 - 20/3*r**3 + 2*r**5 + 10*r. Let a(c) = 0. What is c?
-1, 2/3, 1
Let h(q) be the second derivative of 