e i.
3
Let j(h) = 31*h**2 + 1757*h + 65750. Let i(n) = 10*n**2 + 586*n + 21916. Let a(p) = 19*i(p) - 6*j(p). Suppose a(q) = 0. What is q?
-74
Let i(r) = r**2 + 3*r - 9. Let g be i(-5). Let a(l) = -l**4 + l**3 + l**2 + l. Let u(o) = -3*o**3 - 2*o**2 - o. Let c(h) = g*u(h) + a(h). Factor c(j).
-j**2*(j + 1)**2
Let n(s) be the third derivative of -11*s**7/42 + s**6/3 + s**5/4 - 24*s**2 - 2*s. Factor n(m).
-5*m**2*(m - 1)*(11*m + 3)
Let z(m) be the second derivative of -m**4/96 - 5*m**3/48 - 3*m**2/8 - 11*m. Determine o so that z(o) = 0.
-3, -2
Suppose 5*d = 4*c + 1, c + 2 = d + 2*d. Let m = 1 + c. What is a in 1 + 2 + 2 - a**m - 4*a - 8 = 0?
-3, -1
Suppose -3*a = 3*g - 135, 7*g - 125 = 4*g - 5*a. Let -3*b + g*b**3 - 51*b**3 + 4*b + b**4 - b**2 = 0. What is b?
-1, 0, 1
Suppose 0 = k - 3*k + g + 5, 2*k + 3*g - 9 = 0. Factor -18*q**3 - 5*q**4 - 17*q**2 + 13*q**2 - k*q**4.
-2*q**2*(q + 2)*(4*q + 1)
Suppose 0 = -2*f - 22 + 48. Factor 8*t - 4*t**2 + 4*t - 10 + f*t**2 - 2 - 12*t**3 + 3*t**4.
3*(t - 2)**2*(t - 1)*(t + 1)
Let p(b) = -11*b**3 - 146*b**2 - 256*b - 163. Let h(q) = 7*q**3 + 98*q**2 + 170*q + 109. Let y(u) = -7*h(u) - 5*p(u). Factor y(c).
2*(c + 1)*(c + 2)*(3*c + 13)
Factor -3/4*y**5 - 3/4*y**4 - 39/2*y**2 + 57/4*y + 21/2*y**3 - 15/4.
-3*(y - 1)**4*(y + 5)/4
Let y(s) be the first derivative of -s**3/3 + 16. Let h(r) = -4*r**2 - 2*r - 1. Let j(a) = -2*h(a) + 6*y(a). Solve j(c) = 0 for c.
-1
Let d(g) be the third derivative of g**6/30 + 7*g**5/15 + 4*g**4/3 - 32*g**3/3 - 215*g**2. Solve d(b) = 0 for b.
-4, 1
Let l(d) be the first derivative of -3*d**5/5 + d**4/2 + 451. Factor l(q).
-q**3*(3*q - 2)
Suppose -l + 28 = 8. Let b be 56/10 - (-8)/l. Factor -2*w**2 + 2*w**3 + b*w - 4*w**2 + 0*w + 1 - 3.
2*(w - 1)**3
Let s(f) be the first derivative of -5*f**3/9 + 95*f**2/6 + 100*f/3 + 127. Factor s(a).
-5*(a - 20)*(a + 1)/3
Suppose -1146*m**2 - 59*m + m**3 + 1 + 29 + 1174*m**2 = 0. What is m?
-30, 1
Suppose 4*x + x - 5*p = 15, 0 = x + 4*p + 12. Let l be x + 2 + (-4)/(-4). Factor -99*z - 4 + 93*z - z**l + 3*z**3.
2*(z - 2)*(z + 1)**2
Let w(h) be the second derivative of -1/6*h**2 + 1/36*h**4 + 0*h**3 + 0 + 19*h. Factor w(l).
(l - 1)*(l + 1)/3
Suppose 0 = 4*h + 2*z - 6, 0 = z - 4*z - 15. Let q be ((-54)/4)/(-3) - h. Suppose 0*y**2 - 3/4*y + 1/4*y**3 - q = 0. What is y?
-1, 2
Let i(p) = 11*p**2 - 1373*p - 250. Let d be i(125). Determine f so that -10/3*f**2 + d - 5*f**3 + 5/6*f**4 + 20/3*f + 5/6*f**5 = 0.
-2, 0, 1, 2
Let j(g) = -6*g**2 - 43*g + 7. Let a(l) = -3*l**2 - 22*l + 4. Let b(y) = -7*a(y) + 4*j(y). Solve b(u) = 0 for u.
-6, 0
Suppose -2 = 4*g - x - 3, 4*g = -2*x - 2. Suppose 2*z + 3 - 7 = 0. Let l**2 - 2*l + g*l + z - 1 = 0. What is l?
1
Let t(h) = 8*h**3 - 61*h**2 + 300*h + 1125. Let r(m) = -7*m**3 + 60*m**2 - 300*m - 1125. Let l(y) = -6*r(y) - 5*t(y). What is n in l(n) = 0?
-5/2, 15
Let b(s) be the second derivative of 1/84*s**7 + 0*s**3 + 1/60*s**6 - 1/20*s**5 + 0 - 11*s + 0*s**2 + 0*s**4. Determine l so that b(l) = 0.
-2, 0, 1
Let r = 85363 + -18950641/222. Let s = -3/37 - r. Factor 1/6*t**4 + s*t**3 + 0 - 1/6*t - 1/6*t**2.
t*(t - 1)*(t + 1)**2/6
Determine t, given that -24/5*t + 2/5*t**2 + 72/5 = 0.
6
What is i in -8/15*i - 2/15*i**2 - 8/15 = 0?
-2
Let v = 3 - -1. Suppose 5*w = -4*b + w + 28, -3*b - v*w + 23 = 0. Determine a so that -14*a**3 + 135 - b*a**4 - 22*a**3 - 4*a**3 - 34*a**2 - 56*a**2 = 0.
-3, 1
Let k be -1*-106*(-12)/120 + 11. What is j in 0*j**4 + 0*j**2 - k*j**3 + 2/5*j**5 + 0 + 0*j = 0?
-1, 0, 1
Let f(a) = -a**4 + 2*a**2 + 2*a + 2. Let u(i) = -9*i**4 + 324*i**3 + 24*i**2 + 24*i + 24. Let w(c) = 12*f(c) - u(c). Let w(t) = 0. What is t?
-108, 0
Suppose -64*c - 91 = -475. Let k(y) be the second derivative of 0 - 2/15*y**c + 0*y**2 - 2*y**3 - 1/5*y**5 + 5/3*y**4 - 6*y. Factor k(d).
-4*d*(d - 1)**2*(d + 3)
Let z(t) = -t**4 - t**2 + t. Let n(f) = 64*f - 9*f**2 - 2*f**4 + 4*f**3 - 59*f - 4*f**4. Let l(u) = n(u) - 5*z(u). Suppose l(m) = 0. Calculate m.
0, 2
Let k be (-2)/3 - 260/(-26). Find t such that -k*t - 8/3 - 8/3*t**3 - 28/3*t**2 = 0.
-2, -1, -1/2
Let c = -612 + 618. Let v(d) be the first derivative of 0*d**2 + 3/20*d**5 - 3/4*d**4 - d**3 + 0*d + 11 + 1/8*d**c. Solve v(x) = 0 for x.
-2, -1, 0, 2
Let v be 15/200*-5 - 54/(-16). Let d(h) be the second derivative of 0 + 3/5*h**5 + 3*h - 5/2*h**3 + 2/5*h**6 + 1/14*h**7 - v*h**2 - 1/2*h**4. Factor d(l).
3*(l - 1)*(l + 1)**3*(l + 2)
Suppose 49/4*t - 39/4 - 1/4*t**3 - 9/4*t**2 = 0. What is t?
-13, 1, 3
Let x(u) be the first derivative of -12*u - 3 + 6*u**2 + 3*u**3 + 3/5*u**5 - 3*u**4. Factor x(c).
3*(c - 2)**2*(c - 1)*(c + 1)
Let t(j) = j**3 - 8*j**2 - 40*j + 322. Let y be t(8). Let l be (2/10)/((-4)/(-15)). Determine i, given that l*i + 3/4 - 3/2*i**y = 0.
-1/2, 1
Let k be ((-798)/152 + 7)/(1/6). Factor -18*v**3 + k*v**4 + 3*v + 9/2*v**2 + 0.
3*v*(v - 1)**2*(7*v + 2)/2
Let m(h) = 2*h - 10. Let g be m(-8). Let n = g - -31. Let -42*y - 4*y**n + 28*y + 22*y + 12*y**2 - 12*y**4 - 4*y**3 = 0. What is y?
-2, -1, 0, 1
Let q(c) = 5*c**3 - 12*c**2 + 3*c + 2. Let w be 3*2*(-5)/10. Let t = -4 - w. Let x(s) = s**3. Let r(j) = t*q(j) - 2*x(j). Determine b so that r(b) = 0.
-2/7, 1
Suppose -11*t = -2*t - 45. Suppose -5*a = 0, 0 = -3*o + 7*a - t*a. Solve 3/5*h**2 - 1/5*h**3 + o + 0*h = 0.
0, 3
Let z(u) be the first derivative of 3*u**5/5 - 3*u**4 - 26*u**3 + 90*u**2 + 675*u - 27. Factor z(k).
3*(k - 5)**2*(k + 3)**2
Let r(v) be the first derivative of v**4/18 + v**3/9 - 38*v - 20. Let p(s) be the first derivative of r(s). Let p(h) = 0. What is h?
-1, 0
Let l(g) be the first derivative of -79/9*g**2 - 44/9*g - 35 - 14/27*g**3. Factor l(k).
-2*(k + 11)*(7*k + 2)/9
Let w = -3514 + 3518. Solve 0 + 0*q - 8/15*q**2 + 32/15*q**3 - 14/15*q**w = 0 for q.
0, 2/7, 2
Let d(i) be the third derivative of -i**8/168 + 8*i**7/105 - i**6/12 - 7*i**5/15 - i**2 - 161*i. Let d(z) = 0. What is z?
-1, 0, 2, 7
Let s = -96/7 + 775/56. Factor 0*g - 1/8*g**2 - s*g**3 + 0.
-g**2*(g + 1)/8
Suppose -o = -2*s + 4*s - 17, -56 = -4*o - 4*s. What is k in o*k**3 - 2*k + 5*k**3 - 20*k**3 + 3*k**3 + 3*k**2 = 0?
0, 1, 2
Let u(k) be the first derivative of k**6/360 + k**5/24 - 5*k**3/3 + 2. Let m(q) be the third derivative of u(q). Factor m(v).
v*(v + 5)
Suppose 0*r - 4*r = 3*p + 15, -r + 3*p = -15. Let m(s) be the second derivative of 0*s**3 + 1/30*s**5 + r*s**2 + 0*s**4 + s + 0. Find z, given that m(z) = 0.
0
Factor 2/11*r**2 - 18/11*r + 36/11.
2*(r - 6)*(r - 3)/11
Let s = 60 - 81. Let r(t) = t**2 + 3*t + 10. Let c(o) = 6*o**2 + 15*o + 51. Let x(u) = s*r(u) + 4*c(u). Suppose x(z) = 0. What is z?
-1, 2
Let b(z) = z**2 - 7*z + 3. Let w(m) = 2*m**2 - 4*m**2 + 6*m + 1 - 3. Suppose 19 = 5*f + 4, 3*f = -5*k + 19. Let g(j) = k*b(j) + 3*w(j). Factor g(u).
-4*u*(u - 1)
Let a(s) = s**3 + s**2 - s. Let h(n) = n**4 + 11*n**2 - n - 8. Suppose 15*f - 40 = 11*f. Let j(k) = f*a(k) - 2*h(k). Factor j(r).
-2*(r - 2)**3*(r + 1)
Suppose -10 = -9*j + 4*j. Let w(x) = -j + 2 - 2 + 3*x + 3 - 4*x**2. Let h(c) = c - 1. Let f(l) = -3*h(l) + w(l). Factor f(n).
-4*(n - 1)*(n + 1)
Let 48/19 - 22/19*w**3 + 88/19*w - 6/19*w**4 + 12/19*w**2 = 0. What is w?
-3, -2, -2/3, 2
Suppose 5*n + 3 - 28 = 0. Suppose -2*u = -z - n, -u + 2*u - 4 = 2*z. Solve -8*x + x**2 + x**2 + 4*x**3 + u*x**2 = 0 for x.
-2, 0, 1
Let u = 108 - 103. Determine t, given that 15*t**2 + 21*t**4 + 4*t**5 + t**5 - 8*t**u - 33*t**3 = 0.
0, 1, 5
Let t(g) be the second derivative of 10*g**4/3 - 71*g**3/3 - 19*g**2 - 2*g + 152. Factor t(p).
2*(4*p + 1)*(5*p - 19)
Let r(c) be the first derivative of c**5/45 - 2*c**3/3 - 16*c**2/9 - 5*c/3 + 313. Factor r(h).
(h - 5)*(h + 1)**2*(h + 3)/9
Let o(x) = -x**2 - 77*x - 205. Let a(i) = -1. Let j(g) = -6*a(g) - o(g). Let z(b) = 39*b + 105. Let v(w) = -3*j(w) + 5*z(w). Factor v(y).
-3*(y + 6)**2
Let j be (9 - -3 - 6) + (1 - 3). Let g(m) be the first derivative of -2/15*m**5 - 7 + 0*m - 2/9*m**3 + 0*m**2 - 1/3*m**j. Factor g(q).
-2*q**2*(q + 1)**2/3
Let m(l) be the first derivative of 40 + 1/2*l**4 + 5/3*l**2 + 32/9*l**3 + 0*l. Find x such that m(x) = 0.
-5, -1/3, 0
Let y(g) = -g**2 - 4*g + 22. Let u be y(-6). Let w = u + -8. Find i, given that 2*i + 14/15*i**w + 6/5 + 2/15*i**3 = 0.
-3, -1
Let h(l) be the third derivative of -1/21*l**7 + 1/30*l**5 + 0*l + 0 + 1/12*l*