. Let z(w) = p*k(w) + o(w). Solve z(j) = 0 for j.
1
Let i(h) be the first derivative of 0*h**3 - 3*h - 6 + 1/180*h**6 + 0*h**2 - 1/60*h**5 + 1/72*h**4. Let x(w) be the first derivative of i(w). Factor x(d).
d**2*(d - 1)**2/6
Let m(y) be the third derivative of 2*y**7/105 - 7*y**5/15 - y**4 + y**2 - 16*y. Suppose m(h) = 0. What is h?
-2, -1, 0, 3
Let o(l) be the first derivative of l**4/2 + 22*l**3 + 363*l**2 + 2662*l + 13. Factor o(u).
2*(u + 11)**3
Find h, given that 2526*h**3 - 614*h**3 - 1496*h - 28*h**4 + 4408*h - 4268*h**2 - 528 = 0.
2/7, 1, 66
Suppose -5*u + 4 = -11. Determine w so that 12*w**u - 2*w**4 + 14*w**4 - 43*w**5 + 46*w**5 = 0.
-2, 0
Let l(v) be the third derivative of -v**6/30 + 2*v**4 + 32*v**3/3 + 3*v**2 + 19. Factor l(m).
-4*(m - 4)*(m + 2)**2
Let s = -3 + 3. Suppose s*j - j = 4*h + 6, -j - 3*h - 4 = 0. Find y such that y**4 + 3*y**3 + 0*y - j*y + 3*y**2 + 3*y = 0.
-1, 0
Let o = 10 - 5. Let u be (8/(-10))/(16/(-40)). Factor -4*w**3 - w**u + 5*w**o - 2*w**2 - w**3 + 2*w**4 + w**2.
w**2*(w - 1)*(w + 1)*(5*w + 2)
Let i(l) be the first derivative of -2*l**3 - 3*l**2/2 - 45. Determine b so that i(b) = 0.
-1/2, 0
Suppose g = 7, 4*s + 907*g - 41 = 904*g. Determine k so that 3/5*k**3 - 1/5*k**s - 2/5*k + 0 + 1/5*k**2 - 1/5*k**4 = 0.
-2, -1, 0, 1
Let m = -26731 + 133679/5. Let m*p + 1/5*p**3 - 9/5*p**2 - 4 = 0. What is p?
2, 5
Let t(k) = -41*k - 243. Let m be t(-6). Let l(o) be the first derivative of 0*o + 0*o**2 - 4 - 2/3*o**4 + 2/9*o**m. Suppose l(d) = 0. Calculate d.
0, 1/4
Let p(k) be the first derivative of k**6/1980 - k**5/330 + k**4/132 + 5*k**3/3 - 11. Let t(f) be the third derivative of p(f). Factor t(b).
2*(b - 1)**2/11
Let k = 161 + -159. Let t(x) = x**3 - 3*x**2 + 6*x - 6. Let r be t(k). Factor 2/9*y**r + 4/9*y + 2/9.
2*(y + 1)**2/9
Factor 2/15*a**4 + 2/15*a**5 - 4/5*a**3 - 28/15*a**2 - 22/15*a - 2/5.
2*(a - 3)*(a + 1)**4/15
Let r(y) be the third derivative of -y**7/1260 - y**6/45 - 4*y**5/15 - y**4/24 - y**3/3 - 6*y**2. Let m(l) be the second derivative of r(l). Factor m(i).
-2*(i + 4)**2
Let f be (-74)/(-14) + 4/(-14). Let r be 32/20 - (-2)/f. Factor -5*u**2 - 6*u - 6*u + u**r - 8.
-4*(u + 1)*(u + 2)
Let w(h) be the third derivative of h**8/420 - 4*h**7/525 - 3*h**6/25 - 32*h**5/75 - 23*h**4/30 - 4*h**3/5 + 2*h**2 - 200. Find c such that w(c) = 0.
-1, 6
Suppose -37*a - 14 = -36*a + 4*b, a + 18 = -5*b. Factor 1/2*k**5 + 1/2*k**4 + 0*k**a + 0*k - k**3 + 0.
k**3*(k - 1)*(k + 2)/2
Let d(u) = 6*u**2 + 9*u - 31. Let y(j) = j - 3*j - 3 - 3*j**2 - 2 + 4. Let h be y(-3). Let l(m) = -m**2 - 2*m + 6. Let k(q) = h*l(q) - 4*d(q). Factor k(v).
-2*(v - 2)**2
Let w(h) be the second derivative of -h**5/4 - 245*h**4/12 - 3335*h**3/6 - 7935*h**2/2 + 22*h + 11. Let w(z) = 0. What is z?
-23, -3
Let o(v) be the third derivative of v**7/105 - v**6/20 - v**5/2 - 17*v**4/12 - 2*v**3 + 5*v**2 - 3*v. Factor o(i).
2*(i - 6)*(i + 1)**3
Suppose -12*t = 692 + 1108. Let a = -446/3 - t. What is u in 0*u + u**4 + 2/3*u**3 - 2/3*u**5 - a*u**2 + 1/3 = 0?
-1, -1/2, 1
Let u(d) be the second derivative of -2*d**7/21 - d**6/15 + 19*d**5/10 - 31*d**4/6 + 19*d**3/3 - 4*d**2 - 3*d. Determine q, given that u(q) = 0.
-4, 1/2, 1
Let q be (1/(-5))/(623/(-208) - -3). Let k = 837/20 + q. Solve -k*h**2 + 3/4*h - 1/2 = 0.
1, 2
Let z(h) be the first derivative of -9*h**4 - 55*h**3/2 - 6*h**2 + 18*h - 147. Let z(b) = 0. Calculate b.
-2, -2/3, 3/8
Let v(h) = -4*h**4 - 7*h**3 + 5*h**2 + 6*h - 12. Let s(j) = 5*j**4 + 8*j**3 - 6*j**2 - 4*j + 13. Let q(m) = -3*s(m) - 4*v(m). Factor q(r).
(r - 1)**2*(r + 3)**2
Let k(l) be the first derivative of l**5/10 + l**4/4 - l**3/2 + 150. Factor k(v).
v**2*(v - 1)*(v + 3)/2
Let z(s) = -5*s**2 - 23*s - 4. Let f = -38 - -44. Let a(r) = 29*r**2 + 138*r + 23. Let i(p) = f*a(p) + 39*z(p). What is c in i(c) = 0?
-3, -2/7
Let f be (-4 - (-2 + 2 + 2))/(76 + -78). Suppose -1/4*m + 1/2*m**2 + 0 - 1/4*m**f = 0. Calculate m.
0, 1
Let i = -7044 - -7048. What is t in 0 + 8/9*t**3 + 10/9*t**2 + 4/9*t + 2/9*t**i = 0?
-2, -1, 0
Let x(l) = -l**4 + l**2 - l - 1. Let q(k) = 8*k**4 + 48*k**3 - 56*k**2 + 4*k + 4. Let h(w) = q(w) + 4*x(w). Find g, given that h(g) = 0.
-13, 0, 1
Let q be (-1 - (4 + -8)) + 0. Let n(o) = 4*o - 12. Let u be n(q). Factor 0 - 6 + u*l + 3*l + 3*l**2.
3*(l - 1)*(l + 2)
Suppose -11*u + 20 = -u. Let m(l) be the first derivative of l**3 + 3/2*l**u + 0*l - 3/5*l**5 - 5 - 3/4*l**4. Factor m(a).
-3*a*(a - 1)*(a + 1)**2
Suppose 4*x = -5*j - 5, -x + 10 + 20 = -5*j. Let p(s) be the second derivative of -1/54*s**4 - x*s + 1/9*s**3 + 0*s**2 + 0. Factor p(z).
-2*z*(z - 3)/9
Suppose 1735*n + 18 = 1741*n. Solve 28/15*j**2 - 8/3*j + 16/15 - 2/5*j**n = 0.
2/3, 2
Let k = 35/107 - -224/1605. Let q(l) be the first derivative of k*l**2 + 9 + 2/9*l**3 + 4/15*l. Suppose q(x) = 0. What is x?
-1, -2/5
Suppose -2073 - g**2 + 2175 + 11*g + 20*g = 0. Calculate g.
-3, 34
Let l(s) be the first derivative of 3*s**5/5 - 3*s**4 + 9*s**3/2 - 3*s**2 - 4*s + 4. Let b(y) be the first derivative of l(y). Find i, given that b(i) = 0.
1/2, 2
Let u be (-4)/10 - 189/(-35). Factor -u*j**3 - 104*j - 3*j**2 + 8*j**2 + 114*j.
-5*j*(j - 2)*(j + 1)
Let z(q) be the third derivative of -q**6/72 - q**5/12 - 21*q**2 - 2*q. Suppose z(s) = 0. What is s?
-3, 0
Let j(n) be the third derivative of -n**6/600 + n**5/15 - 86*n**2 - 2*n. Factor j(z).
-z**2*(z - 20)/5
Let t(c) be the first derivative of 3*c**3 + 102*c**2 + 132*c - 124. Solve t(x) = 0.
-22, -2/3
Suppose 214 = 158*o - 51*o. Solve 0 - 2/11*p - 4/11*p**4 + 2/11*p**5 + 0*p**3 + 4/11*p**o = 0.
-1, 0, 1
Let g be 4 + 7/(7/(-6)). Let r be g - -1 - 35/(-25). Factor 0*p + r*p**5 + 0 + 2/5*p**2 + 6/5*p**4 + 6/5*p**3.
2*p**2*(p + 1)**3/5
Let w(k) = k**3 + 24*k**2 + 103*k + 462. Let c be w(-20). Factor 2/3*n**c + 14/3 - 16/3*n.
2*(n - 7)*(n - 1)/3
Let w(c) be the first derivative of -c**2 + 5/2*c**4 + 0*c + 6/5*c**5 + 2/3*c**3 + 9. Factor w(b).
2*b*(b + 1)**2*(3*b - 1)
Suppose 2*i - 28 = -18. Determine u so that 4*u**2 - 3*u + i*u**2 - 6*u**2 = 0.
0, 1
Let d(j) be the first derivative of 17*j**3/15 - 3*j**2/10 - 342. Suppose d(y) = 0. Calculate y.
0, 3/17
Let n(o) = -o + 9. Let w be n(7). Let r be w/(-1)*(-7 + 6). Factor -2 - r*x - 1/2*x**2.
-(x + 2)**2/2
Let v(f) be the first derivative of 18 - 5*f + 7/4*f**2 - 1/6*f**3. Factor v(y).
-(y - 5)*(y - 2)/2
Let 1960 + 140*n + 5/2*n**2 = 0. What is n?
-28
Let m(z) be the third derivative of -z**5/300 + 3*z**4/10 + 37*z**3/30 + 81*z**2. Suppose m(w) = 0. What is w?
-1, 37
Factor -361 - 138*g - 2*g**3 - 261*g + g**3 - 39*g**2.
-(g + 1)*(g + 19)**2
Let f be (-10 + 646/51)/((-52)/(-30)). Solve -40/13*b + 58/13*b**2 - f*b**3 + 8/13 = 0 for b.
2/5, 1/2, 2
Let -6/13*p**4 + 4/13*p**3 - 6/13 - 2/13*p - 2/13*p**5 + 12/13*p**2 = 0. What is p?
-3, -1, 1
Let k be (6/35)/((264/(-252))/(-22)). Let 2/5*n**2 + k - 12/5*n = 0. Calculate n.
3
Suppose 0 = -2*l - 3*l + 35. Suppose -28 = -3*q + l*q. Let s(z) = 3*z**2 + 6*z. Let k(j) = 5*j**2 + 11*j - 1. Let g(w) = q*s(w) + 3*k(w). Factor g(o).
-3*(o + 1)*(2*o + 1)
Suppose 42*r - 211 = -9 + 8. Suppose 7/4*z**4 + 0 - 9/4*z**3 - 1/2*z**r + 5/4*z**2 - 1/4*z = 0. Calculate z.
0, 1/2, 1
Factor -5 + 391*m + 8*m**3 - 125*m - 66*m + 454*m + 157 + 186*m**2.
2*(m + 4)*(m + 19)*(4*m + 1)
Let n(s) be the first derivative of -s**4/10 - 34*s**3/15 + s**2/5 + 34*s/5 + 261. Suppose n(q) = 0. Calculate q.
-17, -1, 1
Factor 53*t**4 - 3*t**2 + 4*t**3 - 4*t - 51*t**4 + t**2.
2*t*(t - 1)*(t + 1)*(t + 2)
Solve 5/2*x**3 + 13/2*x**2 + 4 - 13*x = 0.
-4, 2/5, 1
Let j be 36/28 + 1209/(-1365). Let r be 38/20 + 30/(-20). Let 4/5 - j*w**2 - r*w**4 - 6/5*w + 6/5*w**3 = 0. What is w?
-1, 1, 2
Suppose 3*x + 3*x = 90. Factor -15*j**2 + 0*j**3 - 2*j**3 - 6 + 6*j**2 + x*j**2 + 2*j.
-2*(j - 3)*(j - 1)*(j + 1)
Let d(f) = 10*f**3 - 25*f**2 - 65*f - 5. Let j(v) = v**4 + 11*v**3 - 24*v**2 - 64*v - 4. Let r(q) = -4*d(q) + 5*j(q). Suppose r(s) = 0. Calculate s.
-3, -2, 0, 2
Let z(g) = -g**3 + 11*g**2 - g + 14. Let y(r) = -r**3 + r**2 + 2*r + 3. Let u be y(-2). Let c be z(u). Let 3*h**3 + 0*h**3 - 7*h**c = 0. What is h?
0
Let g(q) be the third derivative of -97/480*q**6 - 1/4*q**3 - 14*q**2 + 0*q + 0 + 37/96*q**4 - 1/30*q**7 - 13/120*q**5. Let g(y) = 0. What is y?
-3, -1, 1/4, 2/7
Let 167765*p**2 + 2*p**3 