.
-2, -1, 0
Let j(d) be the third derivative of 121*d**6/480 + 11*d**5/16 + d**4/2 + d**3/6 - 3*d**2 - 13. Determine q, given that j(q) = 0.
-1, -2/11
Let i(x) be the first derivative of 2*x**3/15 - 16*x**2/5 + 56*x/5 + 322. Solve i(l) = 0.
2, 14
Let o = -1 - -6. Suppose 3*f - 5 + 2 = -b, 2*f + o*b = -11. What is s in 4/3*s**f + 1/3*s - 2/3 + 1/3*s**5 - 2/3*s**4 - 2/3*s**3 = 0?
-1, 1, 2
Let j(v) be the first derivative of v**4/22 - 32*v**3/11 + 621*v**2/11 - 2116*v/11 - 141. Solve j(m) = 0 for m.
2, 23
Let k = -26 - -41. Let b = 18 - k. Let y(a) = -a**2 - 12*a + 21. Let v(f) = f**2 + 24*f - 41. Let h(s) = b*v(s) + 5*y(s). Solve h(r) = 0 for r.
3
Let p(s) = -1. Let l(o) = -5*o**2 + 9*o + 4. Let m(t) = -l(t) + 2*p(t). Let w(q) = -10*q**2 + 19*q + 11. Let h(k) = -11*m(k) - 6*w(k). Let h(i) = 0. What is i?
0, 3
Let u(w) be the second derivative of -7/6*w**6 + 14*w - 10/3*w**4 - 4*w**5 + 0 + 40/3*w**3 - 5/42*w**7 + 40*w**2. Factor u(f).
-5*(f - 1)*(f + 2)**4
Let a be (-2204)/(-872) + 3/(3/(-4)). Let w = 3/109 - a. Factor 0 + 1/2*l**4 - w*l**3 + 2*l + 0*l**2.
l*(l - 2)**2*(l + 1)/2
Let f(j) be the third derivative of j**8/6720 - j**6/240 + j**5/60 - j**4/32 - 5*j**3/2 + 9*j**2. Let h(u) be the first derivative of f(u). Factor h(v).
(v - 1)**3*(v + 3)/4
Let k(q) = q**3 - 5*q**2 - 1. Let h(t) = 10*t**3 - 134*t**2 + 864*t - 775. Let x(i) = -h(i) + 7*k(i). Solve x(r) = 0.
1, 16
Let s = 34/41 - 27/82. Suppose -1/2*d**4 + d**3 + 0*d + 0 - s*d**2 = 0. Calculate d.
0, 1
Solve -7*q**4 + 3*q**2 - 12*q**2 - 7*q**2 - 14*q**3 + 9*q**4 = 0 for q.
-1, 0, 8
Suppose 49*s**3 - 2*s**4 - 35*s**3 + 4*s + 7*s**4 - 23*s**2 = 0. What is s?
-4, 0, 1/5, 1
Find h, given that -63/2*h**3 + 0*h + 0 - 51/2*h**4 + 27/2*h**2 - 9/2*h**5 = 0.
-3, 0, 1/3
Let j(r) be the first derivative of r**6/360 + r**5/60 + r**4/24 + 14*r**3/3 - 34. Let m(h) be the third derivative of j(h). Solve m(y) = 0.
-1
Let q = 32012/26685 - -2/5337. Factor q*n**2 - 4/5 - 2/5*n.
2*(n - 1)*(3*n + 2)/5
Let -1281*c**2 - 125/2*c**3 + 882*c - 3/4*c**4 + 0 = 0. What is c?
-42, 0, 2/3
Let o(m) be the third derivative of -m**5/60 + 97*m**4/24 - 16*m**3 - 416*m**2. Find g such that o(g) = 0.
1, 96
Suppose 3*g + 520 = 2*r - 2*g, 0 = r + 2*g - 260. Suppose -2*j + 4*a + 135 = 15, 4*j = 4*a + r. Suppose 22*d**2 - j - 8*d**2 + 10*d + 66 = 0. What is d?
-1, 2/7
Let d(k) be the first derivative of -k**4/48 + k**3/12 - k**2/8 - 2*k - 12. Let q(h) be the first derivative of d(h). Factor q(t).
-(t - 1)**2/4
Let g be ((-10)/6)/((-36)/27). Let q be (97/(-776))/(1/(-20)). What is m in 5/4*m**2 + g - q*m = 0?
1
Let c(b) be the second derivative of 8*b**6/15 - 3*b**5 + 16*b**4/3 - 2*b**3 - 4*b**2 + 135*b. Factor c(h).
4*(h - 2)*(h - 1)**2*(4*h + 1)
Let r(i) = -16*i**2 + 77*i + 27. Let f(y) = 176*y**2 - 848*y - 296. Let m(q) = -6*f(q) - 68*r(q). Let m(l) = 0. Calculate l.
-3/8, 5
Suppose -28*m + 30*m = -20. Let i be (-94)/m - 6 - (-4)/(-10). Find f such that -6/5*f**2 - i*f + 6/5 + 3*f**3 = 0.
-1, 2/5, 1
Let v(l) be the second derivative of -l**8/2240 - l**7/840 + l**6/120 - 7*l**4/12 - 10*l. Let r(c) be the third derivative of v(c). Find y, given that r(y) = 0.
-2, 0, 1
Let r = -28 + 41. Suppose 0 = -r*v + 2*v + 22. Factor 2*o + 2/3 + 2/3*o**3 + 2*o**v.
2*(o + 1)**3/3
Let i be 3 + (-333)/117 + (-1230)/(-117). What is x in -16/3*x**2 - i*x**3 - 2/3*x + 0 = 0?
-1/4, 0
Let c(f) = 45*f**2 - 360*f + 775. Let t(q) = 5*q**2 - 40*q + 86. Suppose -12 + 0 = 2*b. Let i(s) = b*c(s) + 55*t(s). Solve i(d) = 0.
4
Factor -156 - 332 - 1008*t + 29 - 864 - 192*t**2.
-3*(8*t + 21)**2
Suppose 0 = -3*w + 29 - 17. Factor -85*r**3 - 36*r**w - 55*r - 105*r**2 - 4*r**4 + 15*r**4 - 10.
-5*(r + 1)**3*(5*r + 2)
Suppose -4 + 6 = 2*z. Let f = z + 0. Factor 2*y**2 + 0 - 2*y**2 - y**2 + f.
-(y - 1)*(y + 1)
Let b be (-2 + 232/140)/((-141)/940). Solve -b*u + 2/7*u**2 + 32/7 = 0.
4
Let g(t) be the third derivative of -11*t**5/60 + t**4/24 + 19*t**3/6 + 13*t**2. Let v(c) = 10*c**2 - 2*c - 18. Let d(x) = -6*g(x) - 7*v(x). Solve d(u) = 0.
-1, 3
Let w = 27282 - 27280. What is r in -1/7*r**w - 2*r - 7 = 0?
-7
Suppose 25*m + 12 = 22*m, -3*h + 2*m + 8 = 0. Factor h - 8/3*y - 2/3*y**2.
-2*y*(y + 4)/3
Let v = -431 + 438. Let z(g) be the second derivative of 1/18*g**3 + 0 - 1/3*g**2 + v*g - 1/60*g**5 + 1/18*g**4. Find c, given that z(c) = 0.
-1, 1, 2
Determine a so that 2/13*a**2 - 40/13 - 2/13*a = 0.
-4, 5
Let h be 21/4 - 1/4. Suppose -80 = y - h*y. Determine s so that -2 - 8*s**2 + 2*s**2 - 2*s**5 - 14*s**2 - 10*s**4 - 13*s + 3*s - y*s**3 = 0.
-1
Let f = 689 + -6193/9. Factor 2/9 + 0*b**2 - f*b**3 + 2/3*b.
-2*(b - 1)*(2*b + 1)**2/9
Let u = 179 + -139. Suppose -17*y = 3*y - u. Let 0 + 1/2*m - 1/2*m**y = 0. What is m?
0, 1
Let u(k) be the first derivative of 14 - 3*k - 1/3*k**3 - 7/4*k**2. Suppose u(r) = 0. What is r?
-2, -3/2
Let l(x) = x**3 + x + 2. Let g(z) = z**4 + 15*z**2 - 2*z - 18. Let k(s) = 4*g(s) + 36*l(s). Factor k(u).
4*u*(u + 1)**2*(u + 7)
Let n(q) be the third derivative of -q**7/2520 - q**6/360 + q**5/40 + 11*q**4/24 - 8*q**2. Let s(g) be the second derivative of n(g). Factor s(i).
-(i - 1)*(i + 3)
Factor 15*y**3 - y**5 - 5*y**2 - 4*y**5 - 2*y**2 - 3*y**2.
-5*y**2*(y - 1)**2*(y + 2)
Let g(n) be the second derivative of n**4/3 + 12*n**3 - 9*n - 20. Suppose g(d) = 0. Calculate d.
-18, 0
Let x be (-9 - (-129)/15) + 8/(-20)*-2. Suppose 9/5*g**3 + x*g**2 + 0*g + 7/5*g**4 + 0 = 0. Calculate g.
-1, -2/7, 0
Let k(x) be the first derivative of x**6/60 - 3*x**5/40 + x**4/8 + 5*x**3/3 - 9. Let v(r) be the third derivative of k(r). Factor v(o).
3*(o - 1)*(2*o - 1)
Suppose -39*h**2 - 231*h + 16 - 29 + 12 + 264*h**2 + 7 = 0. What is h?
2/75, 1
Let f be 75/6*(-50)/(-500) + 0 + -1. Determine w so that -w - 1/4*w**4 - w**3 - f - 3/2*w**2 = 0.
-1
Suppose -2 = -2*l - 3*r - 7, l - 5*r = 17. Factor 2/11*j**l - 4/11 + 2/11*j.
2*(j - 1)*(j + 2)/11
Let m(i) be the third derivative of -i**7/1050 + i**6/600 + 3*i**5/100 - 3*i**4/40 + 173*i**2. Factor m(p).
-p*(p - 3)*(p - 1)*(p + 3)/5
Let j(f) be the third derivative of f**7/105 + 3*f**6/20 + f**5/2 + 7*f**4/12 - 5*f**2 + 14*f. Let j(t) = 0. What is t?
-7, -1, 0
Let z(q) be the first derivative of 4*q**3/3 + 46*q**2 - 96*q + 493. Factor z(o).
4*(o - 1)*(o + 24)
Let q = -340 + 140. Let j = -996/5 - q. Suppose -2/5*r**4 - 4/5*r + 0*r**2 + 2/5 + j*r**3 = 0. What is r?
-1, 1
Suppose -10 = -2*g, 44 = 3*y + 4*g - 9*g. Let z = y - 23. Factor 2/5 - 1/5*a**3 + 3/5*a + z*a**2.
-(a - 2)*(a + 1)**2/5
Let y be 6 + -2 + 8 + -6. Let m be 248/168 + (-2)/y. Determine c, given that 8/7 - m*c + 2/7*c**2 = 0.
2
What is r in -5*r**4 - 48*r**3 - 45 + 40*r - 34*r**3 + 50*r**2 + 42*r**3 = 0?
-9, -1, 1
Suppose -86 = -4*d + 18. Suppose -c = -0 - d. Factor 10*i + c*i**2 + 12*i + 8*i**3 - 1 + 5.
2*(i + 1)*(i + 2)*(4*i + 1)
Let p(y) be the second derivative of 2*y**6/15 - 4*y**5/5 - 26*y**4/3 + 40*y**3 + 450*y**2 - 380*y. Factor p(v).
4*(v - 5)**2*(v + 3)**2
Let y = 10/3 - 8/3. Let f be (4/(-66))/(-21 + 3680/176). Solve -f*q**5 - y*q**2 + 0 + 2/3*q**4 + 2/3*q**3 + 0*q = 0 for q.
-1, 0, 1
Let z(c) be the third derivative of 1/100*c**5 + 0 - 1/10*c**3 - 10*c**2 + 0*c**4 + 0*c. Determine a, given that z(a) = 0.
-1, 1
Let o(i) = 145*i**2 + 1885*i + 5. Let z be o(-13). What is f in -6804/5*f**2 + 18954/5*f - 13122/5 - 74/5*f**4 + 2/5*f**z + 1044/5*f**3 = 0?
1, 9
Let t be (-280)/(-14) - 0/2. Find y such that y**5 - 10*y**4 + t*y**4 - 6*y**4 + 0*y**5 - y**3 - 4*y**2 = 0.
-4, -1, 0, 1
Factor -255*q**2 - 260*q**3 + 43992 - 5*q**4 - 43992.
-5*q**2*(q + 1)*(q + 51)
Let p(f) be the second derivative of f**6/24 + 9*f**5/8 + 5*f**4 + 115*f**3/12 + 75*f**2/8 - 111*f. Find w such that p(w) = 0.
-15, -1
Let t(r) be the second derivative of 2*r**3 - 9/2*r**2 + 1/10*r**6 - 11*r - 3/5*r**5 + 0 + 1/2*r**4. Factor t(l).
3*(l - 3)*(l - 1)**2*(l + 1)
Let j be (28/21 + -1)/((-5)/669). Let u = j - -45. Suppose u*i**4 - 2*i**3 + 0 - 4/5*i**2 + 0*i + 12/5*i**5 = 0. Calculate i.
-2/3, -1/2, 0, 1
Let m(v) = -6*v**4 + 3*v**3 - 3*v**2 - 3*v - 3. Let j(g) = -g**4 - g**3 - g - 1. Let o(a) = -3*j(a) + m(a). Factor o(t).
-3*t**2*(t - 1)**2
Let q(l) be the second derivative of -l**5/110 - l**4/11 + 7*l**3/33 - 145*l. Suppose q(v) = 0. What is v?
-7, 0, 1
Let r(k) be the second derivative of -k**5/4