e of 5*t**6/6 + 3*t**5 - 25*t**4/4 - 5*t**3 + 10*t**2 + 136. Factor d(j).
5*j*(j - 1)**2*(j + 1)*(j + 4)
Let r(w) = 374*w**2 + 376*w - 7. Let f(u) = -374*u**2 - 376*u + 4. Let g(t) = -3*f(t) - 2*r(t). Factor g(b).
2*(b + 1)*(187*b + 1)
Let o(f) be the second derivative of 9*f**6/25 - 6*f**5/25 + 2*f**4/45 + 55*f + 2. Factor o(z).
2*z**2*(9*z - 2)**2/15
Let y be (2/(-5)*-1)/(1/10). Suppose -z = 3*v - 8, -v - 5 = -y*z + 1. Let 1/7*k**5 + 12/7*k**3 + 0 - 10/7*k**v - 6/7*k**4 + 3/7*k = 0. What is k?
0, 1, 3
Let x(t) be the second derivative of t**7/21 - t**6/3 + 4*t**5/5 - 2*t**4/3 - 30*t + 4. Solve x(g) = 0.
0, 1, 2
Suppose -2 + 8 = 3*o. Find v, given that 5*v - 9*v**4 + 9*v**o + 12*v**2 - v + 2*v + 6*v**3 = 0.
-1, -1/3, 0, 2
Let b = -26 - -46. Suppose 0*f = -t + 4*f + 20, 5*t + 4*f = -b. What is v in 0*v**4 + 0*v**2 + t*v + 0*v**3 + 0 - 3/2*v**5 = 0?
0
Determine g so that 24 + 30*g**3 - 3*g**2 - 2*g**4 + 2*g**5 + 0*g**5 - 7*g**2 - 32*g - 12*g**4 = 0.
-1, 1, 2, 3
Let b be 1029*(-21)/(-315)*5/2. Suppose -343/2*d**3 - b*d**2 - 56*d - 6 = 0. Calculate d.
-3/7, -2/7
Let z = 15981 - 15979. Factor -2/7*p**z - 16/7 + 18/7*p.
-2*(p - 8)*(p - 1)/7
Let x(z) be the first derivative of z**8/1008 - z**6/360 - 51*z**2/2 - 7. Let d(p) be the second derivative of x(p). What is m in d(m) = 0?
-1, 0, 1
Factor 50*m - 7*m**2 - 80 + 3*m**2 - m**2.
-5*(m - 8)*(m - 2)
Let s = -2/57 - -9/76. Let l(y) be the third derivative of 0*y - 1/24*y**6 - s*y**3 - 1/672*y**8 - 1/12*y**5 - 2*y**2 - 1/84*y**7 - 5/48*y**4 + 0. Factor l(r).
-(r + 1)**5/2
Determine u so that 3*u**3 - 19*u**2 + 11*u**3 - 4*u**3 + 71*u**2 + 8*u - 6*u**4 + 8*u = 0.
-2, -1/3, 0, 4
Let g(b) be the first derivative of -9*b**4 + 40*b**3 + 46*b**2 + 16*b + 255. Let g(l) = 0. Calculate l.
-1/3, 4
Let h(u) be the third derivative of -u**5/100 - 3*u**4/8 + 98*u**2. Factor h(g).
-3*g*(g + 15)/5
Suppose 5*t + k = 22, 10*t - 11*t + 38 = 5*k. Solve 11/4*n**2 + 1/4 + 5/4*n**t + 7/4*n = 0 for n.
-1, -1/5
Let v(s) = 2*s**2 + 7*s - 1. Let q(w) = 3*w**3 - 18*w**2 - 135*w - 78. Let h(i) = q(i) + 6*v(i). Factor h(z).
3*(z - 7)*(z + 1)*(z + 4)
Let i be (3 - 5/((-5)/(-4)))/1. Let q(x) = -x**4 + x**3 - x**2 - x. Let k(p) = -4*p**4 - 6*p**3 + p**2 + p. Let f(d) = i*k(d) - q(d). Find u such that f(u) = 0.
-1, 0
Let u(m) = 6*m**3 + 60*m**2 - 132*m + 4. Let v(o) = -8*o**3 - 57*o**2 + 131*o - 5. Let g(q) = 5*u(q) + 4*v(q). Factor g(w).
-2*w*(w - 34)*(w - 2)
Factor 14/17*b**2 + 6/17 - 20/17*b.
2*(b - 1)*(7*b - 3)/17
Let y be -3 + 75 + -2 + 2. Let h be (-1)/((-2)/4*y/162). Let 3*x**4 - 3*x**2 + 0 + 0*x + h*x**3 - 9/2*x**5 = 0. What is x?
-1, 0, 2/3, 1
Let j(u) be the third derivative of u**7/1470 - 29*u**6/840 + 37*u**5/70 - 5*u**4/6 - 28*u**3/3 - 137*u**2. Solve j(r) = 0 for r.
-1, 2, 14
Let a(b) be the third derivative of b**6/240 - 3*b**5/40 + 9*b**3 + 91*b**2. Determine d, given that a(d) = 0.
-3, 6
Let r(q) be the third derivative of 1/6*q**3 - 24*q**2 - 1/480*q**6 + 0 + 0*q**4 + 0*q - 1/80*q**5. Let r(z) = 0. What is z?
-2, 1
Let c(t) be the first derivative of -t**5/210 + t**4/84 + 2*t**3/21 - 15*t**2 - 27. Let k(r) be the second derivative of c(r). What is y in k(y) = 0?
-1, 2
Let g(n) be the first derivative of -35/12*n**3 + 0*n - 22 - 15/8*n**4 - 5/4*n**2. Factor g(b).
-5*b*(2*b + 1)*(3*b + 2)/4
Let t be ((-3)/(-6) - -2)*36. Let d be 15/7 + 2 + t/(-42). Factor 0*p - 2/7*p**4 + 0*p**3 + 2/7*p**d + 0.
-2*p**2*(p - 1)*(p + 1)/7
Let h(x) be the first derivative of -x**3 + 390*x**2 - 50700*x - 557. Factor h(p).
-3*(p - 130)**2
Let j(q) = q**4 - q**3 - q**2 + q + 1. Let y = 34 + -24. Let i(w) = -5*w**4 + 15*w**2 - 10*w - 10. Let o(f) = y*j(f) + i(f). Suppose o(t) = 0. Calculate t.
0, 1
Let q(m) be the first derivative of -3*m**4/4 + 4*m**3 + 63*m**2/2 + 146. Factor q(b).
-3*b*(b - 7)*(b + 3)
Let a be (-74019)/(-33390) + (-4)/8. Let r = -2/795 + a. Suppose 2/7*d**2 + 18/7 - r*d = 0. What is d?
3
Let g(t) be the first derivative of -t**4/6 - 5*t**3/3 - 6*t**2 - 46*t - 51. Let h(y) be the first derivative of g(y). Factor h(x).
-2*(x + 2)*(x + 3)
Let q(x) be the first derivative of -2*x**3/27 - 34*x**2/9 - 22*x/3 + 119. Find v such that q(v) = 0.
-33, -1
Let b = -1189/4 - -5953/20. Solve 4/5*r**4 - 4/5*r**2 - 2/5*r + 0*r**3 + 0 + b*r**5 = 0 for r.
-1, 0, 1
Let m(f) be the second derivative of -f**7/399 - 2*f**6/19 - 253*f**5/190 - 70*f**4/19 - 196*f**3/57 + 239*f. Determine l, given that m(l) = 0.
-14, -1, 0
Let o(z) be the first derivative of -z**8/2100 + z**7/175 - z**6/50 + 26*z**3/3 - 23. Let t(k) be the third derivative of o(k). Solve t(p) = 0 for p.
0, 3
Let t(a) be the first derivative of a**3/18 - a**2 + 16*a/3 + 42. Factor t(w).
(w - 8)*(w - 4)/6
Let h(v) be the second derivative of 9*v**5/80 + 7*v**4/24 - v**3/3 + 65*v. Factor h(i).
i*(i + 2)*(9*i - 4)/4
Let l = -23 - -26. Solve -4*u**2 + 97*u**3 + 6 - 76*u**l - 21*u - 2*u**2 = 0 for u.
-1, 2/7, 1
Let y(k) = -3*k**5 - 4*k**4 - 5*k**3 + 2*k + 2. Let s(o) = -16*o**5 - 20*o**4 - 25*o**3 + o**2 + 11*o + 11. Let v(n) = -2*s(n) + 11*y(n). Factor v(p).
-p**2*(p + 1)**2*(p + 2)
Let n(x) = -35*x**2 - 40*x. Let b = 25 - 21. Let r(o) = 9*o**2 + 10*o. Let v(a) = b*n(a) + 15*r(a). Let v(t) = 0. Calculate t.
-2, 0
Let o(c) = -c + 4. Let h be o(2). Suppose -4*z - 45 = -9*z. Factor 0*n**3 + z*n**h + 6*n**2 - 4 - 6*n - 4*n**3 - 6*n.
-(n - 2)**2*(4*n + 1)
Let g = 1467/4 + -733/2. Solve -g*k**2 + 0 + 3/4*k**5 + 1/4*k**4 + 1/2*k - 5/4*k**3 = 0 for k.
-1, 0, 2/3, 1
Let j be ((-10)/36)/((-170)/102). Let f(i) be the third derivative of -j*i**3 + 0 + 0*i - 1/240*i**5 + 6*i**2 - 1/24*i**4. Factor f(d).
-(d + 2)**2/4
Solve -966 - 1018 - 184*r + 4*r**2 + 2164 = 0.
1, 45
Let d(c) be the second derivative of c**6/40 - c**5/20 - 5*c**4/8 - 3*c**3/2 + 3*c**2 + 3*c. Let p(q) be the first derivative of d(q). Factor p(r).
3*(r - 3)*(r + 1)**2
Let t(m) be the second derivative of m**5/100 - 2*m**4/15 - m**3/30 + 4*m**2/5 - m - 35. What is r in t(r) = 0?
-1, 1, 8
Let h(d) be the first derivative of 0*d - 1/2*d**2 + 0*d**4 + 0*d**3 + 3 + 0*d**5 + 1/240*d**6. Let o(q) be the second derivative of h(q). Solve o(n) = 0 for n.
0
Let u(t) = -20*t - 100. Let s be u(-5). What is o in 4/3*o + 0 + s*o**2 - 4/3*o**3 = 0?
-1, 0, 1
Let q(x) be the second derivative of -x**4 + 537*x**3/2 - 201*x**2 + 695*x. Factor q(b).
-3*(b - 134)*(4*b - 1)
Let v(u) be the third derivative of u**7/672 - u**5/24 + 7*u**3 - 5*u**2 - u. Let b(k) be the first derivative of v(k). Suppose b(g) = 0. What is g?
-2, 0, 2
Let z(v) be the second derivative of v**6/200 - v**5/25 - 12*v**2 - 10*v. Let a(s) be the first derivative of z(s). Let a(q) = 0. Calculate q.
0, 4
Let c(n) be the third derivative of n**7/168 + n**6/30 + 3*n**5/80 - 5*n**4/48 - n**3/3 + 4*n**2 + 3. Determine f so that c(f) = 0.
-2, -1, 4/5
Solve 36/5 - 6/5*r**2 - 69/5*r = 0.
-12, 1/2
Let l(o) be the second derivative of -6*o**2 - 10*o + 1/4*o**4 + 0 + 0*o**3. Factor l(v).
3*(v - 2)*(v + 2)
Let m(q) = -q + 2. Let h be m(2). Find z, given that 5*z**3 - 3*z**3 + h*z**2 - 4*z + 2*z**2 + 2*z**3 - 2*z**4 = 0.
-1, 0, 1, 2
Let j(o) = -2*o**3 + 2*o**2. Let r(i) = 9*i**3 - 14*i**2 + 8*i. Let c(k) = -4*j(k) - r(k). Factor c(a).
-a*(a - 4)*(a - 2)
Let y(k) be the first derivative of -2*k**3/3 - 3*k**2/2 - 3*k + 16. Let v(p) = -p**2 - 1. Let s(r) = -2*v(r) + 2*y(r). Solve s(c) = 0.
-2, -1
Let t(u) = 2*u**2 + 30*u + 28. Let k(w) = -w - 1. Let b(i) = -12*k(i) - 2*t(i). Factor b(n).
-4*(n + 1)*(n + 11)
Let q(h) be the second derivative of -h**4/30 + 26*h**3/5 - 1521*h**2/5 + 18*h - 1. Factor q(i).
-2*(i - 39)**2/5
Suppose -5*q - 2*h = -h - 7, -5*q + 2*h = -16. Factor -10*l**4 + 3*l**5 - 13*l + q*l**5 - 4*l + 10*l**2 + 12*l.
5*l*(l - 1)**3*(l + 1)
Let j(y) = -y**3 + 3*y**2 + 2*y - 2. Let t(i) = -3*i**3 + 6*i**2 + 4*i - 5. Let f be 8/6*(-9)/6. Let a(g) = f*t(g) + 5*j(g). Find h, given that a(h) = 0.
-2, -1, 0
Let x(o) be the second derivative of o**6/105 - 9*o**5/70 + o**4/7 + 16*o**3/21 + 268*o + 1. Suppose x(s) = 0. Calculate s.
-1, 0, 2, 8
Let q = 390 - 387. Let u(r) be the third derivative of 2*r**2 + 0*r + 0 + 2/15*r**q - 1/300*r**6 + 1/60*r**4 - 1/75*r**5. Factor u(l).
-2*(l - 1)*(l + 1)*(l + 2)/5
Suppose -17*q + 3*s + 30 = -13*q, 0 = -3*q - 4*s + 10. Let k be 1/q - (-3)/6. Factor -2/9*