(p) be the second derivative of p**5/4 + 5*p**4/3 - 70*p**3/3 + 80*p**2 + 325*p + 3. Factor n(i).
5*(i - 2)**2*(i + 8)
Let l(q) be the third derivative of 0 + 0*q - 5/2*q**3 - 1/40*q**6 + 5*q**2 + 9/8*q**4 - 3/20*q**5. Factor l(k).
-3*(k - 1)**2*(k + 5)
Suppose 2*r**3 - 3*r**3 - 200*r - 5*r**3 + 3*r**3 + 35*r**2 - 2000 + 2*r**3 = 0. Calculate r.
-5, 20
Let v(o) be the third derivative of 0 + 1/15*o**6 + 1/15*o**5 - 269*o**2 + 0*o**4 - 2/15*o**7 + 0*o**3 + 1/21*o**8 + 0*o. Suppose v(x) = 0. What is x?
-1/4, 0, 1
Let r(h) be the first derivative of -1/35*h**5 + 108/7*h**2 + 9/14*h**4 + 11 + 0*h - 36/7*h**3. Suppose r(a) = 0. Calculate a.
0, 6
Let b(w) = w**3 + 7*w**2 + 15*w + 9. Let u be b(-3). Suppose -22*c = 3*j - 26*c - 25, u = -c - 4. Let 2*f**j + 1/3*f**4 + 8/3*f**2 - 3 - 2*f = 0. Calculate f.
-3, -1, 1
Let n(h) be the first derivative of h**5 - 94 + 15/2*h**2 - 10*h + 5/3*h**3 - 15/4*h**4. What is u in n(u) = 0?
-1, 1, 2
Let l = -2430 + 7291/3. Let b(s) be the second derivative of 3/10*s**5 + 0 + 0*s**3 - 1/15*s**6 - 28*s + 0*s**2 - l*s**4. Factor b(f).
-2*f**2*(f - 2)*(f - 1)
Let v be 8 - (9 - 7) - 3. Find m such that -3*m + 3929 + v*m**2 + 5*m**3 + 7*m + 7*m**2 - 3977 - 7*m**3 = 0.
-2, 3, 4
Let 39/4*i**5 + 3*i + 17/2*i**4 - 89/4*i**3 + 0 + i**2 = 0. Calculate i.
-2, -1/3, 0, 6/13, 1
Let v(i) = i**3 + 2*i**2 - 4*i - 30. Let h be v(3). Let s(b) be the first derivative of 23 + 9/2*b**2 - b**h - 6*b. Factor s(p).
-3*(p - 2)*(p - 1)
Suppose 0 = -2*p + 4*j + 1264, -869 + 2105 = 2*p + 3*j. Factor 59 - 16*y**3 + 38*y**2 - p*y - 234*y**2 - 203.
-4*(y + 6)**2*(4*y + 1)
Let p(v) = -6*v**3 - 34*v**2 - 60*v - 46. Let h(a) = a**3 + 2*a**2 - a. Let w(n) = 21*h(n) + 3*p(n). Suppose w(i) = 0. What is i?
-2, -1, 23
Suppose 528 - 28*k**3 + 5*k**3 - 7995*k**2 + 12*k**4 - 400*k - 57*k**3 + 7455*k**2 = 0. Calculate k.
-3, -2, 2/3, 11
Let s(x) be the second derivative of -1/4*x**4 + 1/10*x**6 + x + 0*x**2 - 3 + x**3 + 1/14*x**7 - 9/20*x**5. Factor s(b).
3*b*(b - 1)**2*(b + 1)*(b + 2)
Determine a, given that -6450/7*a**4 + 2544*a + 30020/7*a**3 + 250/7*a**5 + 2432/7 + 42376/7*a**2 = 0.
-2/5, 8, 19
Let p(f) be the first derivative of -f**4/4 + 74*f**3/3 - 145*f**2/2 + 72*f + 240. Factor p(y).
-(y - 72)*(y - 1)**2
Let z = 96097/154 - 8675/14. Find r, given that 800/11 - 960/11*r + 368/11*r**2 - z*r**3 + 2/11*r**4 = 0.
2, 10
Let m(b) be the third derivative of 0*b**4 + 0*b**5 + 1/280*b**7 + 1/896*b**8 - 1/40*b**6 + 0*b**3 + 110*b**2 + 0*b + 0. Determine c so that m(c) = 0.
-4, 0, 2
Let h(p) = -7*p**4 - 149*p**3 - 957*p**2 + 3*p - 9. Let t(j) = 34*j**4 + 746*j**3 + 4786*j**2 - 14*j + 42. Let l(b) = -14*h(b) - 3*t(b). Factor l(o).
-4*o**2*(o + 8)*(o + 30)
Let k(a) be the third derivative of 1/60*a**4 + 2 - 1/200*a**6 - 1/1050*a**7 + 1/300*a**5 + 0*a**3 - 33*a**2 + 0*a + 1/1680*a**8. Factor k(f).
f*(f - 2)*(f - 1)*(f + 1)**2/5
Let w = -565/192 + 1759/576. Solve 3*z**2 - 1/3*z**4 + 108 - 5*z**3 + w*z**5 + 72*z = 0 for z.
-3, 6
Suppose -21*a + 2*a + 33 + 62 = 0. Let k(q) be the second derivative of -1/10*q**6 + 0*q**3 - 3/10*q**a - 1/4*q**4 - 31*q + 0 + 0*q**2. Factor k(j).
-3*j**2*(j + 1)**2
Suppose 12*m - 111 = -25*m. What is o in -426*o**2 - 312*o**4 - 12 + 3*o**5 + 109*o + 20*o**5 + 25*o**5 + 579*o**m + 14*o = 0?
1/4, 1, 4
Factor 168*u - 4*u**2 + 445 + 275 + 1548290*u**3 - 1548292*u**3.
-2*(u - 10)*(u + 6)**2
Determine p, given that -14*p**2 - 170822*p**3 - 19*p**2 + 170819*p**3 - 90*p = 0.
-6, -5, 0
Let c(h) be the second derivative of 3*h**7/28 + 31*h**6/15 + 539*h**5/40 + 69*h**4/2 + 73*h**3/3 - 28*h**2 - 2*h - 18. Suppose c(k) = 0. What is k?
-7, -4, -2, -1, 2/9
Factor -259 + 105 - 290*h + 12*h**2 + 154.
2*h*(6*h - 145)
Let k = -56600/3 + 18867. Factor 4/3*i + 5/3*i**3 + 0 - 8/3*i**2 - k*i**4.
-i*(i - 2)**2*(i - 1)/3
Suppose -3*p - 39 = 3*w, -5*w + 6*w = -3*p - 17. Let d be 1 + -5*w/25. Let -2/5*s**2 - 32/5 - d*s = 0. Calculate s.
-4
Let d(f) be the first derivative of -5*f**4/4 + 270*f**2 - 2160*f + 4268. Factor d(y).
-5*(y - 6)**2*(y + 12)
Suppose -22745/3*m + 4550/3 - 25/3*m**2 = 0. What is m?
-910, 1/5
Determine l so that -735*l + 4*l**2 + 320 + 1436*l - 617*l - 7*l**2 + 7*l**2 = 0.
-16, -5
Let a = -54/34525 + 331494/34525. Factor -24*h + 3*h**3 - 3*h**4 + 15*h**2 + a - 3/5*h**5.
-3*(h - 1)**3*(h + 4)**2/5
Suppose 0 - 32 = 4*z. Let d(j) = j**3 + 10*j**2 + 18*j + 18. Let w be d(z). Find q such that -16*q - 36*q**3 + 21*q**2 + 29*q**w - 2*q**2 = 0.
0, 2/3
Let b(v) be the third derivative of -v**5/210 + 91*v**4/3 - 231868*v**3/3 - 17*v**2 + v. Let b(p) = 0. Calculate p.
1274
Find a, given that 74*a + 289 - 3*a**2 - 694 + 91*a - 21*a = 0.
3, 45
Suppose 2*i = 3*i + 5*l + 6, 18 = 3*i - 3*l. Let x(w) be the second derivative of 8/7*w**3 + 9/7*w**2 + 8/21*w**i + 0 + 16*w. Solve x(m) = 0 for m.
-3/4
Let w be (1/5)/(23*15/5175). Find y such that 1 - 5/3*y - 1/9*y**w + 7/9*y**2 = 0.
1, 3
Suppose -x - 4 = l, 5*l = -1171*x + 1175*x + 34. Suppose -1/2*i**l + 1/2*i**4 - 9/4*i**3 + 0 + 1/4*i**5 + 2*i = 0. What is i?
-4, -1, 0, 1, 2
Let o(h) be the first derivative of -h**5/360 + h**4/36 - 31*h**2 - 35. Let d(m) be the second derivative of o(m). Solve d(l) = 0 for l.
0, 4
Let l(m) be the first derivative of m**6/195 - m**5/130 - m**4/39 + 150*m - 232. Let q(o) be the first derivative of l(o). Factor q(h).
2*h**2*(h - 2)*(h + 1)/13
Let t(b) be the second derivative of -45/4*b**4 + 0 - 82*b - 6*b**2 - 243/20*b**5 + 16*b**3. Factor t(r).
-3*(r + 1)*(9*r - 2)**2
Let k(x) = -4*x**5 - x**4 + x**2 + x. Let c(q) = -49*q**5 - 14*q**4 + 13*q**3 + 2*q**2 + 12*q. Let r(v) = c(v) - 12*k(v). Find f, given that r(f) = 0.
-5, 0, 1, 2
Suppose u**3 + 69 + 191*u - 32*u**2 - 3 + 200 + 42*u = 0. Calculate u.
-1, 14, 19
Let d(i) = -16*i**4 + 21*i**3 - 45*i**2 + 13*i. Let s(h) = 5*h**4 + h**3 + 3*h. Let x(p) = -d(p) - 3*s(p). Determine b, given that x(b) = 0.
0, 1, 22
Let f be 8 - ((-3468)/1632)/((-2)/(3 - -1)). Factor 3/8*n**3 + 15/4*n**2 - 3/8*n - f.
3*(n - 1)*(n + 1)*(n + 10)/8
Let d(i) be the first derivative of i**5/50 - 113*i**4/40 - i**3/10 + 341*i**2/20 - 113*i/5 - 1618. Solve d(c) = 0 for c.
-2, 1, 113
Let 7/6*g**4 + 1/6*g**5 - 3*g + 0 + 13/6*g**3 - 1/2*g**2 = 0. Calculate g.
-3, -2, 0, 1
Suppose -176/5*u - 288/5 + 27/5*u**3 - 1/5*u**5 - 8/5*u**4 + 146/5*u**2 = 0. What is u?
-9, -4, -1, 2, 4
Suppose 0*j + 1/6*j**4 + 0 - 5/3*j**3 + 8/3*j**2 = 0. What is j?
0, 2, 8
Let s = -15642 - -15647. Let b(f) be the first derivative of 0*f + 28 + 2/15*f**s + 1/18*f**4 + 0*f**2 + 0*f**3. Solve b(o) = 0.
-1/3, 0
Factor -1688/5*q**2 - 2/15*q**3 + 3378/5*q - 5068/15.
-2*(q - 1)**2*(q + 2534)/15
Let o(k) be the first derivative of 3*k**4/4 - 1429*k**3 + 1529385*k**2/2 + 1533675*k + 4509. Determine w, given that o(w) = 0.
-1, 715
Suppose 15*q = 8*q + 14. Let -q*y**2 + 18*y + 18 + 31 - 65 = 0. What is y?
1, 8
Factor -3*b + 55 + 3*b - 55 - 46*b**2 + b**4 - 21*b**3.
b**2*(b - 23)*(b + 2)
Let r(q) be the third derivative of 0 + 15/4*q**3 + 0*q + 1/24*q**5 + 5/8*q**4 + 215*q**2. Factor r(w).
5*(w + 3)**2/2
Let j(f) be the third derivative of 17/156*f**4 - 37*f**2 - 1/195*f**5 - 8/39*f**3 + 0 + 0*f. Find n such that j(n) = 0.
1/2, 8
Let h(r) be the first derivative of r**6/15 + 16*r**5/25 + 21*r**4/10 + 12*r**3/5 - 672. What is a in h(a) = 0?
-3, -2, 0
Let f(o) be the second derivative of -o**6/105 - o**5/30 + o**4/42 + 15*o**2/2 + 3*o - 7. Let u(z) be the first derivative of f(z). Factor u(d).
-2*d*(d + 2)*(4*d - 1)/7
Suppose 0 = -2*y, -8 = -3*j + 4*j - 2*y. Let w be j + (-84)/(-18) + 5*1. Find m such that -10/3*m**3 + w*m**4 + 0 + 10/3*m - 5/3*m**2 = 0.
-1, 0, 1, 2
Let z = 29 - 34. Let r be (-10047)/z - 14/35. Factor -16*i**3 - 2 - r*i**4 + 2005*i**4 + 2 - 12*i**2.
-4*i**2*(i + 1)*(i + 3)
Let u = -8017539/5 + 1603515. Determine r, given that 0 - u*r**3 + 54/5*r**4 - 21/5*r**5 - 6/5*r**2 + 9/5*r = 0.
-3/7, 0, 1
What is m in 241/6*m + 158/3 + 1/2*m**2 = 0?
-79, -4/3
Let x be (-48)/3 + (20825/35)/17 + -17. Factor -15*l + 5/4*l**x - 65/4.
5*(l - 13)*(l + 1)/4
Let t(d) be the third derivative of d**6/108 + d**5/15 - 11*d**4/108 - 4*d**3/9 + 235*d**2. What is i in t(i) = 0?
-4, -3/5, 1
Let q(a) = -a**3 - 2*a**2. Let t(v) = 2*v**5 + 6*v**4 - 5*v**3 + 4*v**2 + 8*v. Suppose -7 = -w + u, w - 37 = -3*w + u. Let d(g)