. Let d(w) be the third derivative of u*w - 1/780*w**6 + 1/195*w**5 - 30*w**2 - 1/156*w**4 + 0*w**3 + 0. Factor d(i).
-2*i*(i - 1)**2/13
Suppose h - 2*l - 15 = -2*h, -2*h + 4*l + 18 = 0. Suppose -8*z - h*d = -5*z, 4*z - 3*d - 14 = 0. Factor 0 + 2/3*f**z + 1/3*f + 1/3*f**3.
f*(f + 1)**2/3
Let k = -439811 + 3518489/8. Factor -3/4*n**4 + 0 - k*n**5 - 13/8*n**3 - 1/2*n - 3/2*n**2.
-n*(n + 1)**2*(n + 2)**2/8
Determine b, given that 79*b - 100 - 31/2*b**2 + 1/2*b**3 = 0.
2, 4, 25
Let m(v) = 3*v + 80. Let r be (-543)/21 + (-2 - 52/(-28)). Let h be m(r). Factor -345*a**2 + 2*a**5 - 7*a**4 + 3*a**5 + 15*a**3 - 8*a**4 + 340*a**h.
5*a**2*(a - 1)**3
Suppose 50 = -5*x + 5*r, 7*x - 3*r + 0 + 22 = 0. Let 0 + 3/5*k**3 + 18/5*k**x - 21/5*k = 0. Calculate k.
-7, 0, 1
Find r such that 19/4*r**2 - 141/4*r + 1/4*r**3 + 225/4 = 0.
-25, 3
Let b(m) be the second derivative of 14/15*m**6 - 4/21*m**7 + 0 + 5/3*m**4 - 9/5*m**5 + 0*m**2 - 2/3*m**3 - 56*m. Factor b(l).
-4*l*(l - 1)**3*(2*l - 1)
Let l = 38320 + -191594/5. Find z such that -2*z**2 + l*z**4 + 2*z**3 + 4/5 - 2*z = 0.
-2, -1, 1/3, 1
Let g(h) = -7*h**2 + 794*h + 243041. Let v(p) = p**2 + 24*p + 1. Let q(a) = -g(a) - 8*v(a). Factor q(f).
-(f + 493)**2
Let h = 588 + -584. Suppose 6*v + 6*v**3 - h*v**2 + 4*v**4 - 14*v**3 - 10*v**3 + 18*v + 4*v**5 - 10*v**3 = 0. Calculate v.
-3, -1, 0, 1, 2
Let s = 78553/471102 - 6/78517. Find h such that 0 + s*h**3 + 1/6*h**2 + 0*h = 0.
-1, 0
Let r(d) be the first derivative of -d**5/20 - 3*d**4/2 - 10*d**3 - d**2/2 + 14*d - 102. Let a(x) be the second derivative of r(x). Factor a(j).
-3*(j + 2)*(j + 10)
Let d(r) be the first derivative of -6*r - 6/5*r**3 + 1/10*r**4 - 148 + 23/5*r**2. Factor d(v).
2*(v - 5)*(v - 3)*(v - 1)/5
Let o(r) be the third derivative of -r**6/1440 - 11*r**5/10 - 263*r**4/24 - 394*r**3/9 + 2563*r**2 + r. Factor o(z).
-(z + 2)**2*(z + 788)/12
Solve 0 - 144/5*s**2 - 447/5*s**3 + 12/5*s + 144/5*s**4 + 87*s**5 = 0.
-1, -2/5, 0, 2/29, 1
Let l = -555933 + 555935. Suppose 65/3*v - 34/3*v**l - 6 + v**3 = 0. Calculate v.
1/3, 2, 9
Let y(r) = 459*r**2 - 665*r - 8. Let k(s) = -172*s**2 + 222*s + 3. Let h(j) = 8*k(j) + 3*y(j). Factor h(p).
p*(p - 219)
Let s(m) be the first derivative of -4*m**3/3 - 328*m**2 + 1328*m + 2703. Factor s(t).
-4*(t - 2)*(t + 166)
Suppose -6940*q**2 - 95 - 333 + 438 + 1695*q = 0. Calculate q.
-2/347, 1/4
Factor 1425*d**4 - 48*d**5 + 14609*d**3 - 14474*d**3 + 0*d**2 - 112*d**5 + 0*d**2.
-5*d**3*(d - 9)*(32*d + 3)
Let b be 580/435 + -4 + 6 + (-56)/18. Factor 0 - 76/9*x**2 - b*x**3 - 722/9*x.
-2*x*(x + 19)**2/9
Let c(a) = -8*a**5 - 410*a**4 + 978*a**3 + 1010*a**2 - 1078*a - 588. Let n(y) = y**5 + y**3 + 7*y - 1. Let j(i) = -c(i) - 12*n(i). Let j(u) = 0. What is u?
-1, -1/2, 1, 3, 100
Let o = 110/7 + -529/35. Let i = 2266 - 11222/5. Factor o*d**2 + i - 36/5*d.
3*(d - 6)**2/5
Let s(x) be the third derivative of x**8/112 - x**7/5 - 87*x**6/40 - 37*x**5/5 - 19*x**4/2 - 177*x**2 + 4*x. What is u in s(u) = 0?
-2, -1, 0, 19
Let i(w) = -62*w**3 + w**2 - 221*w + 288. Let j(l) = 11*l**3 + 37*l - 48. Let f(p) = -6*i(p) - 34*j(p). Factor f(o).
-2*(o - 3)*(o - 2)*(o + 8)
Suppose 0 = 4*i - 10 + 2. Suppose -2*r + 1 = 2*d - 3, i*r + 6 = 0. Factor -d*g**5 - 6*g**2 + 8*g**2 + g**5 - 6*g**4.
-2*g**2*(g + 1)**2*(2*g - 1)
Let w be (-1)/(-14*(-114)/(-6916)). Determine t so that -w*t - 10 - 1/3*t**2 = 0.
-10, -3
Let f(c) be the third derivative of 7*c**6/360 - 103*c**5/180 - 71*c**4/36 - 16*c**3/9 - 2824*c**2. Find b, given that f(b) = 0.
-1, -2/7, 16
Let r(t) be the second derivative of 10*t**7/7 - 9*t**6/2 + 23*t**5/12 + 115*t**4/18 - 20*t**3/3 + 3710*t. What is k in r(k) = 0?
-3/4, 0, 2/3, 1, 4/3
Let q = -31 + 33. Let j(f) be the first derivative of -5 - 5/3*f**3 - 15*f + 25/2*f**q - 5/4*f**4. Factor j(m).
-5*(m - 1)**2*(m + 3)
Let -1/5*g**3 + 9 - 39/5*g + 11/5*g**2 = 0. What is g?
3, 5
Solve 13420/3*n + 5/3*n**2 + 9004820/3 = 0 for n.
-1342
Let p = -124 + 1366/11. Let j be (-2686)/119*(-21)/33 - (15 - 3). Factor j*x**2 + 16/11*x + p + 12/11*x**3.
2*(x + 1)**2*(6*x + 1)/11
Let t(n) = -n**2 - 12*n - 43. Let d be t(-5). Let f be (-68)/204*(2 + d/1). Factor 2/15*g - 4/15 - 2/15*g**3 + 4/15*g**f.
-2*(g - 2)*(g - 1)*(g + 1)/15
Suppose 5*w - 6*w - 2 = 0, 0 = -5*g - 2*w + 6. Factor -162860*z**g + 162860*z**2 + 3*z**5.
3*z**5
Let u(t) be the first derivative of 7*t**6/2 - 468*t**5/5 + 3345*t**4/4 - 2210*t**3 - 3888*t**2 + 2688*t + 10332. Solve u(f) = 0.
-1, 2/7, 7, 8
Let m be (-4)/3 - (30 - (-14190)/(-450)). Determine d, given that 1/5 + m*d**2 - 2/5*d = 0.
1
Factor -222*r - 606*r + 375*r - 1875*r**2 - 192 - 273*r - 474*r.
-3*(25*r + 8)**2
Let g = 28 - -188. Let y = -198 + g. Suppose 3/2*w**2 + y*w + 54 = 0. Calculate w.
-6
Let z(m) be the first derivative of -12*m - 16*m**3 + 21 - 6*m**4 - 4/5*m**5 - 20*m**2. Factor z(j).
-4*(j + 1)**3*(j + 3)
Let h(a) be the second derivative of -a**9/90720 + a**8/6720 - a**7/1890 + a**4/6 - 19*a**2/2 + 2*a - 17. Let l(w) be the third derivative of h(w). Factor l(c).
-c**2*(c - 4)*(c - 2)/6
Find i such that 11918*i**2 - 11913*i**2 - 7*i - 135*i - 3*i = 0.
0, 29
Let j = 2/6773 + 6763/33865. Let u(h) be the third derivative of -1/105*h**7 - j*h**5 + 1/15*h**6 - 4*h**2 + 0 + 1/3*h**4 - 1/3*h**3 + 0*h. Factor u(l).
-2*(l - 1)**4
Let q(v) be the third derivative of -v**5/150 + 7*v**4/8 - 26*v**3/15 + 2461*v**2. Determine l, given that q(l) = 0.
1/2, 52
Suppose 108*f - 13*f - 94 = 951. Let h(i) be the third derivative of 1/20*i**4 - 1/300*i**6 + 0*i + 0 + 0*i**5 + 2/15*i**3 + f*i**2. Factor h(p).
-2*(p - 2)*(p + 1)**2/5
Let s be 44/22*(6/(-10) + (-574)/(-140) + -2). Factor 288/17*m - 48/17*m**2 + 2/17*m**s + 0.
2*m*(m - 12)**2/17
Let y(q) = 2*q**4 + q**3 - q**2 + 3*q - 3. Let l(n) = -n**5 - 529*n**4 - 70754*n**3 - 70226*n**2 + 3*n - 3. Let t(i) = 3*l(i) - 3*y(i). Factor t(x).
-3*x**2*(x + 1)*(x + 265)**2
Let y = -1/3105 - -46579/12420. Let j(b) be the first derivative of 0*b + 0*b**2 + 4*b**5 + y*b**4 - 5/3*b**3 + 7. Solve j(o) = 0.
-1, 0, 1/4
Let r be 169/((-94809)/374)*(-150)/14. Let l = 5 + -3. Find k, given that 0 - 2/7*k**3 - r*k - 20/7*k**l = 0.
-5, 0
Let h(j) be the first derivative of -j**3 - 33*j**2/2 + 936*j + 1824. Let h(c) = 0. Calculate c.
-24, 13
What is z in -10*z**2 + 1152*z - 7*z**2 + 165888 + 47*z**2 - 28*z**2 = 0?
-288
Let k(y) be the third derivative of 13 + 2*y**2 + 0*y - 1/12*y**5 - 15*y**3 + 95/24*y**4. What is a in k(a) = 0?
1, 18
Suppose -3*q - 30 = -4*g, -2*g = -g + 5*q + 4. Let u be 55/30 + 1/g. Solve -63*m + 40*m**u - 19*m - 5*m**3 + 2*m = 0 for m.
0, 4
Let y(b) = -3*b**4 - 120*b**3 - 729*b**2 - 1014*b - 516. Let z(m) = 4*m**4 + 121*m**3 + 747*m**2 + 1013*m + 516. Let d(q) = -7*y(q) - 6*z(q). Solve d(w) = 0.
-2, -1, 43
Let c(d) be the third derivative of 4*d**2 + 1/180*d**5 - 2/9*d**3 + 0 + 1/24*d**4 + 49*d. Factor c(h).
(h - 1)*(h + 4)/3
Suppose -3*r + 788 - 770 = 0. Let q(p) = -66*p**2 + 36*p + 19. Let l(d) = -34*d**2 + 18*d + 10. Let y(w) = r*q(w) - 11*l(w). Factor y(c).
-2*(c - 1)*(11*c + 2)
Let y be (-60320)/(-200) + (0 - 2). Let x = 300 - y. Factor 1/5*o**3 + x*o + 0 + 3/5*o**2.
o*(o + 1)*(o + 2)/5
Suppose -h = -5*d - 3, 10 = 2*d - h + 13. Suppose 4*c - 22 = 2*g - 6, -2*g - c + 4 = d. Factor 0*v**2 - 2*v**5 + 0*v - 4/7*v**4 + 0*v**3 + g.
-2*v**4*(7*v + 2)/7
Factor -2/7*p**5 - 1376*p - 4800/7 - 2448/7*p**3 - 7264/7*p**2 - 316/7*p**4.
-2*(p + 2)**4*(p + 150)/7
What is v in 0 + 4/5*v**5 + 12/5*v**4 + 0*v + 0*v**3 - 16/5*v**2 = 0?
-2, 0, 1
Let n(l) be the second derivative of 3*l**4/2 - 41*l**3/9 + 14*l**2/3 + 2*l + 27. Factor n(c).
2*(c - 1)*(27*c - 14)/3
Let n(u) = 3*u**2 + 10*u - 2074. Let f be n(25). Let r(o) be the first derivative of -9*o**2 + 3/4*o**4 + 0*o + o**3 - f. Solve r(k) = 0.
-3, 0, 2
Determine j, given that 123*j**2 - 6*j**4 + 1086*j**2 + 2028*j + 80*j**4 + 31*j**4 - 729*j**3 - 18*j**4 - 3*j**5 = 0.
-1, 0, 4, 13
Factor 416/7*h + 2/7*h**2 + 21632/7.
2*(h + 104)**2/7
What is y in 3*y - y - 8*y + 99 - 8*y**2 - 3*y = 0?
-33/8, 3
Suppose 132/7*y - 1872/7 + 2/7*y**2 = 0. Calculate y.
-78, 12
Let n(m) be the third derivative of -m**6/24 + 40*m**5/3 - 36865*m**4/24 + 186515*m**3/3 - 3916*m**2 + 2*m. Factor n(r).
-5*(r - 73)**2*(r - 14)
Let u(y) be the first derivative of y**5/100 - y**4/30 - 7*y**3/3