3 - 601/5*z**2.
(z - 65)*(z - 2)*(9*z + 2)/5
Let d(q) be the third derivative of -q**7/840 + q**6/120 - q**4/6 - 19*q**3/6 - q**2 + 10. Let b(t) be the first derivative of d(t). Factor b(m).
-(m - 2)**2*(m + 1)
Let v(l) be the second derivative of l**2 - 68*l - 1/20*l**5 + 1/6*l**3 + 0 - 1/4*l**4 + 1/30*l**6. Let v(u) = 0. What is u?
-1, 1, 2
Let j(r) = -8*r**3 + 1480*r**2 + 1490*r. Let h(l) = 50*l**3 - 8880*l**2 - 8943*l. Let y(x) = -2*h(x) - 13*j(x). Suppose y(p) = 0. What is p?
-1, 0, 371
Let z(l) be the third derivative of -l**7/28 + 317*l**6/480 - 17*l**5/240 - 7*l**4/16 + 7*l**2 - 35*l. Determine p so that z(p) = 0.
-1/3, 0, 2/5, 21/2
Let s(q) be the first derivative of 106 + 18*q**2 + 0*q - 4/3*q**3. Factor s(i).
-4*i*(i - 9)
Let i(z) be the first derivative of 1/48*z**4 + 1/960*z**6 + 15 - 37/3*z**3 - 1/120*z**5 + 0*z**2 + 0*z. Let m(v) be the third derivative of i(v). Factor m(j).
(j - 2)*(3*j - 2)/8
Let r(n) = 10*n + 8. Let h be r(9). Suppose 6*p + 3*p**4 + 3*p**5 - 98 - 3*p**2 - 9*p**3 + h = 0. Calculate p.
-2, -1, 0, 1
Let v(l) = -l**2 - 7*l + 21. Let n be (-3)/30*86 + (-8)/20. Let d be v(n). Let 2/5*g**d - 1/5*g**5 - 1/5*g + 0*g**2 + 0 + 0*g**4 = 0. Calculate g.
-1, 0, 1
Let d(y) be the second derivative of -11*y**4/4 + 475*y**3/2 - 129*y**2 - 6*y - 925. Factor d(b).
-3*(b - 43)*(11*b - 2)
Let f = -78301/2 + 316463/8. Let t = f - 407. Factor t*w - 1/4*w**2 + 0.
-w*(2*w - 3)/8
Let s(a) = -2*a + 4. Let w be s(-5). Suppose -5*d = 3*n - w, -4*d - 2 = -0*d - 2*n. Factor -1 - 5*g**4 + 10*g**2 - d - 3.
-5*(g - 1)**2*(g + 1)**2
Suppose -267 + 68 = -105*t + 116. Let z(s) be the third derivative of 34*s**2 + 0 - 1/8*s**4 + 0*s - 1/40*s**6 + 0*s**t - 1/10*s**5. Factor z(v).
-3*v*(v + 1)**2
Let t(r) be the third derivative of -r**6/40 + 23*r**5/20 - 55*r**4/4 + 68*r**3 + 2525*r**2 - r. Factor t(u).
-3*(u - 17)*(u - 4)*(u - 2)
Let j(w) be the second derivative of w**4/42 + 80*w**3/21 + 156*w**2/7 - 1537*w. Factor j(x).
2*(x + 2)*(x + 78)/7
Factor 1/3*i**3 + 1/3*i**2 + 5 - 17/3*i.
(i - 3)*(i - 1)*(i + 5)/3
Factor 0 + 27/2*h**3 + 3/8*h**5 - 9/2*h**4 - 12*h**2 + 0*h.
3*h**2*(h - 8)*(h - 2)**2/8
Let m = -1974 + 7901/4. Let b(o) be the first derivative of m*o**4 + 0*o + o**5 + 23 - 5/3*o**3 - 5/2*o**2. Let b(q) = 0. What is q?
-1, 0, 1
Let i(g) be the third derivative of 19*g**2 + 0*g + 0 - 1/30*g**5 - 11/12*g**4 + 4*g**3. Factor i(s).
-2*(s - 1)*(s + 12)
Let z(i) = 10*i**3 - 71*i**2 - 5*i + 87. Let d be z(7). Suppose 7/4*v**2 - 3/2*v + 3/4*v**d - 1/4*v**5 - 3/4*v**4 + 0 = 0. Calculate v.
-3, -2, 0, 1
Suppose 40 = 39*z - 155. Let f(v) = v**3 + 4*v**2 - 6*v - 3. Let y be f(-5). Solve 20*j + 4 - 10 - 11 - z*j**2 + y = 0.
1, 3
Factor 1/4*z**2 + 938961/4 - 969/2*z.
(z - 969)**2/4
Suppose -39*g + 696 = 2061. Let q be 0 + -3 + 3 + (-60)/g. Suppose -6/7*l - 27/7*l**2 + 0 - q*l**3 = 0. What is l?
-2, -1/4, 0
Let u(z) be the second derivative of 77*z + 0*z**2 - 1/32*z**4 + 0 + 0*z**3 - 1/240*z**6 - 1/40*z**5. Determine g so that u(g) = 0.
-3, -1, 0
Suppose 48*y = 45*y + 6. Suppose 4*q**4 + 528*q**y - 182*q - 28*q**2 - 243*q**3 + 21*q**4 + 42*q - 142*q**3 = 0. Calculate q.
0, 2/5, 1, 14
Suppose -5*v - 16 = -26. Let g(d) be the second derivative of 0 + 1/60*d**5 - 13*d - 1/36*d**4 - 1/18*d**3 + 1/6*d**v. Factor g(x).
(x - 1)**2*(x + 1)/3
Let t(c) be the second derivative of -c**5/25 + 47*c**4/5 - 186*c**3/5 + 278*c**2/5 + 74*c + 1. Find d, given that t(d) = 0.
1, 139
What is i in -8*i**2 - 26/3 - 17*i + 1/3*i**3 = 0?
-1, 26
Suppose 0 = 5*t + 2*o - 276, -86 = -5*t + 5*o + 204. Let z = t - 54. Factor 0 + 0*v + 0*v**z + 0*v**3 - 3/5*v**5 - 6/5*v**4.
-3*v**4*(v + 2)/5
Suppose 8*i = 4*w + 3*i - 8, 2*w = 3*i + 4. Let k(h) be the second derivative of 1/48*h**4 + 0 - 1/8*h**3 + 5*h + 0*h**w. Solve k(b) = 0 for b.
0, 3
Determine w so that -5*w**4 - 295*w**2 - 257*w**3 - 37*w**3 + 300 - 11*w**3 + 626*w - 321*w = 0.
-60, -1, 1
Let x(r) be the first derivative of 2*r**5/13 + 4*r**4/13 - 6*r**3/13 - 8*r**2/13 + 8*r/13 - 2478. Solve x(z) = 0.
-2, -1, 2/5, 1
Let j(m) = m**4 - 23*m**3 - 3*m**2 + 21*m - 16. Let y(v) = -v**4 + 23*v**3 + 4*v**2 - 20*v + 24. Let g(c) = -3*j(c) - 2*y(c). Suppose g(l) = 0. Calculate l.
-1, 0, 1, 23
Let i = -634 + 636. Determine t, given that -345*t - 7*t**2 + 13*t**2 - 2*t**2 - 9*t**i = 0.
-69, 0
Suppose -14*s + 18*s + 15 = -5*z, -12 = -5*s + 4*z. Factor s + 14/5*q**2 - 49/5*q - 1/5*q**3.
-q*(q - 7)**2/5
Suppose 3*z = 2*r - 3*r + 24, 2*r + 3*z - 39 = 0. Factor 33*y - 15*y - 12*y**2 + 9 - r*y.
-3*(y - 1)*(4*y + 3)
Let y = 58 - 90. Let l be (-21)/28*y/12. Factor 8 + 44*u - 38*u**3 - 8*u**l + 3*u**3 - 2*u**3 - 7*u**3.
-4*(u - 1)*(u + 1)*(11*u + 2)
Let v(i) = i**2 - 72*i + 1280. Let k be v(40). Let y(u) be the first derivative of 5/4*u**4 - 5/6*u**6 + 12 + 0*u**2 - u**5 + k*u + 5/3*u**3. Factor y(g).
-5*g**2*(g - 1)*(g + 1)**2
Let a(d) be the first derivative of d**5/30 + 5*d**4/2 + 29*d**3/3 - 255*d**2/2 + 70. Let j(g) be the second derivative of a(g). Find m such that j(m) = 0.
-29, -1
Suppose -2439/4*j + 609/2 - 3/4*j**3 + 306*j**2 = 0. Calculate j.
1, 406
Let r(k) = -121*k**4 - 15031*k**3 - 507065*k**2 - 143648*k. Let i(v) = -30*v**4 - 3758*v**3 - 126766*v**2 - 35912*v. Let w(c) = 9*i(c) - 2*r(c). Factor w(q).
-4*q*(q + 67)**2*(7*q + 2)
Suppose 0 = -5*c + 104 - 149. Let p be 3*3/c + 3. Suppose 3/7*i**p + 1/7*i**4 - 5/7*i + 5/7*i**3 - 4/7 = 0. Calculate i.
-4, -1, 1
Let p(b) be the second derivative of b**6/285 + 26*b**5/95 + 225*b**4/38 - 52*b**3/57 - 676*b**2/19 + 599*b. Solve p(z) = 0 for z.
-26, -1, 1
Let 40*w - 5/3*w**4 - 320/3 - 10*w**3 + 100/3*w**2 = 0. Calculate w.
-8, -2, 2
Let h(x) be the second derivative of -x**7/14 - x**6/5 + 9*x**5/20 + 2*x**4 + 2*x**3 + 17*x + 1. Determine z, given that h(z) = 0.
-2, -1, 0, 2
Let w(k) be the second derivative of 0*k**2 + 0 - 1/5*k**4 + 6/5*k**3 - 28*k + 1/100*k**5. What is x in w(x) = 0?
0, 6
Let z(a) be the first derivative of -a**3 + 7*a**2/4 + 3027. Factor z(h).
-h*(6*h - 7)/2
Let q be (-10)/(-45) - 341/279. Let w be q + (4 - 3) - (-15)/20. Suppose -1/4*j**3 - 3/4*j**2 - w*j - 1/4 = 0. What is j?
-1
Let p(s) = -s**3 + 110*s**2 - 31*s - 455. Let t(a) = -a**3 + 166*a**2 - 45*a - 685. Let d(l) = 7*p(l) - 5*t(l). Factor d(f).
-2*(f - 2)*(f + 2)*(f + 30)
Factor -1/6*i**4 + 98/3 - 587/6*i + 195/2*i**2 - 193/6*i**3.
-(i - 1)**3*(i + 196)/6
Suppose -123597*c + 36*c**4 - 123379*c + 40*c**3 - 144*c**2 + 4*c**5 + 246752*c = 0. Calculate c.
-7, -2, 0, 2
Suppose 1536 + 194/3*o**2 - 2/3*o**3 - 1600*o = 0. What is o?
1, 48
Let f = -15/16679 - -233581/83395. Find b, given that -2/5*b**3 + f*b**2 + 16/5 - 28/5*b = 0.
1, 2, 4
Let i(q) = 32*q**3 - 3713*q**2 + 113*q + 348. Let w be i(116). Factor -676/5*l**2 + 0*l + w - 52/5*l**3 - 1/5*l**4.
-l**2*(l + 26)**2/5
Let a = 303 + -295. Suppose 2*h - 2*f + a = 5*h, -2*f = -2*h + 2. What is w in 8/3*w**5 + h*w + 0 - 14*w**4 + 22*w**3 - 38/3*w**2 = 0?
0, 1/4, 1, 3
Let x(w) be the first derivative of -27 + 135/2*w**2 + 100/3*w**3 + 15/4*w**4 + 50*w. Factor x(f).
5*(f + 1)*(f + 5)*(3*f + 2)
Let a be ((-1650)/(-105))/11 - (-8)/(-28). Let n(s) be the first derivative of 26/21*s**3 + a*s + 2/35*s**5 + 12/7*s**2 + 3/7*s**4 + 21. What is k in n(k) = 0?
-2, -1
Let k be -1 - (-34)/10 - 236/590. Suppose -205*d + 200*d = k*q + 4, q - 1 = -d. Factor 0 + 20/3*n**4 - 22*n**q - 32/3*n - 2/3*n**5 + 80/3*n**2.
-2*n*(n - 4)**2*(n - 1)**2/3
Find a, given that 0*a**2 - 118/9*a**3 + 0 + 0*a + 2/9*a**4 = 0.
0, 59
What is f in -3/5*f**3 - 48 - 294/5*f - 57/5*f**2 = 0?
-10, -8, -1
Let d(f) = 17*f**2 + 277*f + 176. Let m(y) = 8*y**2 + 138*y + 88. Suppose -2*w - 44 = 5*a, 3*w - 19 = 6*a - 5*a. Let z(l) = a*m(l) + 4*d(l). Factor z(t).
-4*(t + 22)*(3*t + 2)
Factor -7*y**3 - 660*y**2 + 2*y**3 - 31770*y - 161602 - 24448 + 7065*y.
-5*(y + 10)*(y + 61)**2
Let t(v) = -18*v - 10. Let f be t(-3). Suppose 2*x = -7*a + 11*a + f, -5*a = -5. Factor 12 - 13*z**2 - 7*z**2 + x*z**2 + 16*z.
4*(z + 1)*(z + 3)
Suppose -i = i + 4*k - 8, 4*i - 3*k = 5. Suppose -3 + 7 = i*b. Factor -1/4*c**b + 0 - 1/4*c.
-c*(c + 1)/4
Find g, given that -720 - 202*g**2 + 17*g**3 + 972*g - 11*g**3 - 2*g**3 - 54*g**2 = 0.
1, 3, 60
Let l be (-4)/14 + 14848/224. Suppose 0 = -t + 1, -3*r + l = -4*t - 353. Factor -11 - 94*f - 13 - r*f + 147