(g). Factor j(s).
5*s*(s + 7)
Suppose 0 = -60962*g + 61013*g. Factor 2/7*x**4 + g + 0*x + 8/7*x**2 + 10/7*x**3.
2*x**2*(x + 1)*(x + 4)/7
Let t = -28009 + 28039. Let u(i) be the first derivative of 5/3*i**3 + 2 - t*i + 5/2*i**2. Factor u(d).
5*(d - 2)*(d + 3)
Let j(s) = 2*s**3 - 178*s**2 + 446*s + 462. Let o(k) = 3*k**3 - 217*k**2 + 447*k + 462. Let l(r) = -5*j(r) + 4*o(r). Find y, given that l(y) = 0.
-21, -1, 11
Suppose 0 = -c + 5*t - 4, 0 = c - 4*c - 2*t + 5. Let q be 4*((-6)/(-4) - c). Solve v**2 + 192 + v**q + v**2 - 48*v = 0.
8
Let w(n) = n**2 + 14*n + 17. Let p be w(-13). Let z(q) = -q + 4. Let b be z(-5). Let -7*f + p*f - 2*f**3 - b*f**4 + 7*f**2 + 2*f**2 + 5*f**3 = 0. What is f?
-1, 0, 1/3, 1
Suppose -3*o = -336 - 69. Let t = 139 - o. Let l(m) = -3*m**4 + m**3 - m**2 + 3*m. Let n(v) = -3*v**4 + 3*v. Let y(x) = t*n(x) - 3*l(x). Solve y(z) = 0.
-1, 0, 1
Let z(r) be the second derivative of -2/3*r**3 + 1/78*r**4 + 13*r**2 + 3 + 3*r. Solve z(q) = 0.
13
Let s(k) be the second derivative of -1/28*k**4 + 9/14*k**3 + 2 - k - 3*k**2. Factor s(z).
-3*(z - 7)*(z - 2)/7
Let g(p) = 892*p**2 - 812*p + 338. Let a(x) = -x**2 - 28*x. Let q(v) = -10*a(v) - g(v). Factor q(r).
-2*(21*r - 13)**2
Suppose -m - 27 = 194*p - 199*p, -m + p = 3. Factor -2*g**m + 1/2*g**4 + 3*g**2 - 2*g + 1/2.
(g - 1)**4/2
Let d(p) be the second derivative of -p**6/270 + 26*p**5/45 - 338*p**4/9 - 13*p**3/3 + 4*p. Let s(z) be the second derivative of d(z). Factor s(i).
-4*(i - 26)**2/3
Let z = -230 - -228. Let x(s) = -s**4 - s**3 + s**2 - 1. Let v(q) = -2*q**5 + 29*q**4 - 3*q**3 + 3*q**2 - 3. Let k(j) = z*v(j) + 6*x(j). Factor k(m).
4*m**4*(m - 16)
Let c = -413799 + 413799. Let c + 24/7*j + 22/7*j**2 - 2/7*j**3 = 0. What is j?
-1, 0, 12
Let z be (-34)/(-3)*(-9)/18*-3. Suppose -z*i = 25*i - 43*i. Determine s so that -2/17*s**2 - 2/17*s**5 + 2/17*s**4 + 2/17*s**3 + 0 + i*s = 0.
-1, 0, 1
Factor 19782050*p - 62214547250/3 + 2/3*p**3 - 6290*p**2.
2*(p - 3145)**3/3
Let v(n) = -33*n - 376 + 2610 - 182*n + 181 - 20*n**2. Let g(q) = 15*q**2 + 216*q - 2416. Let x(p) = 5*g(p) + 4*v(p). Determine w, given that x(w) = 0.
22
Let f(n) be the first derivative of n**4/30 - 28*n**3/15 + 31*n**2/3 - 76*n/5 + 3. Solve f(y) = 0.
1, 3, 38
Suppose -2*q**4 - 6370*q**2 - 1446 - 386 + 6376*q**2 - 1300*q + 916*q**3 - 1444*q = 0. Calculate q.
-1, 2, 458
Let d = 748 + -606. Suppose -2*i - d*q = -138*q + 2, 7 = -i - 5*q. Suppose 2/3*p**i + 0 - 2*p**2 + 0*p = 0. What is p?
0, 3
Let b(l) = -l**3 - 4*l**2 + 4*l + 7. Let y be b(-5). Factor -5*f**2 - y*f + 20*f - 10*f - 8*f + 5*f**3.
5*f*(f - 2)*(f + 1)
Let v(r) be the second derivative of -r**5/480 - r**4/48 - 21*r**2/2 + 28*r. Let x(o) be the first derivative of v(o). Solve x(c) = 0.
-4, 0
Let v be (-2)/10 + 1712/(-40). Let r = 45 + v. What is h in 2*h**5 + 8*h + h**2 + 4*h**4 - 9*h**2 - 6*h**3 + 0*h**r = 0?
-2, 0, 1
Let z(f) be the third derivative of f**6/300 - 101*f**5/75 - 41*f**4/4 - 3*f**2 - f - 585. Factor z(v).
2*v*(v - 205)*(v + 3)/5
Let j(q) be the second derivative of -1/55*q**6 + 1/77*q**7 + 0*q**2 + 1/22*q**4 - 3/110*q**5 + 0*q**3 + 2*q - 1. Factor j(t).
6*t**2*(t - 1)**2*(t + 1)/11
Let l = 233925/30646 - -9/2786. Factor -l*s + 2/11*s**2 + 882/11.
2*(s - 21)**2/11
Let k be 4/14 + 3/(-84). Let i = 128095 + -512379/4. Factor -i + 1/4*q - k*q**3 + 1/4*q**2.
-(q - 1)**2*(q + 1)/4
Let z(u) be the third derivative of -u**5/60 - 11*u**4 + 265*u**3/6 + 4*u**2 - 76*u + 1. Suppose z(j) = 0. Calculate j.
-265, 1
Let c be 391/(-85) + (-4)/10. Let a be (c/(-10) + -1)*-6. Suppose -4*d + 2*d + 2*d + a*d - d**2 = 0. What is d?
0, 3
Let x be (-4)/1*(-7)/4. Let b(m) = m**3 - 6*m**2 - 9*m + 14. Let i be b(x). Let -1/6*p**2 + 1/6 + i*p = 0. Calculate p.
-1, 1
Let t be ((-1)/(-12))/((-56)/42*34/(-136)). Let q = 38 + -37. Find b, given that 0*b + q - t*b**2 = 0.
-2, 2
Let n(k) = -60*k - 175. Let s be n(-12). Let c = s - 543. Factor 0 - 1/2*l - 1/4*l**c.
-l*(l + 2)/4
Suppose -2*g - 5 = 3*f, -14*g - 2*f = -11*g. Determine d so that d**4 - 10*d**2 - 4*d**3 - 13*d**2 + 18*d**g = 0.
-1, 0, 5
Suppose -52*s = -502 + 3622. Let p be (136/s - -2)/((-7)/35). Factor -20/9*r + 16/9*r**2 + p*r**3 - 8/9.
4*(r - 1)*(r + 2)*(3*r + 1)/9
Let s(v) be the second derivative of v**6/15 + v**5/10 - v**4/6 - v**3/3 - 3*v - 287. Factor s(x).
2*x*(x - 1)*(x + 1)**2
Let b(c) = 29*c - c**2 - 38*c + 23*c - 38. Let w be b(9). Factor 3*v**5 + 4*v**4 - v**4 - w*v**4 - 2*v**3 + 3*v**4.
v**3*(v - 1)*(3*v + 2)
Let m(t) be the second derivative of -14*t + 0 - 2/3*t**3 - 8*t**2 + 1/6*t**4. Factor m(s).
2*(s - 4)*(s + 2)
Let q(t) be the first derivative of -12 + 0*t + 3*t**2 + 0*t**3 + 1/210*t**5 + 1/42*t**4. Let n(g) be the second derivative of q(g). Solve n(m) = 0 for m.
-2, 0
Factor 1296*c - 37776*c**2 - 262 + 37780*c**2 + 1554.
4*(c + 1)*(c + 323)
Suppose 204*c = 167*c. Find v such that 0*v + 4/9*v**5 + 0*v**2 + 4/9*v**4 - 8/9*v**3 + c = 0.
-2, 0, 1
Let j(g) = g**4 + 8*g**3 - 18*g**2 + 3*g - 4. Let k(p) = 4*p**4 + 40*p**3 - 88*p**2 + 14*p - 22. Let r(d) = 26*j(d) - 5*k(d). What is b in r(b) = 0?
-3, -1/3, 1
Let c(l) = -7*l**2 - 2*l - 25. Let y be c(5). Let w be y/(-28) + (-3)/2 + 2. Factor -3*u**2 + 51 + w*u - 2*u - 56 + 2*u**2.
-(u - 5)*(u - 1)
Let i be (1 - 1)*11*45/(-990). Suppose 4 = 4*p - 4. Factor 3/2 + i*t - 3/2*t**p.
-3*(t - 1)*(t + 1)/2
Solve 98*o**3 - 103*o**3 + 24*o**2 + 21*o**2 + 175 - 715 = 0.
-3, 6
Let g(d) be the first derivative of 0*d - 4 + 1/10*d**5 + 15/8*d**4 + 0*d**2 + 13/3*d**3. Factor g(q).
q**2*(q + 2)*(q + 13)/2
Let f(s) = -119*s**4 + 88*s**3 - 353*s**2 + 357*s - 116. Let j(r) = 108*r**4 - 90*r**3 + 352*r**2 - 356*r + 116. Let k(c) = -10*f(c) - 11*j(c). Factor k(a).
2*(a - 1)**3*(a + 58)
Let w(x) be the second derivative of 43*x**5/10 + 89*x**4/6 + 49*x**3/3 + 3*x**2 + 11*x + 2. Suppose w(g) = 0. What is g?
-1, -3/43
Let g = -343663 - -1718329/5. Solve 0*s + 6/5*s**2 + 34/5*s**4 - 26/5*s**3 + 0 - g*s**5 = 0.
0, 3/7, 1
Let z = -15373811/17 + 904363. Suppose 14/17*p**4 - z*p - 132/17*p**2 + 40/17*p**3 + 54/17 = 0. What is p?
-3, 1/7, 3
Suppose 707*r - 698*r = 81. Suppose 4*m = -r*m + 26. Factor -5/8*b**m + 0 - 1/8*b**3 - 3/4*b.
-b*(b + 2)*(b + 3)/8
Let o(u) be the third derivative of 44*u**2 - 1/15*u**5 + 0*u**3 + 2*u**4 + 0*u + 0. Solve o(t) = 0 for t.
0, 12
Suppose 0 = -10*y - 138 + 508. Suppose -y = -19*w + 1. Factor -1/5*i**w - 1/5 - 2/5*i.
-(i + 1)**2/5
Determine a, given that 330*a**3 + 139*a - 115*a**3 - 110*a**3 + 562*a**2 - 699*a - 107*a**3 = 0.
0, 1, 280
Let p(r) be the third derivative of -r**6/30 - 13*r**5/15 + 11*r**4/2 + 30*r**3 - 139*r**2 - r. Factor p(t).
-4*(t - 3)*(t + 1)*(t + 15)
Let u(a) be the second derivative of -5*a**7/17 + 418*a**6/255 - 311*a**5/85 + 4*a**4 - 97*a**3/51 - 2*a**2/17 + 7599*a. What is x in u(x) = 0?
-2/105, 1
Let q(p) = p**2 + 10*p + 5. Let i be q(-7). Let f = 30 + i. Factor f*c**3 + 5*c**5 - 55*c**4 - 45*c**2 + 0*c**5 + 81*c**3.
5*c**2*(c - 9)*(c - 1)**2
Let r(s) be the first derivative of -s**5/20 - 3*s**4/4 + 11*s**2/2 - 2*s + 77. Let a(d) be the second derivative of r(d). Solve a(k) = 0 for k.
-6, 0
Let v(t) be the second derivative of -t**5/30 - 19*t**4/18 - 16*t**3/9 + 12*t**2 + 3695*t. What is y in v(y) = 0?
-18, -2, 1
Let d(r) = 41*r - 405. Let k be d(10). Suppose k*s - 1 = 2*u, u - 5*s = -3*s. Factor -2/5*j**u - 18/5 + 12/5*j.
-2*(j - 3)**2/5
Suppose 5*x - 7*q = -2*q - 10, x - 4*q = -17. Factor 46*s - 18*s - 8*s**2 - 5*s**3 - 16 + s**x.
-4*(s - 1)**2*(s + 4)
Let c(p) be the third derivative of p**5/80 - 3*p**4/32 - 275*p**3/4 + 71*p**2 - 7*p + 1. Factor c(u).
3*(u - 25)*(u + 22)/4
Suppose 66*n + 76 = 68*n. Let h be 4/n - 4828/(-3230). Determine o so that 4/5 + 14/5*o**3 + 22/5*o**2 - 26/5*o**4 + h*o**5 - 22/5*o = 0.
-1, 1/4, 1, 2
Let c be 20/30*(-4 + (-138)/(-12)) + -2. Determine d so that 12/5*d**2 - 8/5*d**4 + 0*d - 2/5*d**5 + 0 - 2/5*d**c = 0.
-3, -2, 0, 1
Let w be -3 + (57 - 2) - (-12 + 12). Suppose 6*t = w - 16. Factor -t*k + 3/2*k**2 + 9/2.
3*(k - 3)*(k - 1)/2
Let b(z) be the first derivative of 49 + 4/3*z**3 + 1/4*z + z**2. Solve b(w) = 0 for w.
-1/4
Suppose h + 5*u - 53 = 0, 2*h = -u - 83 + 99. Let p = -438/5 - -88. Determine s, given that 2*s**h + 0 + 0*s**2 - p*s**5 - 8/5*s + 0*s**4 = 0.
-2, -1, 0, 1, 2
Let b(s) = s**2 