25
Let j(i) = -i**2 - 4*i - 2. Let k be j(-1). Let z be (0 + 0)*k + 2. Factor -8*l**2 + 6*l**3 + 3*l**z - 13*l**2 - 2*l**3 + 8*l.
2*l*(l - 4)*(2*l - 1)
Let a = 12 - -723. Let w = a - 733. Solve 2*n**w - 20/11 - 106/11*n = 0.
-2/11, 5
Let c = 547326 + -547323. Find w, given that 1/3*w**c + 1/3*w**2 + 1 - 5/3*w = 0.
-3, 1
Let s = -111757 + 335365/3. Factor s*y + 0 - 2/3*y**2.
-2*y*(y - 47)/3
Let d = -48 - -55. Let c(n) = -2*n**2 + 14*n + 7. Let q be c(d). Factor 85*y**2 + q*y**3 + 5*y**3 - 89*y**2 - 16*y**5.
-4*y**2*(y + 1)*(2*y - 1)**2
Let y(p) be the second derivative of -p**6/30 + 43*p**5/20 - 87*p**4/2 + 640*p**3/3 - 400*p**2 - 12471*p. Factor y(s).
-(s - 20)**2*(s - 2)*(s - 1)
Let b(i) = 281*i - 4493. Let x be b(16). Let 12/5*j**2 + 3/5*j**x + 18/5 - 33/5*j = 0. Calculate j.
-6, 1
Let d(s) = -33*s**3 + 54*s**2 - 18*s - 18. Let r(l) = -2*l**3 - l**2 - l - 1. Suppose -10*z + 20*z = 10. Let g(q) = z*d(q) - 18*r(q). Factor g(j).
3*j**2*(j + 24)
Suppose 3*k = 13*k - 7*k + 11*k. Let z(o) be the third derivative of k*o - 5*o**2 - 13/42*o**4 + 0 + 169/21*o**3 + 1/210*o**5. Factor z(h).
2*(h - 13)**2/7
Suppose 3*j - 155 + 27 = -2*r, 5*r - 20 = 0. Suppose -52*n + 64 = -j. Suppose 399/8*b + 9/8*b**3 - 123/8*b**n + 147/8 = 0. What is b?
-1/3, 7
Let s = -50 + 54. Factor -37 - 23*r**2 + 5*r**3 + 19*r + 33 - 17*r**s + 20*r**4.
(r - 1)**2*(r + 4)*(3*r - 1)
Let s(r) be the first derivative of r**6/240 + r**5/30 - r**4/16 - 3*r**3/2 - 6*r**2 + 2*r - 45. Let y(u) be the second derivative of s(u). Factor y(x).
(x - 2)*(x + 3)**2/2
Let n(p) be the second derivative of p**5/40 - p**4/3 + 13*p**3/12 - 3*p**2/2 - 2709*p. Let n(z) = 0. Calculate z.
1, 6
Let n(y) be the second derivative of -y**5/12 + 449*y**4/9 - 2149*y**3/18 + 179*y**2/3 - 1543*y. Determine j, given that n(j) = 0.
1/5, 1, 358
Let c(p) = 10*p**2 + 20322*p + 19. Let k(r) = r**2 + 2258*r + 2. Let q(w) = -2*c(w) + 19*k(w). Determine g so that q(g) = 0.
0, 2258
Let b be -2*2/4*-3. Let s = 1624 + -1620. Solve -4*j + j + s*j**b - j + 4 + 0*j - 4*j**2 = 0 for j.
-1, 1
Let w = -39 - -43. Suppose -2*r + w*n = -72, -3*r - r + 184 = 2*n. Solve 44*s**2 - 6*s**2 - 4*s**5 + 45*s**2 + r*s**3 + 32*s - 11*s**2 = 0.
-2, -1, 0, 4
Suppose 72 = -0*f + 18*f. Suppose c - 3*k = -4*k + f, 2*k = 5*c + 8. Suppose c*j + 0 + 16/5*j**3 - 4/5*j**2 - 7/5*j**5 - j**4 = 0. Calculate j.
-2, 0, 2/7, 1
Let x = 70 - 67. Suppose 8*o = 4*o - 2*t + 50, -x*o + 39 = 3*t. Solve -10*r**2 + 6 + o*r**2 - 2*r + 10*r = 0.
-3, -1
Let u(o) be the third derivative of -o**5/30 + 125*o**4/4 - 372*o**3 - o**2 - 49*o + 1. Factor u(x).
-2*(x - 372)*(x - 3)
Let b(c) = -2 + 3 - 1 - c. Let g be b(-4). Factor 35*i**4 - 15*i**g + 14*i + 75*i**3 + 80*i**2 + i - 10.
5*(i + 1)**2*(i + 2)*(4*i - 1)
Let o be 3/12 + -1 + -2 + 3. Let t(g) be the first derivative of 3/32*g**4 - 16 + 0*g + o*g**3 + 3/16*g**2. Factor t(s).
3*s*(s + 1)**2/8
Let r(k) = k + 364. Let x be r(-47). Suppose 0 = -x*h + 316*h + 3. Factor -24*z - 12 + 15/4*z**4 + 3*z**h + 3/4*z**5 - 12*z**2.
3*(z - 2)*(z + 1)*(z + 2)**3/4
Let v(s) be the first derivative of 15*s**6/2 - 30*s**5 - 535*s**4/4 + 2480*s**3/3 - 1230*s**2 + 720*s + 454. Let v(d) = 0. What is d?
-4, 2/3, 3
Let g(z) be the first derivative of z**4/4 - 16*z**3/3 - 57*z**2/2 + 138. Let o be g(19). Find t, given that o + 8/5*t + 2/5*t**2 = 0.
-4, 0
Let s(q) be the second derivative of -q**4/3 + 536*q**3/3 - 534*q**2 - 33*q. Factor s(k).
-4*(k - 267)*(k - 1)
Let f(z) be the first derivative of 13*z**4/10 + 412*z**3/15 + 160*z**2 - 256*z/5 - 2302. Find k, given that f(k) = 0.
-8, 2/13
Let c(h) be the second derivative of h**4/96 + 3*h**3/16 - 7*h - 3. Factor c(p).
p*(p + 9)/8
Let a = -3278 + 3282. Let l(t) be the first derivative of 0*t**2 - 10/3*t**3 + 25/4*t**a + 3*t**5 + 0*t - 4. Let l(c) = 0. What is c?
-2, 0, 1/3
Let z(o) be the third derivative of -o**7/2520 - o**6/72 - 2*o**5/15 + 8*o**4/9 - 49*o**3/6 + 14*o**2. Let b(i) be the first derivative of z(i). Factor b(s).
-(s - 1)*(s + 8)**2/3
Factor 0 + 3/7*x**3 - 696/7*x - 162/7*x**2.
3*x*(x - 58)*(x + 4)/7
Let q be (3/9)/((-1)/15) - -10. Factor 45 - 25 + q*z**2 + 83*z - 3*z + 55.
5*(z + 1)*(z + 15)
Suppose -2*g + 5*g - 19 = -5*i, -2*i + 2*g = 2. Suppose 2 = b + v - 5, -2*b = -2*v - i. Factor b*s**4 + 27*s**3 + 72*s**2 - 91 + 10*s**3 - 17 - 5*s**3.
4*(s - 1)*(s + 3)**3
Factor -1617815*b**4 + 147*b**2 + 1617776*b**4 - 3*b**5 - 70*b**3 - 35*b**3.
-3*b**2*(b - 1)*(b + 7)**2
Let i be 8/28 + 2/(-7). Let v(k) be the third derivative of -1/330*k**5 + i + 10*k**2 + 0*k**3 + 0*k + 0*k**4. Factor v(x).
-2*x**2/11
Factor -4*d**3 - 212/3*d + 88/3*d**2 + 56.
-4*(d - 3)*(d - 2)*(3*d - 7)/3
Let k(q) = -5*q**4 + 48*q**3 + 3*q**2 + 3. Let u(o) = o**3 + o**2 + 1. Let g be 1*3/(((-90)/(-5))/6). Let s(n) = g*k(n) - 3*u(n). Factor s(f).
-5*f**3*(f - 9)
Let o(a) be the first derivative of -a**6/135 - 2*a**5/45 + 5*a**4/54 + 33*a + 22. Let k(h) be the first derivative of o(h). Factor k(z).
-2*z**2*(z - 1)*(z + 5)/9
Let z be 0 + 8/(32/12). Suppose -z - 5*l - 10*l**2 - 3 + l**3 + 8*l**2 + 4*l**2 = 0. What is l?
-3, -1, 2
Let b be (-3)/7*(173/(-346) - (-10)/(-12)). Factor -8/7*s**2 + 8/7 + b*s - 4/7*s**3.
-4*(s - 1)*(s + 1)*(s + 2)/7
Let s = -117 - -122. Suppose -2*g = -0*w - 4*w + 12, s*g = 0. Factor 2/9*b**w + 2/9*b**2 - 2/9*b - 2/9.
2*(b - 1)*(b + 1)**2/9
Let a(r) = -34*r**2 - 84197*r + r**3 + r**3 + 84400*r. Let j(c) = 4*c**3 - 70*c**2 + 405*c. Let d(u) = -5*a(u) + 3*j(u). Factor d(n).
2*n*(n - 10)**2
Suppose 4/5*y**4 + 196/5*y**2 + 228/5*y + 12*y**3 + 88/5 = 0. Calculate y.
-11, -2, -1
Let r(k) be the first derivative of 184/7*k + 2/21*k**3 - 48/7*k**2 - 164. Factor r(a).
2*(a - 46)*(a - 2)/7
Factor 576*r - 1144 + 56 - 151*r**2 - r**3 + 3*r**3 + 63*r**2 + 4*r**2.
2*(r - 34)*(r - 4)**2
Let h(a) = 80*a**3 + 45*a**2 - 325*a - 575. Let f(u) = 64 + 36*u - 9*u**3 + 7*u**2 - 2*u**2 - 4*u**2 - 6*u**2. Let x(c) = -35*f(c) - 4*h(c). Factor x(l).
-5*(l - 3)*(l + 2)**2
Let h(i) = -i - 5. Let q be h(-7). Suppose 8*r + 3120 = 3144. Factor -5*b**q + 4*b**2 - r*b**3 - 5*b**2 + 0*b**2.
-3*b**2*(b + 2)
Suppose -4 = -5*u + 7*u - s, s = -2. Let r(y) = -11*y**2 + 12*y. Let q(t) = -4*t**2 + 4*t. Let n(j) = u*r(j) + 8*q(j). Suppose n(d) = 0. Calculate d.
0, 4
Let f = -187/168 - -65/56. Let j(d) be the second derivative of 1/35*d**6 + 0 - 1/7*d**2 - 16*d + 1/7*d**3 - 1/35*d**5 - 1/147*d**7 - f*d**4. Factor j(q).
-2*(q - 1)**4*(q + 1)/7
Let t(w) = -w**2 - w + 2. Let o be t(0). Factor 1185*d**o - 10 + 30 + 1721*d**3 - 1496*d**3 + 304*d.
(d + 5)*(15*d + 2)**2
What is z in -537*z - 1397*z + 3*z**2 + 7880*z + 3107865 - 161622 = 0?
-991
Let k(r) be the third derivative of 0 - 30*r**2 + 77/120*r**5 - 481/16*r**4 - 1/240*r**6 + 0*r - 507/4*r**3. Determine b so that k(b) = 0.
-1, 39
Let k(g) be the second derivative of 5*g**4/54 + 36*g**3 + 388*g**2/9 - 1554*g. Factor k(p).
2*(p + 194)*(5*p + 2)/9
Let x(v) = v**4 - 13*v**3 - 43*v**2 + 133*v - 2. Let w(a) = 5*a**4 - 90*a**3 - 300*a**2 + 930*a - 15. Let q(i) = -2*w(i) + 15*x(i). Factor q(n).
5*n*(n - 3)**2*(n + 3)
Let g(p) be the second derivative of p**5/20 - 17*p**4/12 + 5*p**3 - 35*p + 3. Let j be g(15). Factor -1/4*s**3 + 0*s**2 + 0*s + j.
-s**3/4
Let t(a) = a**3 - 15*a**2 - 9*a - 8. Let j be t(16). Suppose -224*c + 11*c**3 - 43*c**3 - 260*c**2 + j*c**2 - c**4 - c**4 - 98 = 0. What is c?
-7, -1
Let q(g) be the second derivative of 23*g**6/105 - 116*g**5/35 + 148*g**4/21 + 544*g**3/7 - 144*g**2/7 + 1279*g. What is m in q(m) = 0?
-2, 2/23, 6
Let n = -6 - -39. Let v be (15/(-20))/(1 - n/24). Factor 193 + 23*q - 5*q**v - 193 - 3*q.
-5*q*(q - 4)
Suppose -t + 37 = 34. Suppose 3*j**3 - 198*j - 4*j**3 + 102*j**2 + 3*j**3 - 4*j**t + 98 + 0*j**3 = 0. Calculate j.
1, 49
Let 648/5*y - 154/5*y**3 + 6/5*y**5 - 4*y**4 + 288/5 + 232/5*y**2 = 0. Calculate y.
-4, -1, -2/3, 3, 6
Let b be ((-2)/18*2)/((-23)/207). Let a(m) be the first derivative of 1/14*m**6 + 0*m**b - 3 + 3/35*m**5 + 0*m - 1/7*m**3 - 3/28*m**4. Factor a(d).
3*d**2*(d - 1)*(d + 1)**2/7
Let d be ((-90)/(-8))/3 + 12/48. Suppose -d*k = -11*k + 14. Factor 6*t - 3 - 1 - 2*t**k + 1 - 1.
-2*(t - 2)*(t - 1)
Let b(r) = -24*r - 95. Let j be b(-6). Let h be ((-7)/j)/(1/(-3)). Factor h*v + 0*v**3 - 6/7*v**2 + 0 - 3/7*v**5 + 6/7*v**4.
-3*v*(v - 1)**3*