v.
1
Let s = -394504 - -789009/2. Let s*k**2 + 6*k + 18 = 0. Calculate k.
-6
Let v be 18 + (1*6)/(282/(-376)). Let w(s) be the third derivative of 0*s + 0 + 5/24*s**4 - 1/12*s**5 + 0*s**3 + v*s**2. Factor w(i).
-5*i*(i - 1)
Let g be (-48)/(-56)*(-2 - ((-46)/8 + 2)). Let p(t) be the second derivative of 7/24*t**4 - 18*t + 3/40*t**5 + 0 + 2*t**2 - g*t**3. Factor p(u).
(u - 1)*(u + 4)*(3*u - 2)/2
Let y(q) = q**2 + 259*q - 784. Let u be y(3). Let d(g) be the first derivative of -1 + 5/2*g**u + 5/3*g**3 + 0*g. Factor d(h).
5*h*(h + 1)
Let i(g) be the third derivative of -1/30*g**5 - 1/600*g**6 - g**2 - 17/120*g**4 - 147 - 4/15*g**3 + 0*g. Determine w, given that i(w) = 0.
-8, -1
Suppose 0 = 5*z - 3519 + 3524. Let p be (z + -8)*-4*7/126. Let 0 - 3/7*s - 3/7*s**p = 0. What is s?
-1, 0
Let q be 8/(-26)*(-451)/902. Factor -4/13*j + 6/13 - q*j**2.
-2*(j - 1)*(j + 3)/13
Let j(g) be the third derivative of -5/14*g**7 - 4*g**3 + 214*g**2 - 11/8*g**6 + 7/2*g**4 + 0 + 3/10*g**5 + 0*g. Solve j(y) = 0 for y.
-2, -1, 2/5
Let b(v) = v**3 - 19*v**2 + 38*v - 63. Let o be b(17). Factor 12*c + o*c - 14*c**2 - 11*c - 25*c**2.
-3*c*(13*c - 2)
Let v = 29827/94380 + 1/1573. Let g(j) be the third derivative of j**3 - 28*j**2 + v*j**5 + 29/24*j**4 + 0 - 1/30*j**6 + 0*j. Factor g(m).
-(m - 6)*(m + 1)*(4*m + 1)
Let c be (-4200)/3080*(-10)/75. Let -2/11*x + 0 + 0*x**2 + c*x**3 = 0. What is x?
-1, 0, 1
Let k(p) be the second derivative of p**6/540 + p**5/27 + p**4/12 - 3*p**2/2 + 2*p - 1. Let s(g) be the first derivative of k(g). Solve s(u) = 0.
-9, -1, 0
Let c(a) be the second derivative of -1/15*a**5 + 0*a**2 - 2048/9*a**3 + 0 - 64/9*a**4 + 121*a. Solve c(l) = 0.
-32, 0
Factor -b**2 - 4*b**2 - 70 + 39 + 50*b + 7 + b**2.
-2*(b - 12)*(2*b - 1)
Find y, given that -695*y + 322*y - 238*y + 519 - 5*y**2 + 95*y + 2*y**2 = 0.
-173, 1
Factor 738/7 + 2/7*u**2 - 36*u.
2*(u - 123)*(u - 3)/7
Let d(o) be the first derivative of -25*o**4/12 + 155*o**3/12 - 15*o**2/4 + 77*o + 8. Let j(t) be the first derivative of d(t). What is k in j(k) = 0?
1/10, 3
Suppose 55 - 15 = 4*b - 3*q, 0 = -3*q - 12. Suppose b*n - 44 = -9. Factor 8*u**2 - 52*u + 62*u + 7*u**2 + n*u**3.
5*u*(u + 1)*(u + 2)
Let i(d) be the third derivative of -d**5 + 175*d**4/6 - 815*d**3/6 + 121*d**2. Let r(m) = -5*m**2 + 58*m - 68. Let t(b) = 3*i(b) - 35*r(b). Factor t(l).
-5*(l - 13)*(l - 1)
Let p(a) = -6*a**2 + 2*a + 1. Let r be p(-2). Let n = r + 64. Factor 41*z**5 - 10*z**4 - 93*z**5 + n*z**5.
-5*z**4*(3*z + 2)
Let b(q) = -q**2 + 26302*q + 52612. Let t be b(-2). Solve 12*p**t - 27/2*p - 3/2*p**5 + 0 - 33*p**3 + 36*p**2 = 0.
0, 1, 3
Suppose 5*s**2 - 2943*s + 4547*s - 10019*s = 0. Calculate s.
0, 1683
Let j be (3/2)/((-30)/320). Let d(y) = -56*y**2 - 52*y - 56. Let n(a) = 18*a**2 + 18*a + 19. Let o(k) = j*n(k) - 5*d(k). Suppose o(h) = 0. What is h?
-2, -3/2
Let m(z) be the first derivative of z**4/8 + 5*z**3/6 - 79*z**2/2 + 144*z + 697. Determine v so that m(v) = 0.
-16, 2, 9
Solve 2450*z + 164 + 316 + 260*z**3 - 2243*z**2 + 1178*z**2 + 6*z**2 - 3256*z**2 = 0.
-2/13, 3/4, 16
Let v(w) = 12*w**3 - 7*w**2 - 278*w. Let u(z) = -2*z**3 + z**2 + 46*z. Let a(p) = 38*u(p) + 6*v(p). Factor a(y).
-4*y*(y - 4)*(y + 5)
Let i(a) = 2*a**3 + 20*a**2 - 4*a - 34. Let c be i(-10). Let l(k) = 2*k**2 - 10*k - 10. Let g be l(c). Factor -28*b**g + 14*b + 149 - 141 + 6*b.
-4*(b - 1)*(7*b + 2)
Let y(h) = 4*h**2 + 3194*h + 526. Let q(v) = v**2 + 68. Let j(r) = 4*q(r) + y(r). Determine p so that j(p) = 0.
-399, -1/4
Let r(k) be the third derivative of -k**5/360 - 235*k**4/72 - 26*k**3 - 8*k**2 - 24. Solve r(x) = 0.
-468, -2
Let i(w) be the third derivative of w**5/42 + 233*w**4/14 - 80*w**3/3 - 1205*w**2. Factor i(l).
2*(l + 280)*(5*l - 2)/7
Let r = -8 - -13. Suppose 0 = 2*q + 53 - 61. Factor r*p**2 - 2*p**q - p**5 - 235*p**3 + 236*p**3 - 3*p**2.
-p**2*(p - 1)*(p + 1)*(p + 2)
Let y = -326 - -328. Let n be (y - 3) + ((-152)/(-16) - 6). What is o in 1/4*o**2 + 0 - n*o = 0?
0, 10
Let w = -35 + 45. Suppose -15 = -w*i + 5*i. Factor -6*q**3 + 25*q**2 - q - q**4 - 28*q**2 + 3*q**i.
-q*(q + 1)**3
Let t(h) be the first derivative of -1/60*h**4 + 1/3*h**3 - 3*h - 5/2*h**2 + 29. Let p(n) be the first derivative of t(n). Factor p(w).
-(w - 5)**2/5
Suppose 0 = 5*x + 9*x - 10*x. Let s(k) be the third derivative of -k**3 + 5/8*k**4 + x*k - 1/5*k**5 + 1/40*k**6 + 0 + 14*k**2. Let s(j) = 0. Calculate j.
1, 2
Let s = 721 + -723. Let y be s/8*(-11)/((-33)/(-6)). Find x, given that -5/4*x - y*x**2 - 1/2 = 0.
-2, -1/2
Let r be -5 - (-16 + (-40)/(-8)). Let a be -10*(-2)/30*r. Factor -2/21*b**2 + 0*b + 0 - 2/21*b**a + 4/21*b**3.
-2*b**2*(b - 1)**2/21
Let a(w) = -105*w**2 - 1652*w - 483. Let q be a(-15). Determine v so that -q*v + 111/5*v**3 - 846/5*v**2 - 3/5*v**4 - 480 = 0.
-2, -1, 20
Let u(g) = -7*g**2 - 1400*g. Let c be u(-200). Factor c + 2/3*f**2 + 2*f.
2*f*(f + 3)/3
Let t(y) = 8*y - 122. Let z be t(28). Find l such that -40 + 42*l + 6*l**3 - z*l + 12*l**2 + 3*l**4 + 4 - 33*l**2 = 0.
-2, -1, 3
Let a(j) be the third derivative of 1/3*j**4 - 14*j + 10*j**2 + 1/15*j**5 + 0 + 2/3*j**3. Factor a(k).
4*(k + 1)**2
Let a be 32/(-280)*14/(-4) + (91/(-35))/13. Factor -5 + 2*y - a*y**2.
-(y - 5)**2/5
Let u(f) be the second derivative of 3*f**6/25 + 48*f**5/25 + 61*f**4/30 + 2*f**3/3 + 33*f + 25. Factor u(z).
2*z*(z + 10)*(3*z + 1)**2/5
Let u(x) = -76*x**3 + 138*x**2 + 2323*x - 2448. Let a(d) = 130*d**3 - 230*d**2 - 3872*d + 4080. Let z(g) = -7*a(g) - 12*u(g). Factor z(k).
2*(k - 34)*(k - 1)*(k + 12)
Let u(y) = 66*y**3 + 111*y**2 - 24*y - 54. Let h(z) = z**2 - z + 9. Let t(b) = -6*h(b) - u(b). Factor t(i).
-3*i*(i + 2)*(22*i - 5)
Let z be 1530/66 + 8/(-44). Factor -2*m**4 + 10*m - 243*m**5 - z*m**4 - 35*m**2 + 248*m**5 + 45*m**3.
5*m*(m - 2)*(m - 1)**3
Let t(y) = 331*y**2 - y + 3. Let x be t(1). Let a be x/24 + -14 + 26/80. Factor -3/5*s**3 - 1/5*s**2 - a*s**4 + 3/5*s + 2/5.
-(s - 1)*(s + 1)**2*(s + 2)/5
Suppose 11 = -22*w + 116 - 61. Let q(f) be the third derivative of 1/105*f**5 + 10*f**w + 0*f**3 + 0*f + 0 + 1/21*f**4. Factor q(x).
4*x*(x + 2)/7
Let q be (-108)/(-24)*(-6)/81*-6. Let j be (-517)/(-22) + (q - 9). Factor -3/2*n**3 + 9*n**2 - j*n + 9.
-3*(n - 3)*(n - 2)*(n - 1)/2
Let k = -70 + 73. Let x be k/(-3)*-5*(0 + 1). Factor 42*z**x + 53*z**2 + 20*z**4 - 32*z - 66*z**3 - 44*z**5 + 27*z**2.
-2*z*(z - 4)**2*(z - 1)**2
Let d(l) be the first derivative of l**5/5 + 3*l**4 + 10*l**3/3 - 6*l**2 - 11*l - 8715. Find n such that d(n) = 0.
-11, -1, 1
Let i(w) be the first derivative of -675*w - 159 + 23 - w**3 + 46*w**2 + 40*w**2 - 41*w**2. Factor i(m).
-3*(m - 15)**2
Solve 2/3*s**5 - 6*s**4 + 0 + 16*s**3 - 40/3*s**2 + 0*s = 0.
0, 2, 5
Suppose -16*r + 21*r - 25*r + 40 = 0. Let o(q) be the first derivative of 21/2*q**r + 7 + q**3 + 18*q. Solve o(y) = 0.
-6, -1
Suppose 13*f = 52 + 13. Determine c, given that 9*c + 2*c + 42*c**3 + 236*c**f + c - 234*c**5 + 38*c**2 + 18*c**4 = 0.
-6, -1, 0
Suppose 91*i = 92*i - p - 28, 2*i - 56 = -5*p. Let n be i/14*1/8. Factor n*d**3 + 5/4*d**2 + 0 + 3/4*d - 1/4*d**4.
-d*(d - 3)*(d + 1)**2/4
Let i(l) be the second derivative of l**5/20 - 6*l**4 + 407*l**3/2 + 1369*l**2 + 122*l. Determine c so that i(c) = 0.
-2, 37
Let z = -4038 - -4042. Let k(s) be the second derivative of 1/12*s**3 - 1/48*s**z + 0*s**2 - 15*s + 0. Determine y, given that k(y) = 0.
0, 2
Let z = 2977/12868 + 60/3217. Factor 1/4*j**3 + 3/4 - 3/4*j**2 - z*j.
(j - 3)*(j - 1)*(j + 1)/4
Let a be 150/250*4230/4. Let v = 635 - a. Solve -1/5 - 9/10*b**3 - v*b**2 + 7/10*b**4 + 9/10*b = 0.
-1, 2/7, 1
Suppose 3*j + 4 = -2. Let o(t) = 12*t**4 - 8*t**3 - 10*t**2 + 10*t - 32. Let a(m) = m**4 - m**2 - m - 1. Let z(v) = j*o(v) + 28*a(v). Factor z(d).
4*(d - 1)**2*(d + 3)**2
Let o(y) = -4 + 3*y - 4*y + 70*y**3 + 0*y - 31*y**2 - 19*y**4 - 23*y. Let w(l) = l**4 - l**2 + l + 1. Let k(d) = o(d) + 4*w(d). Let k(m) = 0. Calculate m.
-1/3, 0, 1, 4
Let b(v) be the second derivative of -v**4/20 + 37*v**3/5 + 228*v**2/5 - 110*v + 1. Solve b(o) = 0 for o.
-2, 76
Let j be (3/5)/((-10122)/(-59045)). Let s = 7 - 5. Solve -1/2*o**4 + j*o**3 - 16*o + 16 - 3*o**s = 0.
-2, 1, 4
Let q(a) be the third derivative of -a**5/60 + 5*a**4/12 + 34*a**3 - 292*a**2. Let z be q(20). Factor -2/15*c**3 + 0 - 2/15*c**z + 0*c + 0*c**2.
-