lculate k.
-3, 0
Let q(l) = l**4 + l**3 - l**2 - l - 1. Let h(x) = -4*x**4 + 14*x**3 - 32*x**2 + 22*x + 2. Let i(v) = -2*h(v) - 4*q(v). Factor i(c).
4*c*(c - 5)*(c - 2)*(c - 1)
Let i = 55 - 51. Suppose -x = -i*x. Factor 1/7*o + 1/7*o**5 + 0 + 0*o**4 - 2/7*o**3 + x*o**2.
o*(o - 1)**2*(o + 1)**2/7
Solve 14/13*i**4 + 0*i - 24/13*i**3 + 0 - 8/13*i**2 = 0 for i.
-2/7, 0, 2
Let u(m) = -47*m**3 + 99*m**2 - 48*m - 1. Let q(i) = i**2 + i - 1. Let k(t) = 3*q(t) - u(t). What is g in k(g) = 0?
2/47, 1
Factor -1/2*k**3 + 1/6*k**4 + 0 - 1/6*k + 1/2*k**2.
k*(k - 1)**3/6
Let m(l) = l**4 + l**2 + l - 1. Let n(p) = 4*p**4 - 2*p**3 + 4*p - 2. Let y be (-3)/((-6)/8) - 5. Let a(i) = y*n(i) + 2*m(i). What is b in a(b) = 0?
-1, 0, 1
Let y = 205 - 134. Let f = 73 - y. Factor 2/5*a**4 + 2*a**f + 0 - 8/5*a**3 - 4/5*a.
2*a*(a - 2)*(a - 1)**2/5
Let x(t) be the second derivative of -t**8/20160 + t**7/1080 - t**6/144 + t**5/40 + 3*t**4/4 + 10*t. Let d(m) be the third derivative of x(m). Solve d(l) = 0.
1, 3
Let w(f) be the third derivative of f**8/1176 - f**7/147 + f**6/60 + f**5/210 - 2*f**4/21 + 4*f**3/21 + 21*f**2 - 2. Solve w(c) = 0 for c.
-1, 1, 2
Let i = 3341/1195 + 1/239. Let v = i + -51/20. Find j such that 1/4*j**2 - v*j - 1/2 = 0.
-1, 2
Suppose -4/3*d**5 - 4/3*d**4 + 8/3*d + 0 + 20/3*d**2 + 4*d**3 = 0. Calculate d.
-1, 0, 2
Suppose 48 + 85 + 2 + 3*u**2 - 36*u - 27 = 0. Calculate u.
6
Let m(t) be the second derivative of -t**7/3 + 2*t**6 - 4*t**5/5 - 2*t - 56. Determine x so that m(x) = 0.
0, 2/7, 4
Let l(j) be the second derivative of j**5/35 - 3*j**4/7 - 68*j**3/21 - 48*j**2/7 - 10*j - 26. Factor l(v).
4*(v - 12)*(v + 1)*(v + 2)/7
Let b = 542 - 538. Solve -22/9*f**3 - 2*f - 4/9 - 10/3*f**2 - 2/3*f**b = 0 for f.
-1, -2/3
Let u(s) be the second derivative of -30*s - 52/3*s**3 + 4*s**2 + 0 + 169/6*s**4. What is j in u(j) = 0?
2/13
Let k = 1052 - 1049. Let y(b) be the first derivative of 0*b - 5/9*b**k - 7/12*b**4 + 1/3*b**2 - 1. Factor y(c).
-c*(c + 1)*(7*c - 2)/3
Let h(w) be the second derivative of 0 - 1/36*w**4 - 16*w - 1/18*w**3 + 1/3*w**2. Factor h(t).
-(t - 1)*(t + 2)/3
Let r(t) be the second derivative of 0 + 1/3*t**3 + 2/3*t**4 - 4/21*t**7 - 4/15*t**6 + 0*t**2 + 14*t + 3/10*t**5. Suppose r(x) = 0. Calculate x.
-1, -1/2, 0, 1
Factor -40/11 + 82/11*h + 18/11*h**2.
2*(h + 5)*(9*h - 4)/11
Let c(g) = g**2 + g - 1. Let s(b) = -2*b**2 - 3*b - 7. Let l(q) = 6*c(q) - s(q). Find k, given that l(k) = 0.
-1, -1/8
Let b = 44 + -26. Let a be (b/4)/(-3) - -5. Find c, given that 1 + a*c + 3*c**2 = 0.
-2/3, -1/2
Factor 1/2*i**3 - 2*i - 5/2*i**2 + 10.
(i - 5)*(i - 2)*(i + 2)/2
Let n be (-24)/14 - (-14)/(-49). Let x be 3 + n + 9 + 0. Factor 3*v + x - 3*v**2 - 10.
-3*v*(v - 1)
Let x(z) be the first derivative of -2/23*z**2 - 18 + 2/69*z**3 - 16/23*z. Factor x(a).
2*(a - 4)*(a + 2)/23
Let k(y) be the first derivative of -2*y**6/15 - 52*y**5/25 - 49*y**4/5 - 316*y**3/15 - 116*y**2/5 - 64*y/5 + 143. Solve k(d) = 0 for d.
-8, -2, -1
Factor -2/13*k**4 - 1096/13*k**3 - 704550722/13 - 225228/13*k**2 - 20570824/13*k.
-2*(k + 137)**4/13
What is a in 1/2*a**2 + 14*a + 0 = 0?
-28, 0
Factor 8*g - 198*g - 299 - 4*g**3 + 811 - 194*g + 72*g**2.
-4*(g - 8)**2*(g - 2)
Let v(t) be the first derivative of -48 + 5*t**3 + 3/2*t**5 + 0*t + 5/2*t**2 + 5/24*t**6 + 65/16*t**4. Factor v(o).
5*o*(o + 1)**2*(o + 2)**2/4
Let c be (-1)/3*(-168 - -162). Suppose -5*b + 15 = -4*n, 0 = b - 3*n - 3. Factor 3*s**2 + b - 5*s**c + 5*s - 7 + s.
-2*(s - 2)*(s - 1)
Let n be 20 - 14 - ((-1148)/364 + 7*1). Factor n*o - 2/13*o**2 - 98/13.
-2*(o - 7)**2/13
Let d(s) be the second derivative of -s**7/357 - 4*s**6/255 - s**5/34 - s**4/51 - 33*s + 2. Factor d(n).
-2*n**2*(n + 1)**2*(n + 2)/17
Let o(j) = -j**2 + 80*j - 639. Let u be o(71). Suppose 0 + u*r - 1/6*r**2 = 0. Calculate r.
0
Let j(z) be the second derivative of -15*z + 0*z**2 - 1/84*z**7 + 0*z**5 + 1/30*z**6 + 0 - 1/12*z**4 + 1/12*z**3. Factor j(u).
-u*(u - 1)**3*(u + 1)/2
Let w(f) = -f**3 + 26*f**2 - 172*f + 59. Let o be w(14). Factor -3/2*x**4 - 3/2*x**2 + o*x**3 + 0*x + 0.
-3*x**2*(x - 1)**2/2
Let f(x) be the third derivative of -x**5/100 - 3*x**4/20 - 63*x**2. Factor f(m).
-3*m*(m + 6)/5
Let z be (-40 - -37)/(2/(-22)). Suppose 18 = -24*w + z*w. Factor 3/2 + 1/2*f**w + 2*f.
(f + 1)*(f + 3)/2
Suppose f = -2*f + 5*i - 4, -3*f = -4*i + 2. Determine d so that -38*d + 2*d**4 + 36*d + f*d**2 + 2*d**3 - 4*d**4 = 0.
-1, 0, 1
Let g(t) be the first derivative of 9 + 2/3*t**3 - 3*t**2 + 4*t. Factor g(w).
2*(w - 2)*(w - 1)
Suppose 1/5*g**5 + 937/5*g**3 + 7334/5*g**2 + 10952/5 + 15836/5*g - 68/5*g**4 = 0. What is g?
-2, 37
Let a = 96 - 9. Let t = a - 83. Determine d so that -1/3*d**t + 0 + 4/3*d**3 - 5/3*d**2 + 2/3*d = 0.
0, 1, 2
Let c(b) = 1. Let v(p) = p**3 + 10*p**2 + p + 7. Let g be v(-10). Let h(l) = -5*l**2 - 5*l - 3. Let t(k) = g*c(k) - h(k). Solve t(n) = 0.
-1, 0
Factor 7*u**2 - 135*u + 16*u**3 - 162 - 43*u**2 - 19*u**3.
-3*(u + 3)**2*(u + 6)
Factor 0 + 348/5*d**4 + 0*d + 12/5*d**5 + 339/5*d**3 + 84/5*d**2.
3*d**2*(d + 28)*(2*d + 1)**2/5
Let v = 58869/31384 - 3/3923. Factor -3/8*q**4 + v*q**2 + 3/8*q**3 + 0 + 9/8*q.
-3*q*(q - 3)*(q + 1)**2/8
Suppose 2*j - 207 = 3*d - 1095, 5*j = -2*d + 573. Let m = -1167/4 + d. Find p such that 3 - 3/4*p**2 - m*p = 0.
-4, 1
Let p(z) be the third derivative of -2/15*z**3 - 17/300*z**5 - 1/5*z**4 + 0*z + 0 + 9*z**2 + 3/40*z**6. Factor p(d).
(d - 1)*(5*d + 2)*(9*d + 2)/5
Let j(l) be the second derivative of -l**6/10 - 3*l**5/20 + 3*l**4/2 - 39*l - 1. Factor j(d).
-3*d**2*(d - 2)*(d + 3)
Let v(a) be the third derivative of a**7/1470 + a**6/168 - a**5/60 - 5*a**4/168 + a**3/7 + 27*a**2 - 1. Factor v(m).
(m - 1)**2*(m + 1)*(m + 6)/7
Factor 24/7 - 22/7*m - 4/7*m**2 + 2/7*m**3.
2*(m - 4)*(m - 1)*(m + 3)/7
Let h(l) = l**3 + l**2 - l - 1. Let g(s) = 2*s**4 + 25*s**3 + 91*s**2 + 99*s - 1. Let p(a) = g(a) - h(a). Suppose p(z) = 0. Calculate z.
-5, -2, 0
Let u(n) = -15*n**3 - 30*n**2 + 15*n + 30. Let x(h) = -5*h**3 + h - 10*h**2 + 6*h - h + 10 - h. Let l(b) = 6*u(b) - 17*x(b). Factor l(s).
-5*(s - 1)*(s + 1)*(s + 2)
Let c = -6342 + 3266129/515. Let s = c + 3101/5665. Factor 2/11 - s*p + 4/11*p**2.
2*(p - 1)*(2*p - 1)/11
Let f(c) be the second derivative of c**5/8 + 7*c**4/12 - 23*c**3/12 + c**2 - 53*c. Factor f(r).
(r - 1)*(r + 4)*(5*r - 1)/2
Let z(r) = -r**3 - r**2 + 3*r - 3. Let a be 5 + (-138)/30 - (-224)/(-10). Let w(i) = -3*i**3 - 3*i**2 + 11*i - 11. Let q(j) = a*z(j) + 6*w(j). Factor q(k).
4*k**2*(k + 1)
Factor 1 + 4/3*g**3 - 10/3*g - 3*g**2.
(g - 3)*(g + 1)*(4*g - 1)/3
Let r(q) be the second derivative of -5*q**4/16 - 17*q**3/4 - 9*q**2 + 578*q. Let r(u) = 0. What is u?
-6, -4/5
Suppose -3*k - 31 = -3*h - 2*h, 0 = h + 5*k + 5. Let y = h - 4. Determine t, given that -y - 1/2*t + 14*t**2 = 0.
-1/4, 2/7
Factor -4*c**2 + 0*c + 0 - 1/3*c**3.
-c**2*(c + 12)/3
Let 11/2*y**3 + 7/2*y**2 - 7/2*y - 1 - 5/2*y**4 - 2*y**5 = 0. Calculate y.
-2, -1, -1/4, 1
Suppose -2*i + 0*i - 5*p = -26, 0 = i + 2*p - 12. Suppose 0*b + 2*b = -i*b. What is j in 2/7*j - 2/7*j**2 + b = 0?
0, 1
Let s(f) be the second derivative of f**6/150 - 19*f**5/100 + 3*f**4/10 + 5*f + 12. Factor s(t).
t**2*(t - 18)*(t - 1)/5
Suppose -5*f + 2*j = 44, -2*f - j = -6*j + 26. Let v = f - -11. Find r, given that -2*r**v - 5 + 2*r**3 + r**2 + r + 4 - r**3 = 0.
-1, 1
Let f(p) = 5*p**2 - 7*p - 7. Let d be f(-1). Let j(i) be the first derivative of 0*i - 2/25*i**d + 0*i**2 + 0*i**3 - 3 + 0*i**4. Factor j(q).
-2*q**4/5
Let p(o) be the second derivative of o**7/21 + 13*o**6/15 - 21*o. Solve p(k) = 0 for k.
-13, 0
Suppose -5*b - 40 = -7*b. Let -20*v**2 - 50*v**5 + 155*v**2 + 20*v**2 - b + 15*v**5 - 265*v**3 + 165*v**4 = 0. Calculate v.
-2/7, 1, 2
Factor 15*z - 53*z - 5*z**2 + 17*z + 18*z.
-z*(5*z + 3)
Factor -1/6*m**3 - 4/3*m + 8/3 - 7/6*m**2.
-(m - 1)*(m + 4)**2/6
Let z = 751/4 - 187. Let a be (-36)/(-16)*(2 + (-10)/6). Let 3/4*b - 3/4*b**4 + 0 - a*b**3 + z*b**2 = 0. Calculate b.
-1, 0, 1
Let w(r) be the third derivative of r**5/180 + 41*r**4/72 + 210*r**2. Solve w(c) = 0.
-41, 0
Suppose -10*d + 32 = -2*d. Let o(m) be the second derivative of -1/48*m**d + 9*m + 0 - 9/8*m**2 + 1/4*m**3. Factor o(s).
-(s - 3)**2/4
Let t(s) = -2*s**3 - 28*s**2 - 5*s - 67. Let z be t(-14). Suppose 2/3*p**4 + 2*p*