 l(n) = 2*n**3 - 2*n**2 - n - 1. Let p(k) = -9*k**3 + 34*k**2 - 19*k - 46. Let v(h) = -4*l(h) - p(h). Determine s so that v(s) = 0.
-1, 2, 25
Suppose -6*c + 5*c + 4*c = -2*c. Determine s so that 3/4*s**2 - 3/4*s**4 + c*s + 0*s**3 + 0 = 0.
-1, 0, 1
Let x be (-2)/(5 + -6 - 2/(-4)). Suppose -252*m + 40 - 29*m**2 + 321 - 39*m**2 - x*m**3 - 37 = 0. Calculate m.
-9, 1
Let z(d) = -11*d**3 + 4*d**2 + 5*d - 4. Let b(l) = -10*l**3 + 5*l**2 + 5*l - 5. Let f(s) = 6*b(s) - 5*z(s). Find a, given that f(a) = 0.
-1, 1, 2
Let o = -1/2460 + 923/1230. Let 0 + 3/4*b - o*b**3 - 3/4*b**4 + 3/4*b**2 = 0. What is b?
-1, 0, 1
Let f(g) be the third derivative of 7*g**6/40 - 11*g**5/2 + 41*g**4/2 + 28*g**3 + 78*g**2. Find h, given that f(h) = 0.
-2/7, 2, 14
Suppose -380*y + 2*x = -382*y + 18, -3*y = -6*x + 18. Determine o so that -1/6*o**3 + 0 + 4/3*o**2 - 1/3*o**y + 2/3*o = 0.
-2, -1/2, 0, 2
Let o(w) be the first derivative of -1/20*w**5 + 1/8*w**4 + 3 + 0*w**3 + 0*w + 4*w**2. Let d(k) be the second derivative of o(k). Factor d(p).
-3*p*(p - 1)
Factor -17*i**2 - 21*i**2 + 69*i**2 - 107 - 15*i**2 - 17*i**2 + 108*i.
-(i - 107)*(i - 1)
What is c in 237*c**2 + 909*c**2 - 184*c - 676*c**3 - 65*c - 183*c**2 + 145*c**3 - 162 - 21*c**4 = 0?
-27, -2/7, 1
Let y(l) = -3*l**5 + l**4 + l**2 + l. Let k(g) = -5*g**5 - 10*g**4 + 21*g**3 - 8*g**2 + 2*g. Let x(d) = k(d) - 2*y(d). Factor x(u).
u**2*(u - 10)*(u - 1)**2
Suppose 0 = 17*f - 9*f - 24. Let h(c) be the third derivative of 1/4*c**4 - 1/60*c**5 - 3/2*c**f - c**2 + 0*c + 0. Factor h(x).
-(x - 3)**2
Let n(r) = -12*r + 24. Let l be n(-3). Let f be (-54)/l*(-5)/6. Factor -1/4*b**2 + 1/4*b**4 - 3/4*b + 0 + f*b**3.
b*(b - 1)*(b + 1)*(b + 3)/4
Let s = 439/11 - 2359/66. Factor 2/3 + s*f**2 + 10/3*f.
(5*f + 2)**2/6
Let i(f) be the first derivative of -f**4/22 + 6*f**3/11 - 15*f**2/11 + 14*f/11 - 230. Let i(o) = 0. Calculate o.
1, 7
Suppose 3*m = p - 10, 4*m + 12 = 3*p + m. Let c be 1*-4*-1*p. Suppose -48*b**2 - 32 - 2*b**4 + 11*b**3 + 64*b + 0*b**c + 5*b**3 = 0. Calculate b.
2
Let h(o) be the first derivative of o**7/168 - o**5/40 + o**3/24 + 8*o - 7. Let c(l) be the first derivative of h(l). Determine g, given that c(g) = 0.
-1, 0, 1
Factor 0 - 20/9*x**3 + 2/9*x**4 + 34/9*x**2 - 16/9*x.
2*x*(x - 8)*(x - 1)**2/9
Let p(u) = -4 - 1 - 2 - 2*u + u**3 + 6*u**2 + 2. Let c be p(-6). Factor c + 2*x + 18*x**3 - 12*x**2 - 7 + 0.
2*x*(3*x - 1)**2
Let k(o) = 4*o**4 + 24*o**3 - 38*o**2 - 646*o + 1464. Let n(p) = -p**4 + p**2 - p - 3. Let a(c) = -k(c) - 2*n(c). Factor a(j).
-2*(j - 3)**2*(j + 9)**2
Factor 3/8*c**2 - 369/8 + 57/4*c.
3*(c - 3)*(c + 41)/8
Find b, given that 21/2*b - 441/4 - 1/4*b**2 = 0.
21
Suppose 5*q - 6 = 94. Let r = q + -18. Suppose -2*l**r + 4 + 13*l**3 - l**2 - 14*l**3 = 0. Calculate l.
-2, 1
Let c(v) = -v - 2. Suppose 4*y + 24 = -4*a, 5*a - 6 = 5*y + 14. Let h be c(y). Factor m**3 + 6*m**3 + 16 - h*m**3 - 12*m**2.
4*(m - 2)**2*(m + 1)
Factor -15/4*h**3 - 3/2*h**4 + 0*h + 0 + 1/4*h**5 - 2*h**2.
h**2*(h - 8)*(h + 1)**2/4
Let l(i) be the second derivative of -i**4/42 - 20*i**3/21 - 100*i**2/7 - 74*i. What is j in l(j) = 0?
-10
Let z(w) be the third derivative of 1/20*w**6 + 1/4*w**3 - 28*w**2 + 0 - 1/40*w**5 - 1/4*w**4 + 0*w. Factor z(n).
3*(n - 1)*(n + 1)*(4*n - 1)/2
Let g(s) be the third derivative of -s**6/40 + 7*s**5/40 + s**4/4 + 421*s**2. Factor g(h).
-3*h*(h - 4)*(2*h + 1)/2
Factor -59*a - 9873 - 15*a**2 - 9867 + 19744.
-(a + 4)*(15*a - 1)
Suppose -3*z = -9 + 3. Let x be (-1491)/1704*(-2)/14. Factor 1/4*u + x*u**z + 1/8.
(u + 1)**2/8
Factor -80 + 38*h**3 - 11*h**3 + 30*h + 45*h**2 - 22*h**3.
5*(h - 1)*(h + 2)*(h + 8)
Factor -1/3*a**2 - 50/3*a - 625/3.
-(a + 25)**2/3
Suppose 2*c + 22 - 26 = 0. Let h(a) be the first derivative of 1/6*a**3 - 1/8*a**4 + 1/4*a**2 - 1/2*a - c. Factor h(q).
-(q - 1)**2*(q + 1)/2
Suppose 3*y + 68 = 20*y. Let s(m) be the second derivative of 4/5*m**2 - 1/50*m**5 + 0 + 0*m**3 - m - 1/10*m**y. Factor s(a).
-2*(a - 1)*(a + 2)**2/5
Factor 8*g - 10*g**3 + 12*g - 5*g**3 - 10*g**4 + 20*g**2 + 7*g**5 - 2*g**5.
5*g*(g - 2)**2*(g + 1)**2
Let v be 4/2 + -13 + 14. Determine h, given that 82*h + 2*h + 29*h**2 + 26*h**2 + 44 - 4*h**v - 19*h**2 = 0.
-1, 11
Let v(l) be the third derivative of -l**7/7560 + l**6/540 - l**5/120 - 9*l**4/8 - l**2. Let y(s) be the second derivative of v(s). Suppose y(q) = 0. What is q?
1, 3
Factor -2*s**2 - 19/4*s - 3 - 1/4*s**3.
-(s + 1)*(s + 3)*(s + 4)/4
Let o(i) be the first derivative of 0*i**2 - 7 - 1/8*i**4 + 0*i**3 + 0*i + 1/10*i**5. Factor o(h).
h**3*(h - 1)/2
Let f(l) = 4*l - l**3 - 3*l - 3 + 2 - l**4. Suppose 4*s + 2 = 6*s. Let w(q) = 9*q**4 + 3*q**3 - 6*q + 6. Let y(o) = s*w(o) + 6*f(o). What is m in y(m) = 0?
0, 1
Find a, given that -2/13*a**3 - 96/13*a + 2*a**2 + 72/13 = 0.
1, 6
Let y(w) = -w**2 - 7*w - 2. Let b be y(-6). Let m = 66 - 64. Factor -m*q**3 + 3*q**2 - 2*q + 1/2*q**b + 1/2.
(q - 1)**4/2
Let g = -27 - -43. Suppose 2*c + g = 5*f, f = 3*f - 8. Suppose -18 - 7*a**c - 3*a**2 + 4*a**2 + 12*a + 4*a**2 = 0. What is a?
3
Let l(s) be the second derivative of -3/5*s**2 - 9*s + 0 - 1/10*s**3 + 1/20*s**4. Factor l(y).
3*(y - 2)*(y + 1)/5
Let g(b) be the second derivative of 0 + 2/3*b**3 + 2/21*b**7 - 11*b - 4/3*b**4 - 8/15*b**6 + 0*b**2 + 6/5*b**5. Factor g(z).
4*z*(z - 1)**4
Let o(f) be the third derivative of -f**10/302400 - f**9/30240 - f**8/13440 + 7*f**5/60 - 17*f**2. Let b(w) be the third derivative of o(w). Factor b(r).
-r**2*(r + 1)*(r + 3)/2
Suppose 10*l**3 - 12*l + 22*l**4 - 7296*l**5 + 7298*l**5 - 8*l**4 - 14*l**2 = 0. Calculate l.
-6, -1, 0, 1
Let a(j) = 18*j**4 + 39*j**3 + 351*j**2 + 987*j + 942. Let c(o) = -o**4 + o**3 - o + 2. Let y(u) = a(u) + 15*c(u). Find v such that y(v) = 0.
-6, -3
Let c(h) = -31*h + 191. Let l be c(6). Factor 0 + q**3 + 2/3*q**2 - 1/2*q + 5/6*q**l - 2*q**4.
q*(q - 1)**3*(5*q + 3)/6
Let a(t) = -t**2 + 13*t + 35. Let k be a(15). Find v, given that -2*v**2 - 7*v**3 - 72*v**4 - 69*v**4 - 3*v**k + 133*v**4 = 0.
-1, -2/3, 0
Suppose -14 - 1 = -5*b. Suppose 0 = b*f - 3*u + 6, 2*u = 2*f + 3*u - 11. Determine t so that t**5 - 6*t**5 - 2*t**4 - 3*t**f + 2*t**3 + 4*t**5 = 0.
-1, 0
Suppose z + 9*j = 32, -8*z + 4*j = -9*z + 17. Factor 0*m - 2/5*m**z - 6/5*m**3 + 0 + 2/5*m**2 + 6/5*m**4.
-2*m**2*(m - 1)**3/5
Let -200*f - 139/4*f**3 + 125 + 485/4*f**2 - 1/4*f**5 + 19/4*f**4 = 0. What is f?
2, 5
Let s be (-60)/52 + 2/13. Let m be 5 + (s - 2) + 0. Determine j, given that -j - 2*j - 3*j**4 - 9*j**m + 4*j**4 - 9*j**3 - 4*j**4 = 0.
-1, 0
Find v, given that -1/7*v**2 - 2*v - 24/7 = 0.
-12, -2
Let d be (3 - (-136)/(-40))*-10. Let w(m) be the third derivative of 0*m - 4/27*m**3 - m**2 - 1/270*m**5 + 0 + 1/27*m**d. Let w(u) = 0. Calculate u.
2
Let t(f) be the third derivative of f**8/224 + 9*f**7/140 + 13*f**6/80 - 9*f**5/8 - 25*f**4/8 + 220*f**2. Suppose t(i) = 0. Calculate i.
-5, -1, 0, 2
Let y be -1 + 11/((-495)/(-105)). Factor y*q - 2/3*q**2 - 2/3.
-2*(q - 1)**2/3
Determine p so that 16*p**2 - 16 - p**3 + 29*p - 13 + 2*p**3 + 43 = 0.
-14, -1
Let f(r) = 14*r**4 + 2*r**3 - 42*r**2 + 20*r + 10. Let b(m) = m**3 - 2*m - 1. Let g(o) = 4*b(o) + 2*f(o). Find t such that g(t) = 0.
-2, -2/7, 1
Let q(n) be the first derivative of -5 + 1/3*n**3 + 9*n + 3*n**2. Determine k so that q(k) = 0.
-3
Let a be (-143)/65 - (3/(-5))/3. Let p be (-6)/(-18) - a*(-1)/6. What is u in p - 2/9*u**2 + 0*u = 0?
0
Let y(x) be the second derivative of -x**8/6720 + x**6/480 + x**5/240 - x**3/6 - 10*x. Let g(j) be the second derivative of y(j). Factor g(n).
-n*(n - 2)*(n + 1)**2/4
Let y = 12 + -28. Let g(q) = 6*q**4 - 10*q**3 - 16*q + 16. Let x(i) = -i**4 + 2*i**3 + 3*i - 3. Let t(b) = y*x(b) - 3*g(b). Determine c so that t(c) = 0.
-1, 0
Factor 90/11*r**2 + 2/11*r**4 + 0 + 24/11*r**3 + 100/11*r.
2*r*(r + 2)*(r + 5)**2/11
Suppose -5*o + 3 = -12. Let r(s) be the third derivative of -1/30*s**5 - 1/12*s**4 + 0*s + 2*s**2 + 0*s**o + 0. Factor r(l).
-2*l*(l + 1)
Let n be (-28)/8*(-16)/28. Let c(v) be the second derivative of 0 + 0*v**n + 1/18*v**4 - 2*v - 1/9*v**3. Factor c(u).
2*u*(u - 1)/3
Let l(v) be the first derivative of 4*v**5/5 + 4*v**4 + 4*v**3 - 3. Determine h, given that l(h) = 0.
-3, -1, 0
Let v be 2 - 1 - 9/9. Factor -15*l - 4 + 8 + 6 + v + 5*l**3.
5*(l - 1)**2*(l + 2)
Let w(z) be the