.
-4
Suppose 0*k - k - 2*x = 8, -12 = -3*k + 3*x. Let m be (0 - -3)*(k + 1). What is n in 261*n**4 + 10*n**m - 260*n**4 + 36*n**2 + 54*n + 12 + 15 = 0?
-3, -1
Let x(p) be the third derivative of -1/420*p**7 + 0 + 12*p**2 + 1/40*p**5 + 1/240*p**6 + 1/6*p**3 + 0*p - 5/48*p**4. Factor x(s).
-(s - 1)**3*(s + 2)/2
Let q(s) be the third derivative of s**7/1680 - 3*s**6/320 + s**5/20 - s**4/12 - 35*s**2. Factor q(n).
n*(n - 4)**2*(n - 1)/8
Let x(m) be the second derivative of -m**4/12 - 7*m**3/3 - 49*m**2/2 - 93*m. Let x(j) = 0. What is j?
-7
Let g(d) = d**2 + d - 1. Let x(a) = -18*a**2 - 24*a + 20. Let n(u) = -u**2 - u. Let p(s) = 6*n(s) - x(s). Let l(k) = 20*g(k) - 2*p(k). Factor l(w).
-4*(w - 1)*(w + 5)
Let y(j) be the third derivative of -2*j**7/525 - 2*j**6/75 + j**5/75 + 2*j**4/15 - 54*j**2. Factor y(f).
-4*f*(f - 1)*(f + 1)*(f + 4)/5
Let c(n) be the third derivative of n**7/630 - n**6/40 + 2*n**5/15 - 5*n**4/18 - 5*n**2 + n. Factor c(j).
j*(j - 5)*(j - 2)**2/3
Let x = -463/5 - -93. Let p(g) = 8*g + 117. Let j be p(-14). Factor 7/5*i**2 - 1/5*i**j + i**4 - 9/5*i**3 - x*i + 0.
-i*(i - 2)*(i - 1)**3/5
Let y = 227/322 + -33/161. Factor -2*o + 0 + y*o**2.
o*(o - 4)/2
Let f be (-20)/(-42)*(-243)/(-45). Find m such that 27/7*m**3 + 0 + 0*m + 0*m**2 + 3/7*m**5 - f*m**4 = 0.
0, 3
Suppose -j = 5*b - 1412, 4*b + 6940 = 5*j - b. Suppose 2500*k**4 + 6608*k**3 + 5102*k + 621 + 403 + 9600*k**2 + j*k**3 + 18*k = 0. Calculate k.
-4/5
Let v(x) be the first derivative of -x**7/1470 + x**6/126 - 2*x**5/105 - x**3 - 21. Let w(n) be the third derivative of v(n). Factor w(l).
-4*l*(l - 4)*(l - 1)/7
Let c be -4*4/4 + 11. Suppose -c*y = -4 - 129. Factor 2 - 5*q**2 - 2 + 9*q - y*q.
-5*q*(q + 2)
Suppose 5*i = 3*i + 8. Let s = 38 - -70. Determine x so that -37*x**3 - s*x**i + 46*x**2 + 109*x**3 - 13*x**2 + 3*x = 0.
-1/6, 0, 1
Let v(q) be the third derivative of 17/24*q**4 - 7/30*q**5 - q**2 + 0*q + 0 - 5/6*q**3. Factor v(f).
-(2*f - 1)*(7*f - 5)
Let w(z) be the third derivative of -z**5/270 + 55*z**4/108 + 59*z**2 + 2*z. What is m in w(m) = 0?
0, 55
Let u be 35/15 - (-8)/12. Let y(r) be the second derivative of 1/42*r**7 + 4*r + 0*r**u + 0*r**2 + 0*r**4 + 0*r**6 + 0*r**5 + 0. Find t such that y(t) = 0.
0
Let m(o) = -14*o**2 + 6*o - 19. Let g(y) = 5*y**2 - 2*y + 6. Let n(i) = 17*g(i) + 6*m(i). Let w be n(-5). Determine x so that -7/2*x - x**2 - 1 + 3/2*x**w = 0.
-1, -1/3, 2
Let f(s) be the third derivative of s**6/1260 + 3*s**5/70 + 27*s**4/28 - 11*s**3/3 - 32*s**2. Let j(h) be the first derivative of f(h). Factor j(z).
2*(z + 9)**2/7
Let t = 157/6 + -1715/66. Factor t*p**4 + 0*p + 0 - 4/11*p**2 + 2/11*p**3.
2*p**2*(p - 1)*(p + 2)/11
Let k(w) be the third derivative of 0*w + 0 - 150*w**3 - 1/15*w**5 - 5*w**4 - 25*w**2. Factor k(r).
-4*(r + 15)**2
Let g = 4/921 + 1168/13815. Let u(b) be the first derivative of 0*b - 1/15*b**2 - 1/30*b**4 - 5 + g*b**3. Let u(y) = 0. What is y?
0, 1
Suppose -10 = 2*x - 14. Factor -13*l**4 - l - 12*l**4 + 9*l**x - l**3 - 14*l**3.
-l*(l + 1)*(5*l - 1)**2
Solve -w**3 - 9*w**2 + 8*w**4 - 10*w**4 + 10*w**2 = 0.
-1, 0, 1/2
Let l(p) be the second derivative of 8/21*p**3 - 1/21*p**6 + 18*p + 4/7*p**2 - 1/10*p**5 + 0 - 1/147*p**7 + 1/42*p**4. Determine y, given that l(y) = 0.
-2, -1, 1
Suppose 4*o - 4*u = 2 - 14, -4*o - 22 = -6*u. Factor 0*g - 18/7*g**4 + 0*g**o - 3/7*g**5 + 0 - 27/7*g**3.
-3*g**3*(g + 3)**2/7
Let d(a) = -9*a**3 - 42*a**2 + 3*a + 42. Let t(p) = -p**3 - p**2 + 1. Let f(k) = -d(k) + 6*t(k). Factor f(q).
3*(q - 1)*(q + 1)*(q + 12)
Suppose -4*m - 30 = -19*m. Let v be (-16)/(-64) + m/24. Solve 2/3*l**2 - 1/3*l + v*l**3 - 2/3 = 0 for l.
-2, -1, 1
Let a = -110 - -70. Let m be (-1)/5 - 16/a. Let 0*w**2 - w**4 + 0*w + 4/5*w**5 + 0 + m*w**3 = 0. What is w?
0, 1/4, 1
Let m = 623 - 620. Let n(s) be the first derivative of 1/10*s**5 + 1 + 0*s + 1/8*s**2 - 1/24*s**6 - 1/6*s**m + 0*s**4. Let n(j) = 0. What is j?
-1, 0, 1
Factor -17/7*y**2 - 24/7 - 206/7*y.
-(y + 12)*(17*y + 2)/7
Suppose 1 - 86 = -5*u. Suppose -5*j + 24 = 3*c, -2*c - u*j + 3 = -18*j. Factor 1/4*b**c + 0 - 1/2*b**2 + 1/4*b.
b*(b - 1)**2/4
Factor -270/7*g - 6075/7 - 3/7*g**2.
-3*(g + 45)**2/7
Suppose -344*g + 19*g**2 - 41306*g**3 - g**4 - g**4 + 137*g**2 + 240 + 41288*g**3 = 0. Calculate g.
-15, 2
Factor -3/5*j - 1/5*j**3 + 2 - 6/5*j**2.
-(j - 1)*(j + 2)*(j + 5)/5
Let d(u) be the second derivative of -73*u**4/18 + 16*u**3 + 4*u**2/3 - 509*u. Factor d(o).
-2*(o - 2)*(73*o + 2)/3
Let v = -25/316 + 391/948. Suppose 1/3*i**2 + 0*i - v = 0. Calculate i.
-1, 1
Factor 2*d**3 - 6*d**3 - 72 + 54*d - 6*d**2 + 6*d - 4*d**3 + 5*d**3.
-3*(d - 2)**2*(d + 6)
Suppose 28 = 3*i + 5*k, 0*i + 4*k - 38 = -5*i. Let p(o) be the second derivative of 1/25*o**5 - i*o + 2/15*o**4 + 0*o**2 + 2/15*o**3 + 0. Solve p(h) = 0 for h.
-1, 0
Let t be (-9)/((-18)/(-92))*(-2)/(-12). Let m = -10/3 - t. Suppose 2/3*a + 19/3*a**3 - 11/3*a**2 + a**5 - m*a**4 + 0 = 0. What is a?
0, 1/3, 1, 2
Let v(m) = -9*m**5 + 6*m**4 + 9*m**3 - 6*m + 6. Let g(d) = 8*d**3 + 28*d**4 + 4 + 1 - 23*d**4 - 8*d**5 - 5*d. Let y(k) = -6*g(k) + 5*v(k). Factor y(c).
3*c**3*(c - 1)*(c + 1)
Let r(w) be the first derivative of -w**4/2 - 4*w**3/3 + w**2 + 4*w - 70. Find k, given that r(k) = 0.
-2, -1, 1
Find z, given that 8/3 + z**2 - 10/3*z = 0.
4/3, 2
Suppose -79*r**5 - 99*r - 2*r**5 - 12 - 139*r**2 - 117*r**4 + 72*r**2 + 11*r + 365*r**3 = 0. What is r?
-3, -2/9, 1
Let s(i) be the second derivative of 0*i**2 + 5/42*i**7 - 14*i + 5/6*i**6 + 0 + 2*i**5 + 0*i**3 + 5/3*i**4. Factor s(g).
5*g**2*(g + 1)*(g + 2)**2
Suppose m - 5*m - h + 268 = 0, -3*m - h + 200 = 0. Let x = -68 + m. Factor -1/6*n**2 + 0*n - 1/6*n**3 + x.
-n**2*(n + 1)/6
Let i(w) be the third derivative of w**9/6720 + w**8/6720 - w**7/210 + w**6/60 + 3*w**5/20 - 2*w**2. Let v(b) be the third derivative of i(b). Factor v(h).
3*(h - 1)*(h + 2)*(3*h - 2)
Let t be 62/22 - (420/(-132) + 3). Suppose -2/5*u**2 + 2/5 - 2/5*u**t + 2/5*u = 0. Calculate u.
-1, 1
Let b(q) = q**2 - q. Let a(l) = -5 - 2*l**2 + 4*l**3 + 6*l - 4 + 1. Let x be (-3)/(-5) + (-16)/120*-3. Let d(z) = x*a(z) + 10*b(z). Factor d(v).
4*(v - 1)*(v + 1)*(v + 2)
Let d(t) be the second derivative of t**7/5040 + t**6/360 + t**5/80 - 19*t**4/12 - 14*t. Let i(k) be the third derivative of d(k). Determine s so that i(s) = 0.
-3, -1
Suppose -17*t + 266 = -40. What is q in 3*q**5 - 51/2*q**2 + t + 6*q + 15/2*q**4 - 9*q**3 = 0?
-2, -1, 1, 3/2
Let n(b) be the third derivative of 8*b**2 + 5/3*b**4 + 0 + 0*b + 1/2*b**6 + 19/12*b**5 + 5/6*b**3. Factor n(g).
5*(g + 1)*(3*g + 1)*(4*g + 1)
Let g(z) = 2*z**4 - 7*z**3 + 19*z**2 + 22*z - 6. Let w(f) = 3*f**4 - 6*f**3 + 21*f**2 + 22*f - 8. Let p(n) = -4*g(n) + 3*w(n). Solve p(k) = 0.
-11, -1, 0, 2
Suppose 0 = 2*x - 2*p - 20, x - 2*p = 6*x - 36. Let d be ((-9)/72)/((-6)/x). Determine j, given that -1/2*j - 1/3 - d*j**2 = 0.
-2, -1
Let d(t) be the second derivative of t**7/7 + 8*t**6/15 + 3*t**5/5 - t**3/3 - 88*t. Determine c so that d(c) = 0.
-1, 0, 1/3
Let r(l) be the first derivative of l**5/15 - 17*l**4/6 + 11*l**3/3 + 195. Factor r(o).
o**2*(o - 33)*(o - 1)/3
Let i(y) be the first derivative of 5*y**6/12 + 19*y**5/10 + 13*y**4/4 + 7*y**3/3 + y**2/4 - y/2 + 549. Factor i(g).
(g + 1)**4*(5*g - 1)/2
Let w = -2/13407 + 13411/26814. Determine n so that w*n**2 - 1/2 + 1/4*n**3 - 1/4*n = 0.
-2, -1, 1
Suppose 3*j = -3*a - 0*j, -j - 15 = -4*a. Let z = 5 - a. Determine r, given that -37 - r - r**z + 37 = 0.
-1, 0
Let d be -1*62*(-1)/(-4). Let i = 16 + d. Factor i*c**3 + 0 - c + 1/2*c**2.
c*(c - 1)*(c + 2)/2
Suppose 3*t = -m + 10, 5*m = -4*t - 0 + 6. Let s(g) = -g**2 + g + t + 0*g**2 - 5. Let v(f) = -4*f**2 + 3*f + 1. Let d(w) = 3*s(w) - v(w). Factor d(x).
(x - 2)*(x + 2)
Let z(f) be the second derivative of f**9/3780 - f**8/840 + f**7/630 - f**4 - f. Let h(b) be the third derivative of z(b). Factor h(y).
4*y**2*(y - 1)**2
Let z(o) = o + 4*o**3 - 2*o**3 + o**3 - 2*o**3 + 12*o**2 + 14. Let u be z(-12). Let -6*n**3 + 11*n**2 + 3*n**4 - 3 - 11*n**u + 6*n = 0. Calculate n.
-1, 1
Let 32/5*t + 14/5*t**2 + 8/5 = 0. Calculate t.
-2, -2/7
Let d(z) = -z**3 + z**2 - z + 1. Let u(a) = -4*a**4 - 58*a**3 - 198*a**2 - 258*a + 6. Let x(i) = -6*d(i) + u(i). Factor x(p).
-4*p*(p + 3)**2*(p + 7)
Suppose -12*v + 10 = -11*v. Facto