*x. Determine f so that j(f) = 0.
-1, 64
Suppose -36 = -4*x + 4*j, -4*x - 4 = 5*j - j. Let t(z) be the first derivative of 2/5*z**3 + 5 + 1/5*z + 1/25*z**5 + 1/5*z**x + 2/5*z**2. Factor t(i).
(i + 1)**4/5
Let t(q) = -2*q**2 + 4*q - 5. Let w(d) = -10 - 3 - 5*d**2 + 3*d + 6*d + 2. Let x(z) = -7*t(z) + 3*w(z). Suppose x(v) = 0. What is v?
-2, 1
Let n(c) be the first derivative of -c**5/10 + 4*c**3/3 - 17*c - 3. Let x(o) be the first derivative of n(o). Factor x(s).
-2*s*(s - 2)*(s + 2)
Let d(a) be the second derivative of a**7/21 - 2*a**6/15 + a**5/10 - 17*a + 2. Suppose d(b) = 0. Calculate b.
0, 1
Let q be ((-5)/(-4))/((-1)/(-4)). Let c = -6 - -8. Factor -4*n**2 + 6*n**c - q*n**2 + 3.
-3*(n - 1)*(n + 1)
Let t(i) be the first derivative of -5*i**2 + 6*i + 1/4*i**4 - 1/10*i**5 + 7/6*i**3 + 40. Factor t(x).
-(x - 2)**2*(x - 1)*(x + 3)/2
Let q = 242 - 237. Let l(o) be the second derivative of -1/15*o**6 - 1/3*o**3 - o**2 - 1/21*o**7 + 1/3*o**4 + 0 + 1/5*o**q + 4*o. Factor l(j).
-2*(j - 1)**2*(j + 1)**3
Let f(b) = -42*b**2 - 86*b + 490. Let s(w) = 2*w**2 + w + 1. Let d(r) = 2*f(r) + 44*s(r). Find x such that d(x) = 0.
16
Factor -64 + 2*k**2 - 85 + 31*k - 79 + 212.
(k + 16)*(2*k - 1)
Let g(n) = -2*n + 18. Let s be g(-6). Let c = 32 - s. Factor -2/5*b**c - 8/5 - 8/5*b.
-2*(b + 2)**2/5
Suppose -51*v - 47*v = -392. Let x(u) be the first derivative of 6/5*u**5 + 20*u**2 + 8*u - 4 + 8*u**v + 58/3*u**3. Let x(l) = 0. Calculate l.
-2, -1, -1/3
Factor 22/5*m - 2/5*m**2 + 24.
-2*(m - 15)*(m + 4)/5
Let u be (-10 - -1) + (-2)/(-1). Let z = u + 7. Factor -8*f**2 - 2*f + z + 0 + 6*f.
-4*f*(2*f - 1)
Let c = -17 - -31. Let u be c/12*(1 - -5). Factor 2*n**3 + 3*n + u*n + 6*n + 16*n**2 + 2*n**3.
4*n*(n + 2)**2
Let x(m) be the first derivative of -4/39*m**3 - 12/13*m**2 - 16/13*m + 3/26*m**4 + 2/65*m**5 + 1. What is a in x(a) = 0?
-2, -1, 2
Let n = 5341 - 5338. Factor -3/2*v + 3/2*v**5 + 0 + 0*v**3 - n*v**4 + 3*v**2.
3*v*(v - 1)**3*(v + 1)/2
Let f(p) = 2*p**3 + p - 1. Let l(j) = -3*j**3 - 2*j**2 + 2*j + 1. Let m(c) = -3*f(c) - 3*l(c). Factor m(y).
3*y*(y - 1)*(y + 3)
Let k = 7 + -6. Suppose c - 3 = k. Solve -12*b - 2 - 2 - 7*b**2 - c + b**2 - b**3 = 0.
-2
Let m(t) be the third derivative of -10*t**2 + 0 + 0*t**5 + 0*t**7 + 1/84*t**8 + 0*t**4 + 0*t**3 + 0*t - 1/30*t**6. Determine k so that m(k) = 0.
-1, 0, 1
Let u be (-16)/1 - (-25960)/1475. What is h in 0 + 6/5*h**4 - 4/5*h + u*h**3 - 2/5*h**2 = 0?
-1, 0, 2/3
Let p(b) be the first derivative of b**6/15 - 2*b**5/25 - 2*b**4/5 + 8*b**3/15 + 183. Solve p(a) = 0.
-2, 0, 1, 2
Let f(s) be the first derivative of 9/5*s**2 - 2/5*s**3 + 13 - 7/30*s**4 + 36/5*s - 2/75*s**5. Determine a, given that f(a) = 0.
-3, 2
Solve -1/2*y + 0*y**3 - 5*y**2 + 2*y**4 + 3 + 1/2*y**5 = 0.
-3, -2, -1, 1
Let x(q) be the third derivative of q**8/672 + q**7/210 - q**6/60 - q**5/60 + q**4/16 + 148*q**2. Suppose x(b) = 0. What is b?
-3, -1, 0, 1
Let x(n) be the second derivative of n**6/15 - 9*n**4/2 + 50*n**3/3 - 24*n**2 + 54*n + 1. Let x(t) = 0. Calculate t.
-6, 1, 4
Let v(k) be the first derivative of -k**4/4 + 7*k**2/2 - 6*k - 45. Solve v(s) = 0.
-3, 1, 2
Let j(r) be the second derivative of -r**5/5 - 38*r**4/3 - 280*r**3/3 - 272*r**2 + r + 355. Factor j(i).
-4*(i + 2)**2*(i + 34)
Suppose -75*m - 6 = -77*m. Let y(i) be the first derivative of -i - 2 - i**m + 1/4*i**4 + 3/2*i**2. Find f, given that y(f) = 0.
1
Let t be (1/(-14))/((-2)/12). Let u(d) = 553*d - 3316. Let n be u(6). Factor t*q**n + 9/7*q + 6/7.
3*(q + 1)*(q + 2)/7
Let -123*b + 107*b**2 - 126 - 48*b**2 - 56*b**2 = 0. Calculate b.
-1, 42
Suppose -8/17 - 2/17*d**4 + 8/17*d - 4/17*d**3 + 6/17*d**2 = 0. Calculate d.
-2, 1
Let d(v) be the second derivative of v**4/36 - 10*v**3/3 + 150*v**2 + v + 1. Solve d(k) = 0 for k.
30
Let c be 1 - (5 - (1 + 3)). Suppose c*y + 12 = 4*y. Let 7*a**3 - 2*a**3 + a**4 - 8*a**2 - y*a**3 + 9*a**2 = 0. Calculate a.
-1, 0
Let c(n) = -4*n**3 + 2*n**3 - 3*n**2 + 3 + 5*n**3 + 5*n. Let r(i) = 4*i**3 - 4*i**2 + 6*i + 4. Let j(d) = 5*c(d) - 4*r(d). Find p, given that j(p) = 0.
-1, 1
Find m such that -3*m**3 + 30*m**2 - 8*m + 21*m + 20*m + 0*m**3 = 0.
-1, 0, 11
Factor -42439/3*m - 101306/3 + 1/3*m**4 - 109/3*m**3 + 1295*m**2.
(m - 37)**3*(m + 2)/3
Suppose 2*x - 2*t = 3 - 1, 4*t = 2*x + 2. Suppose -2*f = 3*y - 3, -x*y + 5 = 5*f - 7. Factor 33 - 37 + 87*c**3 - 32*c + 0*c**3 - 6*c**f - 45*c**2.
(c - 1)*(9*c + 2)**2
Let s(a) = a + 38. Let y(k) = k. Let p(r) = s(r) - 3*y(r). Let g be p(18). Solve -2/3*x**5 - 2/3*x**g - 2*x**4 + 0 - 2*x**3 + 0*x = 0.
-1, 0
Let p(h) be the first derivative of 2*h**5/45 - 7*h**4/18 - 2*h**3/27 + 7*h**2/9 - 3. Determine z, given that p(z) = 0.
-1, 0, 1, 7
Let d(k) = 2*k**4 - 15*k**3 - 47*k**2 + 18*k. Let p(v) = v**4 - 15*v**3 - 46*v**2 + 12*v. Let i(c) = 2*d(c) - 3*p(c). Factor i(s).
s**2*(s + 4)*(s + 11)
Let x be ((-3)/(-6) + 1)/((-450)/(-180)). Suppose -4*r - 14 = 3*m, 3*m + 1 = 3*r + 22. Factor -9/5 + x*k + 12/5*k**m.
3*(k + 1)*(4*k - 3)/5
Factor 0 + 5/6*v**2 - 2/3*v - 1/6*v**3.
-v*(v - 4)*(v - 1)/6
Let g(i) be the second derivative of -i**5/4 + 505*i**4/12 - 4165*i**3/2 - 13005*i**2/2 - 320*i. Factor g(r).
-5*(r - 51)**2*(r + 1)
Let o be 2/10 - 84/(-80). Solve o*s - 5/4*s**4 - 15/4*s**2 + 0 + 15/4*s**3 = 0.
0, 1
Let f be (-16)/6*(-12)/8. Let v = 4733/2635 - -2/527. Factor 0*g - 6/5*g**2 - 3/5*g**f + 0 + v*g**3.
-3*g**2*(g - 2)*(g - 1)/5
Let l = 31 - 40. Let k be l/(45/2)*(-10)/12. Determine z so that 0 - k*z - 1/3*z**2 = 0.
-1, 0
Let r(x) = x**3 - x + 4. Let d(y) = -y**2 + y - 1. Let h(v) = -4*d(v) - r(v). Factor h(f).
-f*(f - 3)*(f - 1)
Let -4006 - 3*u**3 - 384*u + 30*u**2 + 36*u**2 + 4678 = 0. What is u?
4, 14
Let z be (-2)/8 + (-13)/(-4). Suppose -o + 3*d - 9 = 0, 0 = 4*o - 2*d + 4*d - 34. Find t, given that 4*t**3 - t**3 - 2 + o*t**2 + z*t + 2 = 0.
-1, 0
Let o(b) be the second derivative of b**7/168 + 23*b**6/120 + 57*b**5/40 + 53*b**4/12 + 17*b**3/3 + 11*b - 1. Factor o(v).
v*(v + 2)**3*(v + 17)/4
Let p(m) be the second derivative of m**4/12 - m**3/2 - 2*m**2 + 60*m. Factor p(d).
(d - 4)*(d + 1)
Suppose -5*v = -43*g + 47*g, -g + v = 0. Solve g - 1/9*s**2 - 1/3*s = 0.
-3, 0
Let a(u) = 5*u**2 + 25. Let m(d) = d**2 + d + 1. Let t(p) = a(p) - 15*m(p). Factor t(z).
-5*(z + 2)*(2*z - 1)
Let w(j) = -20*j**5 - 2*j**4 + 19*j**3 + 2*j**2 - j. Let d(q) = -q**4 + q**3 + q**2 + q. Let t(r) = -5*d(r) - 5*w(r). Let t(b) = 0. What is b?
-1, -3/20, 0, 1
Let z(p) = -16*p**3 + 6*p**2 + 32*p + 2. Let i(a) = 5*a**3 - 2*a**2 - 11*a - 1. Let u(c) = -8*i(c) - 3*z(c). Find l such that u(l) = 0.
-1, 1/4, 1
Let p be 6*(7/21 + 1/3). Factor 0*q**2 - q + 4*q**3 + p - 5*q**2 + q**2 - 3*q.
4*(q - 1)**2*(q + 1)
Let a = -500270/11 + 45550. Solve -48/11*y + 0 + 250/11*y**5 - 450/11*y**4 - 344/11*y**2 - a*y**3 = 0.
-2/5, 0, 3
Factor -31250/3 + 33125/3*l + 151/12*l**3 - 1275/2*l**2 - 1/12*l**4.
-(l - 50)**3*(l - 1)/12
What is x in -16/7 + 32/7*x + 4/7*x**3 - 20/7*x**2 = 0?
1, 2
Let o = 1881473/501724 - 2/125431. Factor -5/4*i**2 + 5*i**3 + 0*i + 0 - o*i**4.
-5*i**2*(i - 1)*(3*i - 1)/4
Let k(m) = -m**3 - 14*m**2 - 17*m - 32. Let l be k(-13). Find z, given that l*z**4 + 4*z**3 + z**3 + 19*z**4 - 44*z**4 = 0.
0, 1
Let g(u) be the second derivative of -u**5/80 + 21*u**4/16 - 341*u**3/8 + 961*u**2/8 - 2*u + 42. Let g(r) = 0. What is r?
1, 31
Let j(s) be the second derivative of 0*s**5 + 1/360*s**6 - 8*s - 5/6*s**3 + 0*s**2 + 0*s**4 + 0. Let x(n) be the second derivative of j(n). Factor x(c).
c**2
Let i(h) = -31*h**2 - 118*h - 3486. Let x(m) = -37*m**2 - 118*m - 3487. Let c(f) = -6*i(f) + 5*x(f). Solve c(w) = 0 for w.
-59
Let o(l) = 27*l + 166. Let k be o(-6). Let w(c) be the second derivative of c - 1/6*c**k + 2/3*c**3 + 0 - c**2. Factor w(j).
-2*(j - 1)**2
Factor 0 - 1/4*x**5 - 83/4*x**2 - 25/4*x**4 + 7*x + 81/4*x**3.
-x*(x - 1)**3*(x + 28)/4
Determine n, given that -66*n**3 - 24*n + 22*n**4 - 8 - 18*n**3 - 33*n**2 + 127*n**2 = 0.
-2/11, 1, 2
Let f be ((-4)/14)/(160/(-70)). Let s = f - -35/8. Find v, given that 1/2*v**2 + s + 3*v = 0.
-3
Let a be (1*6 + -2)/((-10)/(-10)). Let r(t) be the second derivative of 0 + 1/30*t**5 - 4*t + 5/18*t**a + 4/3*t**2 + 8/9*t**3. Factor r(v).
2*(v + 1)*(v + 2)**2/3
Suppose 221 = -86*y - 427 + 820. Suppose 1/4*n - 1/4*n**y + 1/4*n**4 - 1/4*