 y, given that 0*y + 36/7*y**2 + 0 + 4/7*y**q - 24/7*y**3 = 0.
0, 3
Let d(y) be the third derivative of y**6/40 - y**5/2 + 31*y**4/8 - 15*y**3 + y**2 - 31*y. Factor d(r).
3*(r - 5)*(r - 3)*(r - 2)
Let u be 18/(-135) + 1/(15/197). Suppose u*f - 45 + 19 = 0. Determine d, given that 2/3 + 2/3*d + 1/6*d**f = 0.
-2
Factor 0*s - 16/9*s**3 - 20/9*s**4 + 0 + 0*s**2 + 2/3*s**5.
2*s**3*(s - 4)*(3*s + 2)/9
Let c = -16 - -20. Let v be -3*c*(-4)/24. Factor 2*u**4 - u**2 + 5*u**5 - 4*u**3 - u**5 - 3*u**v + 2*u**4.
4*u**2*(u - 1)*(u + 1)**2
Suppose -5*w - r = -15, 3*r + 105 = 3*w + 96. Solve 0 - 6*f + 6*f**2 - 3/2*f**w = 0.
0, 2
Let z(i) = -i**2 - 9*i + 1. Let y be z(-9). Let g = 2 + y. What is b in -b - 12*b**4 - 21*b**3 + 3*b - 6*b**2 - g*b + 4*b = 0?
-1, 0, 1/4
Suppose 2*l - 66 = -9*l. Let f be (-4 + -1 + l)/(2/8). Determine n so that -54/5*n**2 + 0*n + 81/5 - 24/5*n**3 - 3/5*n**f = 0.
-3, 1
Let v = -1681 + 1683. Find m, given that -2/3*m**2 - v - 8/3*m = 0.
-3, -1
Let g be (6/45)/(15/50). Let x = 845/3 + -281. What is y in g - x*y + 2/9*y**2 = 0?
1, 2
Let q(c) be the third derivative of -c**6/1080 + c**5/45 - 5*c**4/24 + 25*c**3/27 + 229*c**2 + 1. Determine a so that q(a) = 0.
2, 5
Suppose -4*s = -13*s - 342. Let t = s + 41. Factor 2*u**3 - 3*u**t - 179*u**2 + 5*u + 180*u**2 + 3.
-(u - 3)*(u + 1)**2
Determine p, given that 3/7*p**2 + 54/7*p + 0 = 0.
-18, 0
Let b(k) be the third derivative of k**7/560 + k**6/320 - 7*k**5/160 - 13*k**4/64 - 3*k**3/8 + 35*k**2. Factor b(w).
3*(w - 3)*(w + 1)**2*(w + 2)/8
Let 4/5*x - 2/5*x**2 - 1/5*x**3 + 8/5 = 0. Calculate x.
-2, 2
Let n(z) = -34*z**4 - 152*z**3 - 346*z**2 - 14*z - 14. Let p(w) = -7*w**4 - 30*w**3 - 69*w**2 - 3*w - 3. Let j(d) = 3*n(d) - 14*p(d). Let j(b) = 0. Calculate b.
-6, -3, 0
Let d(h) = -5*h**3 + 13*h**2 - 7*h - 13. Let b(r) = r**3 - r**2 + r + 1. Let y(o) = 6*b(o) + d(o). Determine k so that y(k) = 0.
-7, -1, 1
Let t(r) be the second derivative of -3*r**5/20 - 5*r**4/4 - r**3 + 12*r**2 + 35*r. Factor t(y).
-3*(y - 1)*(y + 2)*(y + 4)
Let q(f) be the first derivative of -f**7/735 + f**6/420 - 13*f**2/2 + 16. Let m(g) be the second derivative of q(g). Determine z, given that m(z) = 0.
0, 1
Let o(u) be the first derivative of -u**6/900 - u**5/75 - u**4/20 + 3*u**3 - 45. Let t(y) be the third derivative of o(y). Find z, given that t(z) = 0.
-3, -1
Let w be 14*(70/175 + (-34)/160). Let g(r) be the first derivative of 12*r - 2 + 3/10*r**5 + 9*r**3 - w*r**4 - 15*r**2. Factor g(a).
3*(a - 2)**3*(a - 1)/2
Let r be (-2)/(1*4 - (-98)/(-21)). Determine q, given that -41*q**4 - 128 - 23*q**2 + 223*q + 129*q - 158*q**r + 15*q**2 - 5*q**5 - 12*q**4 = 0.
-4, 2/5, 1
Let g = 224 - 116. Let y be ((-4)/7)/(g/(-84)). Factor -2/9*s**2 - y*s + 0.
-2*s*(s + 2)/9
Let p be 18 + -18 - (-36 + 1). Suppose 0 = -p*l + 38*l. Factor l + 1/5*x**3 + 3/5*x**2 + 2/5*x.
x*(x + 1)*(x + 2)/5
Let a be ((-695)/278)/(3/(-6)). Factor -16/3*o**3 + 0 - 20/9*o**4 - 2/9*o**a - 44/9*o**2 - 14/9*o.
-2*o*(o + 1)**3*(o + 7)/9
Let t = -204 - -206. Factor 1/2*v + 1/4 + 1/4*v**t.
(v + 1)**2/4
Suppose 0 = -4*a + 15 + 1. Let t be 1 - (-1 - 0)*1. Factor 3*w - a + 4*w**3 + 2*w**4 + t - 8*w + w.
2*(w - 1)*(w + 1)**3
Determine p, given that -4*p**2 + 52 - 72 + 144*p - 51 - 31 - 38 = 0.
1, 35
Let h(a) be the third derivative of -13*a**2 + 1/20*a**4 + 1/15*a**3 + 1/75*a**5 - 1/175*a**7 - 1/150*a**6 - 1/840*a**8 + 0*a + 0. Solve h(x) = 0.
-1, 1
Let i(n) be the third derivative of n**6/40 + n**5/20 - 5*n**4/8 + 3*n**3/2 - 179*n**2. Suppose i(r) = 0. What is r?
-3, 1
Let q(u) = 6*u - 4. Let z be q(-28). Let j = -168 - z. What is t in -2*t + 4*t**3 + 4/3 + 4/3*t**j - 8/3*t**2 - 2*t**5 = 0?
-1, 2/3, 1
Let l(r) be the second derivative of 0*r**2 - 7/80*r**5 - 1/16*r**4 + 1/40*r**6 + 5/168*r**7 - 2*r + 0 + 1/12*r**3. Determine c so that l(c) = 0.
-1, 0, 2/5, 1
Let b(g) be the first derivative of g**4/12 - 10*g**3/9 + 7*g**2/2 - 140. Determine x, given that b(x) = 0.
0, 3, 7
Let j = 745 - 1489/2. Factor n**3 - 1/2*n**5 - 1/2*n + j + 1/2*n**4 - n**2.
-(n - 1)**3*(n + 1)**2/2
Factor -19/4*h**2 - 1/2 - 21/4*h.
-(h + 1)*(19*h + 2)/4
Let s(j) be the second derivative of -j**5/60 + 8*j**4/9 - 128*j**3/9 - 21*j - 1. Find d such that s(d) = 0.
0, 16
Let h(l) = 2*l**2 - l. Let x(i) be the third derivative of -i**5/6 + i**4/6 - 14*i**2. Let g(n) = -14*h(n) - 3*x(n). Factor g(q).
2*q*(q + 1)
Let a(m) = -24*m - 72. Let c be a(-3). Let q(t) be the second derivative of -t + c*t**2 + 0 - 1/100*t**5 - 1/60*t**4 + 0*t**3. Factor q(d).
-d**2*(d + 1)/5
Let q be -4 + 3 + 3/3. Let w(f) be the second derivative of 1/30*f**4 + 0 + 5*f + q*f**2 + 0*f**3. Let w(j) = 0. Calculate j.
0
Let z(d) be the second derivative of d**4/6 - 14*d**3/3 - 32*d**2 - 197*d. Solve z(l) = 0 for l.
-2, 16
Let l(v) = 23*v**2 + 60*v - 17*v - 75*v**3 - 21*v - 18*v + 7. Let u(f) = -25*f**3 + 8*f**2 + f + 2. Let o(j) = -2*l(j) + 7*u(j). Solve o(k) = 0 for k.
0, 1/5
Let t(x) = -x - 4. Let w be t(5). Let f be 12/w*(-9)/6. What is z in 17*z**3 + 12*z**4 + 12*z**3 - 4*z**5 - 5*z**3 - 36 - 40*z**f - 84*z = 0?
-1, 3
Suppose 13*v + 132 = 158. Factor 35/2*k**2 + v - 13*k + 49/4*k**3.
(k + 2)*(7*k - 2)**2/4
Suppose 23 = u - 3*z, 0 = 4*u - 3*u + z - 7. Factor 11 - x**2 - x - u.
-x*(x + 1)
Let b = -15/2398 + -3614/5995. Let k = -6/55 - b. Factor 1/2*m**4 + 1/2*m - k*m**3 - 1/2*m**2 + 0.
m*(m - 1)**2*(m + 1)/2
Let p be 5*-2*(-3)/6. Suppose 0 = -8*s - p + 21. Suppose 0*o + 0 + 1/3*o**s + 1/3*o**3 = 0. What is o?
-1, 0
Let b(f) = f**3 + 7*f**2 - 3*f - 1. Let d be b(-7). Let u be ((-15)/d)/((-3)/36). Factor -u*n**3 + 30*n**3 - 50*n**2 + 24*n + 12 - 7*n**2.
3*(n - 2)*(n - 1)*(7*n + 2)
Suppose -13*k - 191 = -1543. Suppose -g + 3*u = 4, 2*g = -3*u + 4 + 6. Solve k*f**2 + 3*f**4 + 3*f**3 - 101*f**g + 3*f**3 = 0.
-1, 0
Solve -10*o + 800*o**3 + 4*o**2 + 2*o**2 - 798*o**3 - 2*o - 16 = 0.
-4, -1, 2
Let c(r) = 5*r + 15. Let x(g) = -4*g - 14. Let j(w) = 6*c(w) + 7*x(w). Let n be j(5). What is m in -3/7*m**4 + 0*m + 0 + 3/7*m**n + 0*m**3 = 0?
-1, 0, 1
Suppose 0 = -12*f - 130 + 130. Let m(q) be the third derivative of -1/6*q**5 + 0*q - 1/15*q**6 + 0 + f*q**3 - 11*q**2 - 1/6*q**4 - 1/105*q**7. Factor m(n).
-2*n*(n + 1)**2*(n + 2)
Suppose 24*p**2 + 170*p**3 - 4*p**4 - 96*p - 130*p**3 - 76*p**2 = 0. Calculate p.
-1, 0, 3, 8
Suppose 10 - 26 = -8*b. Let q(a) be the first derivative of -1 - 2/3*a**3 + 0*a + a**b. Factor q(m).
-2*m*(m - 1)
Determine i so that -92/3*i**2 - 4/3*i**4 - 40/3*i + 40/3*i**3 + 32 = 0.
-1, 1, 4, 6
Let r = 13655 - 13655. Factor r*t**4 + 3/2*t**3 - 3/4*t**5 + 0 + 0*t**2 - 3/4*t.
-3*t*(t - 1)**2*(t + 1)**2/4
Let q(v) = -v**4 - 5*v**3 + 4*v + 2. Suppose -5*d + 25 = 0, 2*k - 2*d - 8 = -6*d. Let r(z) = -z**3 + 1. Let j(a) = k*r(a) + 3*q(a). Factor j(n).
-3*n*(n - 1)*(n + 2)**2
Let b(d) = 18*d**4 + 29*d**3 + 115*d**2 + 115*d + 7. Let l(c) = 10*c**4 + 14*c**3 + 58*c**2 + 58*c + 4. Let x(z) = -4*b(z) + 7*l(z). Solve x(s) = 0.
-3, 0
Suppose 0 = -26*h + 11*h - 135. Let z be (h/(-6))/(1/2). Let -2/3*g**2 - 4/3*g + 0 + 2/3*g**z = 0. What is g?
-1, 0, 2
Factor 60*t**3 + 45/2*t**4 + 0*t + 5/2*t**5 + 40*t**2 + 0.
5*t**2*(t + 1)*(t + 4)**2/2
Let c(k) = -2*k**4 - 14*k**3 - 2*k**2 + 62*k - 28. Let b(t) = -t**4 - 15*t**3 - 3*t**2 + 61*t - 30. Let z(s) = -4*b(s) + 3*c(s). Factor z(y).
-2*(y - 9)*(y - 1)**2*(y + 2)
Let m(y) be the first derivative of 1/2*y**2 - 2 - 1/20*y**5 - 1/2*y**3 - 1/4*y + 1/4*y**4. Determine o so that m(o) = 0.
1
Suppose -5*y + 9 + 11 = 0. Suppose 3*o - w - 6 = 0, -3*o + w - 2 = -y*o. Determine z so that -1/3*z**4 + 0 - 1/6*z**5 + 1/3*z**o + 1/6*z + 0*z**3 = 0.
-1, 0, 1
Suppose -6 + 17*h**2 - 16*h - 7*h - 14*h**2 - 10*h**2 = 0. What is h?
-3, -2/7
Let l(s) be the second derivative of 0 - 1/220*s**5 - 5/66*s**3 - 1/11*s**2 - 1/33*s**4 - 10*s. Determine v, given that l(v) = 0.
-2, -1
Suppose -2/11*o**3 + 76/11*o**2 + 1296/11 - 72*o = 0. Calculate o.
2, 18
Let s(g) be the second derivative of -1/60*g**4 + 0*g**3 + 0*g**2 - 32*g - 2 - 1/50*g**5 - 1/150*g**6. Find v such that s(v) = 0.
-1, 0
Factor 35/8*n**2 + 3/8*n**3 + 11/4*n + 0.
n*(n + 11)*(3*n + 2)/8
Factor 3/4*i**2 + 9 + 6*i.
3*(i + 2)*(i + 6)/4
Let t(h) = -h**2 + 7*h - 30. Let y be t(10). Let j be ((-72)/15)/(54/y). Suppose -8*x - 2/3*x**3 + 4*x**2 + j = 0. What is x?