*(g - 3)
Let l(v) be the first derivative of v**6/180 + v**5/54 + v**4/54 + 21*v**2/2 - 36. Let g(w) be the second derivative of l(w). Factor g(q).
2*q*(q + 1)*(3*q + 2)/9
Suppose m + 1 - 3 = 0. Factor 0*h**m + 5*h**2 + h - 4*h**2 - 3*h.
h*(h - 2)
Let q(d) be the third derivative of -1/84*d**4 - 1/210*d**5 + 0*d + 0 - d**2 + 0*d**3. Factor q(h).
-2*h*(h + 1)/7
Let m(c) = -12*c**3 - 92*c**2 + 184*c - 88. Let g(y) = -10*y**3 - 91*y**2 + 185*y - 90. Let k(v) = 4*g(v) - 3*m(v). Factor k(z).
-4*(z - 1)**2*(z + 24)
Let n(r) = r - 1. Let o(t) = 4*t**2 - 26*t + 22. Let c(v) = -6*n(v) - o(v). Find k such that c(k) = 0.
1, 4
Let k(r) = 2*r - 21. Let l be k(12). Solve 24*n**2 + 3*n**4 - 62 + 17*n**3 + n**l + 62 = 0 for n.
-4, -2, 0
Let n(m) be the second derivative of 4*m**5/5 - 7*m**4 + 58*m**3/3 - 12*m**2 + 259*m. Find j, given that n(j) = 0.
1/4, 2, 3
Let u be ((-12)/(-8))/(15/40). Suppose 7*i = -u*i. Factor 0 + i*d**2 + 2/15*d**4 + 0*d + 2/15*d**3.
2*d**3*(d + 1)/15
Let s(o) be the third derivative of o**5/12 - 20*o**4/3 - 287*o**2. Factor s(i).
5*i*(i - 32)
Suppose 4*u = 10*p - 12*p + 4, -5*u + 12 = -p. Factor -2/13*y**u + 10/13 - 8/13*y.
-2*(y - 1)*(y + 5)/13
Let u(h) be the first derivative of -h**4/6 - 14*h**3/9 - 5*h**2 - 6*h - 173. Factor u(w).
-2*(w + 1)*(w + 3)**2/3
Let l(y) = y**3 - 7*y**2 + 11*y - 27. Let a be l(6). Let h(c) be the first derivative of 1/2*c**4 + 4*c + 1/5*c**5 - 2*c**2 + 10 - c**a. Factor h(j).
(j - 1)**2*(j + 2)**2
Suppose 25*m - 42 = 18*m. Factor 4*p**4 + 14*p**2 - 90*p**3 + 76*p**3 - m*p + 2*p.
2*p*(p - 2)*(p - 1)*(2*p - 1)
Let -21/4*r + 3/2 + 3/4*r**4 + 27/4*r**2 - 15/4*r**3 = 0. What is r?
1, 2
Let w be 4/120*7/((-42)/(-344)). Let n = 28/9 - w. Find l, given that 2/15*l**2 + n + 4/5*l = 0.
-3
Suppose 5*u = 23 - 8. Factor 12*c**3 + 78*c**2 + 15 - 36*c**u + 33 + 3*c**4 - 96*c - 6*c**2.
3*(c - 2)**4
Factor 3/2*w**4 - 600*w - 408 - 288*w**2 - 42*w**3.
3*(w - 34)*(w + 2)**3/2
Let u(a) be the first derivative of -3*a**4/4 - 4*a**3/3 - 3*a**2/2 + 11. Let d(m) = -4*m**3 - 5*m**2 - 4*m. Let s(r) = 2*d(r) - 3*u(r). Factor s(p).
p*(p + 1)**2
Let v(g) be the second derivative of -1/21*g**4 + 0*g**2 + 3/70*g**5 + 0*g**6 + 0 + 0*g**3 - 15*g - 1/147*g**7. Find x, given that v(x) = 0.
-2, 0, 1
Let p be 130/39 + 2/(-6). Let u(h) be the second derivative of -1/21*h**p + 4*h - 1/42*h**4 + 0*h**2 + 0. Factor u(a).
-2*a*(a + 1)/7
Suppose 0 = 3*x - 2*x, 3 = 4*y - y + 4*x. Factor 1/2*s**5 + 4*s**2 - s**3 - 7/2*s + y - s**4.
(s - 1)**4*(s + 2)/2
Let y(m) = -m**2 + 26*m. Let o(w) = 4*w**2 - 78*w. Let k(r) = 3*o(r) + 10*y(r). Find u such that k(u) = 0.
-13, 0
Let r(k) be the first derivative of 5*k**2/2 - 2*k + 7. Let g be r(1). Solve 2*u**2 - u - 101*u**3 + 0 - 2 + 102*u**g = 0.
-2, -1, 1
Let r be ((-2)/(-3))/(-2)*-9. Let k(a) be the third derivative of 1/120*a**5 + 0*a + 0 - 1/16*a**4 - 3*a**2 + 1/6*a**r. Factor k(p).
(p - 2)*(p - 1)/2
Factor 4 - i - 1/2*i**2.
-(i - 2)*(i + 4)/2
Let d(r) be the second derivative of -r**4/60 + r**3/6 - 3*r**2/5 + 40*r. Suppose d(l) = 0. Calculate l.
2, 3
Factor 12 + 103*a**2 - 67*a**2 + 12*a**3 - 35*a**2 - 63*a**2 - 62*a.
2*(a - 6)*(a + 1)*(6*a - 1)
Let 7/3*d - 95/6*d**2 + 5/6*d**4 + 26/3*d**3 + 4 = 0. What is d?
-12, -2/5, 1
Let q be 10*(3 - (-110)/(-40)). Factor t**4 + 0 + 0*t - q*t**3 + t**2.
t**2*(t - 2)*(2*t - 1)/2
Suppose 0*n + 7*n = 91. Factor 15*m**2 - 4*m**5 - 15*m**4 - 10*m + 5*m**3 - n*m**5 + 22*m**5.
5*m*(m - 2)*(m - 1)**2*(m + 1)
Let t = 1535 - 4597/3. Let h(i) be the first derivative of 4/3*i**4 + 8/9*i**3 - t*i**2 - 5 + 4/15*i**5 - 4*i. Determine q so that h(q) = 0.
-3, -1, 1
Let s(i) = i**3 - 12*i**2 - 1. Let o be s(12). Let a be 2/56 - o/4. Let -a*d**3 + 0 + 0*d**2 + 2/7*d**4 + 0*d = 0. Calculate d.
0, 1
Let h(g) be the second derivative of -g**6/108 - 7*g**5/180 - g**4/18 - 35*g**3/6 - 15*g. Let w(b) be the second derivative of h(b). Factor w(y).
-2*(y + 1)*(5*y + 2)/3
Factor 1/8*k**3 + 0*k + 3/8*k**2 + 0.
k**2*(k + 3)/8
Let -7/5 + 6/5*t + 1/5*t**2 = 0. Calculate t.
-7, 1
Let y(z) be the third derivative of -z**5/60 - z**4/8 + 5*z**3/3 + 15*z**2 + 2. Factor y(n).
-(n - 2)*(n + 5)
Let v = -25 - -27. Let c = -8 - -10. Find g, given that 4*g**4 + 43*g**3 - 38*g**3 + 0*g**5 + g**5 + v*g**c = 0.
-2, -1, 0
Let q(i) be the second derivative of -38/21*i**3 - 12/7*i**2 - i + 0 + 1/3*i**4. Factor q(y).
4*(y - 3)*(7*y + 2)/7
Determine r, given that 7087*r**3 - 5*r**5 - 10*r**4 - 4 + 4 - 7092*r**3 = 0.
-1, 0
Let u(w) = 2*w**4 - w**2 + w. Let h(r) = 19*r**4 - 7*r**3 - 17*r**2 + 9*r. Let q(x) = -2*h(x) + 18*u(x). Suppose q(l) = 0. What is l?
-1, 0, 8
Let g = -2/5347 + 53476/16041. Suppose 0 = 2*t + 2*w - 14, 0*t - 3*t = -3*w + 9. Factor 2*j**3 - 22/3*j**2 + t + g*j.
2*(j - 3)*(j - 1)*(3*j + 1)/3
Let l(d) be the first derivative of 8*d**2 - 2/3*d**6 - 40/3*d**3 + 7 - d**4 + 16/5*d**5 + 32*d. Solve l(w) = 0 for w.
-1, 2
Let k(z) be the second derivative of z**5/330 + z**4/66 - z**3/11 - 15*z**2/2 + 2*z. Let m(f) be the first derivative of k(f). Factor m(y).
2*(y - 1)*(y + 3)/11
Let -3/4*z**4 - 3/2*z**3 + 3/4*z**2 + 0 + 3/2*z = 0. What is z?
-2, -1, 0, 1
Suppose -5 - 1 = 3*g, 29 = 3*k - g. What is x in 21*x**4 + 12*x**5 - k*x**5 + 24*x**2 - 48 + 42*x**3 - 48*x + 6*x**3 = 0?
-2, 1
Determine h so that 3/2*h**4 + 75/2*h**2 + 15*h**3 + 0*h + 0 = 0.
-5, 0
Let m(u) = u**2 + 16*u - 17. Let l(z) = 34*z - 16. Let g(y) = 8*y - 4. Let f(p) = 9*g(p) - 2*l(p). Let b = -24 - -15. Let d(k) = b*f(k) + 2*m(k). Factor d(j).
2*(j - 1)**2
Let l(x) be the second derivative of x**7/14 - x**6/10 - 3*x**5/10 + x**4/2 + x**3/2 - 3*x**2/2 + 6*x. What is r in l(r) = 0?
-1, 1
Let v(l) be the first derivative of -l**4/18 + l**3/9 + 2*l**2/3 + l + 3. Let d(a) be the first derivative of v(a). What is m in d(m) = 0?
-1, 2
Let c be 798/(-570) + 327/5 + 0. Factor -256/3 + c*n - 16*n**2 + 4/3*n**3.
4*(n - 4)**3/3
Let g(d) be the third derivative of -d**8/14 + 3*d**7/7 - 31*d**6/40 + d**5/10 + 9*d**4/8 - d**3 + 425*d**2. Let g(x) = 0. What is x?
-1/2, 1/4, 1, 2
Factor 4*r**3 - 144*r + 208*r - r**3 - 4*r**3 + 42*r**2 + 21*r**2.
-r*(r - 64)*(r + 1)
Let s(m) be the third derivative of 0*m**5 + 1/210*m**7 + 0*m + 0*m**3 - 12*m**2 + 0*m**6 + 0 + 1/336*m**8 + 0*m**4. Factor s(r).
r**4*(r + 1)
Suppose 4*p = -2*s + 50, -2*s = -5*p + 9 - 41. Suppose l + 3*w = -4 + s, 2*l = 3*w - 2. Factor -1 + 2*d**2 - 6*d - l*d**2 - 1 - d.
-(d + 2)*(3*d + 1)
Let x(z) be the third derivative of z**6/60 - z**5/15 - 18*z**2. Factor x(r).
2*r**2*(r - 2)
Let p(y) = -5*y**2 - 7*y + 2. Let j(b) = b**2 - 2. Let t(w) = 4*j(w) + p(w). Factor t(o).
-(o + 1)*(o + 6)
Suppose -4 = -24*c - 31*c - 4. Find k, given that c - 20/3*k**2 - 8*k + 4/3*k**3 = 0.
-1, 0, 6
Let i(n) = -19*n**2 - 61*n + 196. Let x(c) = -51*c**2 - 184*c + 589. Let y(d) = -11*i(d) + 4*x(d). Factor y(h).
5*(h - 8)*(h - 5)
Let m(j) = j**2 + j - 3. Let k(p) = 4*p**2 - 951*p + 45128. Let v(l) = k(l) + m(l). Suppose v(d) = 0. What is d?
95
Let f(q) = -q**3 + 4*q**2 + 5*q - 1. Suppose 0 = 4*x - 5*z + 2*z - 31, -7 = 2*x + 3*z. Let l be f(x). Factor -8 - l*a + 19*a + 6*a**2 + 2*a**3.
2*(a - 1)*(a + 2)**2
Suppose -4*d + 5*d = -3*o + 3, 0 = -4*o + 3*d - 9. Determine f, given that o*f - 3/8 + 3/8*f**2 = 0.
-1, 1
Let y(l) be the third derivative of l**8/336 - l**7/84 - l**6/24 + 41*l**3/6 + 9*l**2 - 2. Let k(g) be the first derivative of y(g). Factor k(x).
5*x**2*(x - 3)*(x + 1)
Let t be (-510)/168 + 4 + -1. Let d = 9/28 + t. Factor 4/7*l**2 + 0 - d*l**3 + 0*l.
-2*l**2*(l - 2)/7
Let p(n) be the third derivative of -n**6/210 + 8*n**5/35 + 17*n**4/14 + 52*n**3/21 - 143*n**2. Let p(g) = 0. What is g?
-1, 26
Let r(y) be the first derivative of -y**4/4 + 5*y**3/3 + 13*y**2/2 + 7*y - 118. Factor r(b).
-(b - 7)*(b + 1)**2
Let c(z) be the first derivative of -2*z**3/3 - 34*z**2 - 133. Factor c(a).
-2*a*(a + 34)
Let r(h) be the first derivative of h**4/8 + 3*h**3 - 21*h**2/4 - 19*h - 545. Solve r(w) = 0.
-19, -1, 2
Let t(j) be the first derivative of -21*j**4/4 + 9*j**3 - 3*j**2 + 154. Factor t(d).
-3*d*(d - 1)*(7*d - 2)
Let t = 3516/481 - 32703/4810. Let o = -2/185 + t. Factor 1/2*f**3 - 1/2*f**2 + 1/2 - o*f.
(f - 1)**2*(f + 1)/2
Suppose 74*u = 75*u - 3. Let -f**4 - 8*f**2 + 9 + 63*f - 18*f - 19*f - 20*f - 6*f**u = 0. What is f?
