+ 13. Let p(k) = 2*k**2 + k**2 + 8*k**4 - 5*k**2 + 6 + 14*k**3 - 2*k**3. Let d(f) = 13*p(f) - 6*u(f). Factor d(j).
2*j**2*(j + 1)*(j + 2)
Let y(s) = -5*s**4 + 18*s**3 - 18*s**2 + 5*s + 3. Let u(j) = 35*j**4 - 125*j**3 + 125*j**2 - 35*j - 20. Let z(g) = 3*u(g) + 20*y(g). Factor z(a).
5*a*(a - 1)**3
Let r = -70 - -72. Let a(j) be the first derivative of 1/5*j**r + 0*j**3 - 1/10*j**4 + 0*j - 3. Factor a(p).
-2*p*(p - 1)*(p + 1)/5
Suppose -y + 2*y - 5 = 0. Let d(r) be the second derivative of -r - 1/3*r**3 - 1/3*r**4 + 0 + 0*r**2 - 1/10*r**y. Factor d(z).
-2*z*(z + 1)**2
Suppose 11*m = 4*m + 147. Suppose -m*c = -16*c - 15. Factor 48/7*w**2 - 18/7*w - 32/7*w**c + 2/7.
-2*(w - 1)*(4*w - 1)**2/7
Suppose -18 - 2 = -5*v. Suppose 5*l - 3 = v*l. Factor -3/2*o**2 + 2*o**4 - 1/2 - 2*o**l + 2*o.
(o - 1)*(o + 1)*(2*o - 1)**2/2
Suppose -5 = -3*d + 1. Solve d*c**2 + 2 + 4*c**2 + 3*c - 5*c**2 = 0 for c.
-2, -1
Let f(x) be the second derivative of x**6/120 - x**5/20 + x**4/8 + x**3/2 - 2*x. Let j(c) be the second derivative of f(c). Factor j(b).
3*(b - 1)**2
Let l(i) = i**2 - i - 1. Let m(k) = k**2 - 2*k - 2. Let b = -3 - -2. Let c(y) = b*m(y) + 2*l(y). Find t, given that c(t) = 0.
0
Let s(u) = 2 - 5*u - 2*u**2 - u + u**2. Let v be s(-6). Solve -b + 6*b**v + b - 4*b - 2*b**4 = 0 for b.
-2, 0, 1
Suppose 0 = f - 4. Suppose l - 4*b + 4 = -7, -31 = -3*l - f*b. Determine s so that -5*s**3 + 3*s**3 + 4*s**3 - 2*s**l - 2*s**4 + 2*s**2 = 0.
-1, 0, 1
Let h = -870 - -872. Factor 2/3 + 0*z - 2/3*z**h.
-2*(z - 1)*(z + 1)/3
Let i(r) be the third derivative of 0 + 0*r + 1/84*r**4 + 0*r**5 + 1/1176*r**8 + 3*r**2 + 0*r**7 - 1/210*r**6 + 0*r**3. Factor i(m).
2*m*(m - 1)**2*(m + 1)**2/7
Let w(c) be the third derivative of 1/18*c**3 + 0 + 0*c + c**2 + 1/180*c**5 + 1/36*c**4. Solve w(h) = 0.
-1
Factor 39/5*z**3 + 0 - 8/5*z**2 - 5*z**5 + 2*z**4 - 16/5*z.
-z*(z - 1)**2*(5*z + 4)**2/5
Suppose 0 = 3*s - 2*o - 42, 2*s - o = -13 + 41. Let c = 16 - s. Factor -5/2*v**2 + 0 - 1/2*v**4 - v - c*v**3.
-v*(v + 1)**2*(v + 2)/2
Let d(u) = -3*u**3 + 7*u**2 - 5*u + 5. Let t be (-12)/2*1/(-3). Let o(z) = z**3 - 3*z**2 + 2*z - 2. Let j(k) = t*d(k) + 5*o(k). Suppose j(w) = 0. What is w?
-1, 0
Factor -7*j + 6*j**2 - 10*j**2 - 9*j - 16.
-4*(j + 2)**2
Let p = 14 + -9. Factor p*r**4 - 2*r**5 - r**3 - r**4 - r**3.
-2*r**3*(r - 1)**2
Let c(x) be the third derivative of -x**9/68040 + x**8/30240 + x**7/11340 - x**6/3240 - x**4/8 - 3*x**2. Let g(r) be the second derivative of c(r). Factor g(w).
-2*w*(w - 1)**2*(w + 1)/9
Let c(m) be the third derivative of m**9/30240 - m**8/5040 - m**7/2520 + m**6/180 - m**5/30 + 2*m**2. Let g(l) be the third derivative of c(l). Factor g(f).
2*(f - 2)*(f - 1)*(f + 1)
Let t(p) = -p**3 + p**2 + p. Let d(l) = 12*l**3 + 9*l**2 + 6*l + 3. Let i(a) = d(a) + 6*t(a). Factor i(k).
3*(k + 1)**2*(2*k + 1)
Let z(x) be the first derivative of 3*x**7/140 - x**6/10 + 11*x**5/60 - x**4/6 + x**3/12 + 3*x**2/2 - 2. Let g(y) be the second derivative of z(y). Factor g(m).
(m - 1)**2*(3*m - 1)**2/2
Let d(r) be the second derivative of r**6/20 + r**5/4 - 5*r**4/24 - 5*r**3/3 + 3*r**2 + 14*r. Determine a, given that d(a) = 0.
-3, -2, 2/3, 1
Factor 1/3*t**2 - 1/3*t - 1/3*t**4 + 0 + 1/3*t**3.
-t*(t - 1)**2*(t + 1)/3
Let v be 4*((-9)/6)/(-3). Factor 2*c**2 + 2*c - v*c**2 + 2*c**2 - c - 2 - c**3.
-(c - 2)*(c - 1)*(c + 1)
Let m be (2 + 1 + -4)*(-6)/5. What is j in m*j + 2/5*j**2 + 4/5 = 0?
-2, -1
Let d(o) be the second derivative of -o**6/80 - 3*o**5/16 - 33*o**4/32 - 5*o**3/2 - 3*o**2 + 4*o. Solve d(g) = 0.
-4, -1
Suppose 0 = -2*r - 10*r. Solve -6/13*y**2 + 2/13*y + r = 0 for y.
0, 1/3
Factor 0*u + 6/5*u**3 - 4/5*u**4 - 2/5*u**5 + 0*u**2 + 0.
-2*u**3*(u - 1)*(u + 3)/5
Suppose 5*l + 3*l = 7*l. Factor -4/3*m - 6*m**2 + l.
-2*m*(9*m + 2)/3
Solve 0 + 1/5*a**4 + a**3 + 3/5*a + 7/5*a**2 = 0 for a.
-3, -1, 0
Let g(d) be the second derivative of -3*d + 1/5*d**2 - 1/105*d**7 + 0 + 1/15*d**6 - 1/5*d**5 + 1/3*d**4 - 1/3*d**3. Find j such that g(j) = 0.
1
Let w(a) be the second derivative of 0 + 3/100*a**5 - 4*a + 1/20*a**4 - 3/10*a**2 - 1/10*a**3. Suppose w(g) = 0. What is g?
-1, 1
Suppose 0 = 5*u - 4*h - 33, -h + 3*h = -4. Suppose 4 - 10*g - 2*g**4 + 3*g**u - 5*g**2 - 7*g**5 + 3*g**2 + 14*g**3 = 0. What is g?
-2, -1, 1/2, 1
Let r be 0/2 + (-12)/(-3). Let t = -4 - -6. Let -10*y + 2*y**3 + 6*y**2 + 0 + 0 - t*y**4 + r = 0. What is y?
-2, 1
Suppose 0 = -2*x - 8, -3*x = 2*i + 8 - 2. Find z such that 8/3*z + 2/3 + 10/3*z**2 + 4/3*z**i = 0.
-1, -1/2
Let i = -5 - -7. Let 0*o**4 - o**3 - o**3 + i*o**5 + 0*o**4 = 0. What is o?
-1, 0, 1
Let l(r) be the first derivative of 9/2*r**2 + 0*r + r**3 - 1. Factor l(c).
3*c*(c + 3)
Let f be ((-72)/27)/(-4) + (-14)/(-6). Determine r, given that 2/9*r**5 + 2/9 + 2/9*r - 4/9*r**f - 4/9*r**2 + 2/9*r**4 = 0.
-1, 1
Let s be ((-2)/(-30))/(1248/120). Let w(p) be the third derivative of s*p**4 + 0*p - 1/390*p**5 + 2*p**2 + 0*p**3 + 0. Find q, given that w(q) = 0.
0, 1
Let y be 1/((-78)/(-81) + -1). Let m = y + 136/5. Factor 1/5*h - 1/5*h**3 + 1/5 - m*h**2.
-(h - 1)*(h + 1)**2/5
Let p(y) be the first derivative of -54*y**3 + 72*y**2 - 32*y - 20. Factor p(v).
-2*(9*v - 4)**2
Let b be ((-4)/24 - 0)*-2. Let w(r) be the first derivative of 0*r**4 - 4/15*r**5 + 0*r - 2 + 1/9*r**6 + 4/9*r**3 - b*r**2. Factor w(g).
2*g*(g - 1)**3*(g + 1)/3
Let m be 4/6*(2 + 1). Factor 0*v**5 + 0*v**5 - m*v**3 - 3*v**5 - v**3 + 6*v**4.
-3*v**3*(v - 1)**2
Let u(w) = 177*w**3 - 849*w**2 + 1122*w - 351. Let t(y) = -11*y**3 + 53*y**2 - 70*y + 22. Let j(z) = 33*t(z) + 2*u(z). Let j(b) = 0. Calculate b.
2/3, 1, 4
Let u = 7613/7 - 1085. Let s = 22/7 - u. Solve 10/7*r - s - 8/7*r**2 + 2/7*r**3 = 0 for r.
1, 2
Let o(b) be the first derivative of -b**4 + 2*b**2 - 1. Factor o(v).
-4*v*(v - 1)*(v + 1)
Let l be (-110)/(-45) - (-1 - -3). Factor 2/9*x**2 + 2/9 + l*x.
2*(x + 1)**2/9
Let n(z) = -47*z**3 + 85*z**2 - 113*z + 24. Let r(c) = 16*c**3 - 28*c**2 + 38*c - 8. Let x(y) = 6*n(y) + 17*r(y). Find a, given that x(a) = 0.
2/5, 1, 2
Let 162*v - 243 - 5*v**4 - 18*v**3 + 11*v**4 - 3*v**4 = 0. Calculate v.
-3, 3
Let v(q) be the second derivative of -4/3*q**4 + 4/3*q**3 + 1/5*q**6 + 0 + 0*q**2 + 1/10*q**5 + 2*q. Factor v(l).
2*l*(l - 1)*(l + 2)*(3*l - 2)
Suppose 0 = 4*q + n - 11, 4*n + 11 = -5*q + 33. Determine z, given that -3/5*z**3 - 2/5*z**q - 2/5 + 7/5*z = 0.
-2, 1/3, 1
Let u = -126 + 129. Determine c so that u*c + 1/2*c**2 + 9/2 = 0.
-3
Let v(d) be the first derivative of -5*d**4/4 - 20*d**3/3 - 10*d**2 + 39. Factor v(n).
-5*n*(n + 2)**2
Let t(l) be the first derivative of -2*l**3/15 + l**2/5 + 12*l/5 + 2. Factor t(x).
-2*(x - 3)*(x + 2)/5
Let m(a) be the second derivative of -7*a**5/150 + a**4/30 + a**2 + 5*a. Let x(h) be the first derivative of m(h). Factor x(s).
-2*s*(7*s - 2)/5
Let f(k) = k**2 + k - 9. Let q be f(-4). Let h be 0 - q/12*-2. Suppose h + 0*o - 1/2*o**2 = 0. Calculate o.
-1, 1
Let d(s) be the second derivative of 2/5*s**2 - 1/15*s**4 - 1/5*s**3 + 0 + s. Factor d(v).
-2*(v + 2)*(2*v - 1)/5
Let f = 2 + -4. Let o be f/(-2 - (-9)/6). Factor 0*p**o - 3*p - 2*p**3 + p**5 + 4*p + 0*p**4.
p*(p - 1)**2*(p + 1)**2
Let f(z) = -5*z**2 - 24*z + 21. Let m(y) = 5*y**2 + 25*y - 20. Let n(k) = -5*f(k) - 4*m(k). Determine q so that n(q) = 0.
-5, 1
Let b = 24 - 16. Suppose -h - 5*a + 20 = -3*h, -3*h = -2*a + b. What is i in 2*i**2 + 4 + 0 + h - 2 + 4*i = 0?
-1
Let c(l) be the first derivative of l**8/420 + l**7/140 - l**5/60 + 2*l**3/3 - 4. Let h(a) be the third derivative of c(a). Factor h(x).
2*x*(x + 1)**2*(2*x - 1)
Let d be 2/8 + (-103)/(-840)*-2. Let t(b) be the second derivative of 1/150*b**6 + b + d*b**7 - 1/50*b**5 - 1/30*b**4 + 0 + 1/10*b**2 + 1/30*b**3. Factor t(c).
(c - 1)**2*(c + 1)**3/5
Let f(o) be the second derivative of -o**10/120960 + o**9/60480 + o**8/26880 - o**7/10080 - o**4/12 - o. Let l(p) be the third derivative of f(p). Factor l(t).
-t**2*(t - 1)**2*(t + 1)/4
Let r(k) = 3*k - 21. Let n be r(8). Find p such that -1/2*p**4 + 0*p**n + 1/2*p**2 - 1/4*p**5 + 1/4*p + 0 = 0.
-1, 0, 1
Let r(o) be the second derivative of -3*o**5/10 - 7*o**4/15 - o**3/5 - 18*o. Factor r(v).
-2*v*(3*v + 1)*(5*v + 3)/5
Factor 3*w**4 - w**2 + 5*w**3 + 4 + 0 + 1 - 7 - 5*w.
(w - 1)*(w + 1)**2*(3*w + 2)
Let n(w) be the second derivative