+ 21. Let h(j) be the second derivative of 0*j**2 + 0 + p*j + 1/60*j**6 - 1/24*j**4 + 0*j**5 - 1/168*j**7 + 1/24*j**3. Let h(a) = 0. What is a?
-1, 0, 1
Suppose -5*a = 33 - 83. Let 1 + a*l**4 - 1 + 9*l**2 + 6*l - 13*l**4 = 0. What is l?
-1, 0, 2
Suppose -25 = 3*i + 5*d, 3*i + 5*d + 25 = 5*i. Find f such that 1/3*f**5 + 0*f**2 + 0*f + 2/3*f**4 + i + 1/3*f**3 = 0.
-1, 0
Factor -30/13*m**2 + 8/13 + 8/13*m**3 + 24/13*m.
2*(m - 2)**2*(4*m + 1)/13
Factor 1/7*f**3 + 1/7*f + 0 - 2/7*f**2.
f*(f - 1)**2/7
Let w = -1 - 0. Let h be (2 - (1 + 1))/w. Suppose -2*o**2 - 4*o + 3 - 5 + h*o = 0. What is o?
-1
Let x(l) = 3*l**2 - 2*l + 5. Let y(o) be the second derivative of -o**4/4 + o**3/2 - 3*o**2 - 6*o. Let t(b) = -6*x(b) - 5*y(b). Factor t(h).
-3*h*(h + 1)
Let l be 45/6*2/3. Suppose 17 = 4*u - l*m, -u - m + 23 = 4*m. Factor 0*t - 4*t**2 - 8*t**3 + 7*t**4 + u*t - t**4 - 2.
2*(t - 1)**2*(t + 1)*(3*t - 1)
Let q(v) be the first derivative of -1/50*v**5 - 1/5*v**2 + 1/15*v**3 + 1/30*v**4 - v + 3. Let f(t) be the first derivative of q(t). Factor f(w).
-2*(w - 1)**2*(w + 1)/5
Let u = 11 + -11. Let q(a) be the first derivative of -7/18*a**4 + u*a - 10/27*a**3 + 2/9*a**2 - 2. Factor q(p).
-2*p*(p + 1)*(7*p - 2)/9
Let p be (4 - (-175)/(-45))/1. Let t(h) be the first derivative of -p*h**3 - 1 - 1/6*h**2 + 2/3*h. Find y such that t(y) = 0.
-2, 1
Let v be 5 - 0 - 2/1. Suppose 2*d - d - v = 0. Factor -u**4 + u**d - 1 + 1.
-u**3*(u - 1)
Let z(h) be the first derivative of h**6/36 + h**5/30 - 5*h**4/24 - h**3/18 + 2*h**2/3 - 2*h/3 - 28. Suppose z(l) = 0. Calculate l.
-2, 1
Let j = -64956/721 - 432/103. Let d = -94 - j. Suppose -2/7*p**4 + 0*p**3 + 4/7*p**2 - d + 0*p = 0. Calculate p.
-1, 1
Let z(w) be the second derivative of -w**7/6300 + w**6/2700 + w**5/900 - w**4/180 + w**3/6 + w. Let p(k) be the second derivative of z(k). Factor p(g).
-2*(g - 1)**2*(g + 1)/15
Let i(c) be the third derivative of 4*c**2 + 0*c**3 + 0*c - 1/90*c**5 + 1/315*c**7 + 0 + 1/180*c**6 - 1/36*c**4. Factor i(w).
2*w*(w - 1)*(w + 1)**2/3
Let o be (-51)/(-15) + 2/(-5). Determine u so that u - 22*u - 22*u**3 + 43*u**o - 6 + 6*u**2 = 0.
-1, -2/7, 1
Factor 2*o**3 - 2 + 10*o**2 - 16 - 6*o - 4*o**3 + 0*o**3.
-2*(o - 3)**2*(o + 1)
Let b be ((-20)/(-2))/5 + 57/(-30). Let m(g) be the third derivative of -1/60*g**6 + 0 + 0*g**3 + 0*g + 2*g**2 - b*g**5 - 1/6*g**4. Factor m(r).
-2*r*(r + 1)*(r + 2)
Let l(h) = -5*h**2 - h + 4. Let s(o) = 11*o**2 + 2*o - 9. Let n(r) = -9*l(r) - 4*s(r). Factor n(j).
j*(j + 1)
Let x = -7 + 10. Factor -2*z**3 - z - 3*z + 6*z**x.
4*z*(z - 1)*(z + 1)
Let w(h) be the third derivative of -h**8/112 - h**7/70 + 3*h**6/40 + h**5/20 - h**4/4 - 4*h**2. What is v in w(v) = 0?
-2, -1, 0, 1
Let d(p) be the first derivative of p**5/20 + p**4/16 - 5*p**3/12 + 3*p**2/8 + 9. Factor d(n).
n*(n - 1)**2*(n + 3)/4
Let d(j) be the first derivative of j**3 - 1 + 0*j - 9/2*j**2. Factor d(y).
3*y*(y - 3)
Let k = -5 + 8. Let n(a) = -a - 7*a**2 + 8 + k*a - a. Let w(g) = 20*g**2 - 3*g - 23. Let p(h) = 17*n(h) + 6*w(h). Suppose p(f) = 0. Calculate f.
-1, 2
Let b be 2*(-3)/(-2 - 4). Let u = b + 2. Factor -4*q - q**3 + u*q + 2*q**3.
q*(q - 1)*(q + 1)
Let z(i) = 2*i + 14. Let m be z(-7). Let y(r) be the second derivative of 0*r**2 - 2*r + 0 + 7/18*r**7 + 0*r**4 + 14/45*r**6 + 1/15*r**5 + m*r**3. Factor y(s).
s**3*(7*s + 2)**2/3
Let c(f) = 4*f**4 + 68*f**3 - 216*f**2 + 224*f - 96. Let o(a) = -a**4 - 23*a**3 + 72*a**2 - 75*a + 32. Let r(v) = 5*c(v) + 16*o(v). Factor r(d).
4*(d - 2)**3*(d - 1)
Let j(i) be the third derivative of -i**9/11340 - i**8/2520 - i**7/1512 - i**6/2160 + i**4/8 + 3*i**2. Let b(w) be the second derivative of j(w). Factor b(q).
-q*(q + 1)*(2*q + 1)**2/3
Let -188/3*d**2 - 88/3*d - 194/3*d**3 - 32*d**4 - 6*d**5 - 16/3 = 0. What is d?
-2, -1, -2/3
Suppose -34 = -9*p + 20. Let o(x) be the second derivative of 0*x**2 + 0 - 1/21*x**7 + 0*x**4 - 2*x + 1/5*x**5 + 0*x**p - 1/3*x**3. Factor o(k).
-2*k*(k - 1)**2*(k + 1)**2
Let 0*f + 8/5*f**2 - 18/5*f**4 - 14/5*f**5 + 0 + 24/5*f**3 = 0. Calculate f.
-2, -2/7, 0, 1
Let f(w) be the second derivative of -w**6/30 + w**5/10 + w**4/3 - w**3/3 - 3*w**2/2 + 13*w + 1. Factor f(k).
-(k - 3)*(k - 1)*(k + 1)**2
Find h such that 5/6*h - 5/6*h**3 + 5/3 - 5/3*h**2 = 0.
-2, -1, 1
Let f(b) be the second derivative of -b**4/12 + 4*b**3/3 - 8*b**2 + 2*b. Determine v, given that f(v) = 0.
4
Let v(s) = -13*s**4 + 7*s**3 + 38*s**2 - 28*s - 8. Let m(z) = -12*z**4 + 7*z**3 + 38*z**2 - 28*z - 8. Let k(a) = -4*m(a) + 3*v(a). Solve k(i) = 0 for i.
-2, -2/9, 1, 2
Factor 8*y**2 + 3*y - 6*y**2 - 5*y**2.
-3*y*(y - 1)
Let x(f) = f**3 - 2*f**2 + f + 2. Let d be x(2). Let h be (-3)/(-1) + (d - 5). Solve 1 + p**h + p**2 - 1 = 0 for p.
0
Find b, given that 2/7*b**2 + 2/7*b - 2/7 - 2/7*b**3 = 0.
-1, 1
Let k(h) = h - 12. Let f be k(17). What is g in -1/3*g - 2/3*g**2 + 1/3*g**4 + 2/3*g**3 + 1/3 - 1/3*g**f = 0?
-1, 1
Let x be (-14)/21 + 206/300. Let f(j) be the second derivative of 0*j**3 + 1/30*j**4 + 0 + 0*j**2 - 2*j + x*j**5. Factor f(p).
2*p**2*(p + 1)/5
Let q = 2390/9 - 267. Let i = 187/117 + q. Factor 4/13 - i*c - 2/13*c**2.
-2*(c - 1)*(c + 2)/13
Let d(l) be the first derivative of -1/4*l**2 + 1/80*l**5 + 1/24*l**4 - 3*l + 3 - 1/24*l**3. Let b(x) be the first derivative of d(x). Factor b(w).
(w - 1)*(w + 1)*(w + 2)/4
Let s(t) = 2*t**4 + 5*t**3 + 6*t**2 + 5*t - 3. Let q(h) = h**4 + 4*h**3 + 6*h**2 + 4*h - 3. Let w(a) = 5*q(a) - 4*s(a). Factor w(p).
-3*(p - 1)**2*(p + 1)**2
Let m(x) = -x**4 + x**3 + x**2. Let r(b) = -15*b**4 + 25*b**3 + 15*b**2 - 5*b. Let l(y) = 20*m(y) - r(y). Let l(a) = 0. Calculate a.
-1, 0, 1
Let l(k) = -k**3 + 11*k**2 - 4*k + 2. Let r(i) = 15*i**3 - 177*i**2 + 63*i - 33. Let c(t) = -33*l(t) - 2*r(t). Factor c(s).
3*s*(s - 2)*(s - 1)
Let f be ((-6)/35)/((-3)/10). Let q be (4/35)/(2/5). Find j, given that f*j**3 - q*j**4 - 2/7*j**5 - 2/7*j - 2/7 + 4/7*j**2 = 0.
-1, 1
Let i(q) be the second derivative of q**9/7560 + 5*q**4/12 - 10*q. Let f(b) be the third derivative of i(b). Factor f(u).
2*u**4
Suppose j = 4*k - 14, 2*k - 2*j = -k + 13. Let h be 10/k + (-1)/3. What is l in 0*l + 2/3*l**h + 0*l**2 + 0 = 0?
0
Suppose 0 = a + 4*z + 8, -z + 10 = 2*a + 12. Suppose -2/3*i**2 + a + 0*i = 0. Calculate i.
0
Let c be (-8)/9*6/(-8). Let q = 57 - 55. Factor 0*u + c*u**q - 2/3.
2*(u - 1)*(u + 1)/3
Factor r**2 + 0*r**2 + 0*r**2 + 2*r - 4 + 1.
(r - 1)*(r + 3)
Suppose -5*g + 15 = -5*d, 5*g - g - 2*d - 12 = 0. Let h(q) = -q**2 + 5*q - 6. Let l be h(g). Suppose -1/3*w**2 + l*w + 0 = 0. Calculate w.
0
Let c(i) be the first derivative of 4*i**5/5 + 2*i**4 - 4*i**3/3 - 4*i**2 + 9. Suppose c(k) = 0. What is k?
-2, -1, 0, 1
Let o(k) be the first derivative of -8*k**3/15 - 9*k**2/5 - 4*k/5 - 5. Solve o(v) = 0.
-2, -1/4
Factor -2*q**2 + 50*q + q**3 - 104*q + 49*q + 6.
(q - 3)*(q - 1)*(q + 2)
Let k(l) be the third derivative of 0*l**3 + 3*l**2 + 1/420*l**7 - 1/1344*l**8 + 0*l**4 + 0*l - 1/480*l**6 + 0 + 0*l**5. What is p in k(p) = 0?
0, 1
Let v be (-28)/(-6) + 4/(-6). Find r, given that v*r**2 - 4*r + 7*r + 2 - 2*r**2 + r = 0.
-1
Find a, given that a**2 - 1/2*a**3 + 0 - 1/2*a = 0.
0, 1
Let o(w) be the third derivative of w**5/180 + w**4/36 - 17*w**2. Factor o(j).
j*(j + 2)/3
Let n(a) be the second derivative of -a**9/5040 + a**8/2240 + a**7/420 - a**4/6 + a. Let c(d) be the third derivative of n(d). Suppose c(x) = 0. What is x?
-1, 0, 2
Let h(i) = -1. Let q(b) = -2*b**2 - 6*b - 2. Let p(o) = -4*h(o) - 2*q(o). Factor p(c).
4*(c + 1)*(c + 2)
Let p = -281/88 - -27/8. Determine x so that 2/11 - 4/11*x + p*x**2 = 0.
1
Suppose 0 = -18*w + 14*w + 108. Let h be 24/w - 4/6. Factor 4/9*p + 2/9*p**2 + h.
2*(p + 1)**2/9
Let n(g) be the second derivative of -g**6/105 + 2*g**5/35 - 2*g**4/21 - 19*g. Solve n(l) = 0.
0, 2
Let s = 2 - 2. Suppose 2*z - 8 = s, z + 4 = 4*b - 0*b. Factor -2/3 + 4/3*h - 2/3*h**b.
-2*(h - 1)**2/3
Suppose -m - 2*k + 2 = 0, 5*m = -0*k - 2*k + 10. Find v such that -2/3*v + 0 + 2/3*v**m = 0.
0, 1
Let w(p) be the third derivative of -p**7/42 + p**6/6 + 11*p**5/12 + 5*p**4/4 - 2*p**2 + 9*p. Factor w(i).
-5*i*(i - 6)*(i + 1)**2
Let q be (-1)/2 + 26/36. Suppose -h = -i + 3, -3*h + 4*i = 3*i - 1. Solve 0*p - q*p**3 + 2/9*p**h + 0 = 0.
0, 1
Let a(w) be the third derivative of -w**9/272160 - 