 1)
Suppose 0*j - 3*j = 15, -3*j - 31 = -o. Suppose -i + 6*i - 20 = 5*b, b - o = -4*i. Suppose 8*w**3 - 5 - i*w**2 + 5 + 4 + w - 9*w = 0. Calculate w.
-1, 1/2, 1
Let p(z) be the third derivative of -8/35*z**7 - 2/15*z**6 + 14/15*z**5 - 1/2*z**4 + 0*z + 0 - 4/3*z**3 + 1/12*z**8 - 35*z**2. Factor p(g).
4*(g - 1)**3*(g + 1)*(7*g + 2)
Let r(w) be the first derivative of 0*w**2 + 0*w**4 - 4/25*w**5 + 16/15*w**3 + 0*w - 8. Suppose r(b) = 0. What is b?
-2, 0, 2
Let n be (1 + -1)/((72/4)/9). Let n*s + 1/3*s**3 + 1/6*s**4 + 0 + 0*s**2 = 0. Calculate s.
-2, 0
Suppose 4*v - 56*v = 6*v. Factor 14*z**2 + 6*z + v + 8/3*z**4 + 32/3*z**3.
2*z*(z + 1)*(2*z + 3)**2/3
Let j(k) = 28*k**2 + 29*k - 19. Suppose -77 = 5*h + 23. Let o be h/(-30) + (-8)/3. Let y(i) = 9*i**2 + 10*i - 6. Let b(m) = o*j(m) + 7*y(m). Factor b(c).
(c + 2)*(7*c - 2)
Let p = 2 - 0. Let s be ((-90)/(-9))/(p/1). Factor 0*j**5 - 4*j - 36*j**4 + 3*j**3 + 38*j**4 - 4*j**2 - j**s.
-j*(j - 2)**2*(j + 1)**2
What is l in -2/13*l**5 + 0 - 2/13*l - 8/13*l**4 - 12/13*l**3 - 8/13*l**2 = 0?
-1, 0
Let u be (15/(-45))/(2/(-228)). Solve -u*r + 4*r**2 + 38*r - 16 = 0.
-2, 2
Let a(l) be the second derivative of 0 + 2/3*l**3 + 5/2*l**2 - 1/12*l**4 - 11*l. Let a(i) = 0. What is i?
-1, 5
Suppose -t - 154 = 10*t. Let k be -3*(t/(-6) - 4). Factor 0*b**2 - 2/5*b**k + 4/5*b**4 - 2/5*b**3 + 0 + 0*b.
-2*b**3*(b - 1)**2/5
Let l(u) = -u**3 - 46*u**2 + 203*u + 159. Let k be l(-50). Suppose -k + 5*f**3 - 33/2*f - 4*f**2 + f**4 - 1/2*f**5 = 0. What is f?
-2, -1, 3
Factor -6/5*x**2 + 0*x + 0 - 2/5*x**3.
-2*x**2*(x + 3)/5
Let h(k) be the third derivative of k**8/5040 + k**7/1260 - k**6/90 - 17*k**5/60 + 22*k**2. Let s(c) be the third derivative of h(c). Solve s(n) = 0 for n.
-2, 1
Let v(n) = 3*n**2 + 30*n + 10. Let t(g) = g**2 + 15*g + 4. Let z(h) = -5*t(h) + 2*v(h). Solve z(w) = 0.
0, 15
Let m(y) be the first derivative of 5 + 0*y**2 + 0*y**3 + 5/8*y**4 + 0*y. Find g such that m(g) = 0.
0
Suppose 2*r - 50 = -0*r. Let l be ((-10)/r)/(6/(-20)). Find p, given that -8/3*p**3 + l + 8/3*p - 1/3*p**2 - p**4 = 0.
-2, -1, -2/3, 1
Let m(z) = -14*z - 158. Let v be m(-12). Let k(g) be the second derivative of v*g - 8/21*g**3 + 0 - 1/35*g**5 + 0*g**2 - 4/21*g**4. Factor k(y).
-4*y*(y + 2)**2/7
Suppose 0 = 14*w - 152 - 2. Let m be (-138)/(-330) + 2/w. Factor 6/5*b**3 - 3/5*b**4 - m*b**2 + 0*b + 0.
-3*b**2*(b - 1)**2/5
Suppose 3*o + 5 + 4 = -5*g, 0 = -4*o + 2*g + 14. Let x = -12 + 14. Find t, given that 2*t**o - 3*t**x + 2*t - t**2 = 0.
0, 1
Let m = 739/3545 - 6/709. Find d, given that -m*d**2 - 4/5 + d = 0.
1, 4
Suppose 2*j + 0*v = 2*v + 14, -2*v + 49 = 5*j. What is s in s + j*s**3 - 4*s - 5*s**3 - s**3 = 0?
-1, 0, 1
Let d(o) be the third derivative of o**8/4480 + o**7/560 + o**6/240 + o**4/6 + 6*o**2. Let g(y) be the second derivative of d(y). Factor g(v).
3*v*(v + 1)*(v + 2)/2
Let t be 6*(-2)/3 + 8. Factor -21*s**2 - 16*s**4 - 56 - 51*s**2 - 208*s - 104 + 20*s**4 + t*s**3.
4*(s - 5)*(s + 2)**3
Let q(g) be the second derivative of -g**4/21 + 106*g**3/21 - 29*g. Factor q(c).
-4*c*(c - 53)/7
Let y(h) be the third derivative of h**5/12 - 14*h**2. Factor y(q).
5*q**2
Solve -79/6*b - 41/2*b**2 - 3/2*b**3 - 13/6 = 0 for b.
-13, -1/3
Suppose -5*i + 222 = 2*o, 222 = 2*o + 3*i + i. Let t = o - 221/2. Let 3/2*j + 0 - t*j**5 - j**3 - 2*j**2 + 2*j**4 = 0. What is j?
-1, 0, 1, 3
Let l be -1*(-5 + (11 - 6)). Let 0*t + 2/7*t**2 + l + 2/7*t**3 = 0. What is t?
-1, 0
Let c(r) be the second derivative of -31*r - 3/28*r**4 + 9/14*r**2 + 0 - 3/140*r**5 + 1/14*r**3. Factor c(g).
-3*(g - 1)*(g + 1)*(g + 3)/7
Let z(o) be the first derivative of o**3/15 + 11*o**2/10 - 12*o/5 - 510. Determine h, given that z(h) = 0.
-12, 1
Let j(y) be the third derivative of 1/252*y**4 + 1/630*y**5 + 0 - 2/63*y**3 + 7*y**2 + 0*y. What is s in j(s) = 0?
-2, 1
Let o = -340 + 2388/7. Solve 0*a**2 + 36/7*a**3 - 16/7*a + 0 - o*a**4 - 12/7*a**5 = 0.
-2, -2/3, 0, 1
Let b(x) be the second derivative of 0 + 0*x**2 - 1/45*x**4 - 1/150*x**5 - 1/45*x**3 - 17*x. Factor b(p).
-2*p*(p + 1)**2/15
Let f be (170/(-25))/((-2)/(-10)). Let o = 38 + f. Factor -o*b**2 - 3 + b**3 + 0*b**2 + 7*b**2 - b.
(b - 1)*(b + 1)*(b + 3)
Let t(q) be the second derivative of 4*q + 1/60*q**5 + 0*q**2 + 2/9*q**3 + 0 - 1/9*q**4. Suppose t(w) = 0. Calculate w.
0, 2
Let o(v) be the third derivative of -v**10/15120 + v**8/1680 - v**6/360 + 7*v**4/24 - 7*v**2. Let w(l) be the second derivative of o(l). Factor w(t).
-2*t*(t - 1)**2*(t + 1)**2
Suppose -4 = -2*x, 3*m - 9 = -x + 2. Factor -r**4 - 4*r**2 - 3*r**3 - 4*r**m - 2*r**2.
-r**2*(r + 1)*(r + 6)
Let g(l) be the second derivative of -3*l**5/40 + 3*l**4/2 - 9*l**3 + 24*l**2 - 133*l. Factor g(u).
-3*(u - 8)*(u - 2)**2/2
Let q(w) = -w**2 + 11*w - 13. Let l be q(9). Suppose 5*k - l*f - 22 = 48, -k + 20 = f. Factor -6*t + 3 - k*t**2 - 3 + 20*t**2.
3*t*(t - 2)
Let p(h) be the third derivative of h**6/180 - h**5/90 + 188*h**2. Determine r so that p(r) = 0.
0, 1
Let m be (14/28)/(35/28). Solve -4/5*c**3 - m + 2/5*c**5 + 2/5*c + 4/5*c**2 - 2/5*c**4 = 0 for c.
-1, 1
Let q(m) be the second derivative of m**6/90 - 7*m**5/20 - m**4/36 + 7*m**3/6 + 18*m. Factor q(i).
i*(i - 21)*(i - 1)*(i + 1)/3
Solve 5*t**2 - 5*t**4 + 10*t**3 - 157*t + 474*t - 161*t - 166*t = 0 for t.
-1, 0, 1, 2
Suppose 5 = 4*n - k, 4*n - 3*k - 2 = -3. Let h(w) = w**3 + w**2 - 4*w - 1. Let f be h(n). Factor 0 + 1/3*q**f + 2/3*q**2 + 0*q.
q**2*(q + 2)/3
Factor 2/5*p**3 + 22/5*p - 42/5 + 18/5*p**2.
2*(p - 1)*(p + 3)*(p + 7)/5
Let a = -26 - -32. Factor 4*r + 6*r**2 - a*r**3 + 6*r**3 + 2*r**3.
2*r*(r + 1)*(r + 2)
Let x(z) be the third derivative of -z**5/12 - 10*z**4/3 + 30*z**3 - 479*z**2. Factor x(b).
-5*(b - 2)*(b + 18)
Let y be 16/28 - (-7835)/70. Let d = -112 + y. Solve 0*u + d - u**2 + 1/2*u**4 + 0*u**3 = 0 for u.
-1, 1
Let m be 0 - 0 - (-13)/650. Let d = m - -293/350. What is h in 0*h + d*h**2 + 8/7*h**3 + 0 + 2/7*h**4 = 0?
-3, -1, 0
Let m(r) be the second derivative of -9/8*r**3 - 1/15*r**6 - 20*r + 0*r**2 + 9/40*r**5 + 0*r**4 + 0 + 1/168*r**7. Find j such that m(j) = 0.
-1, 0, 3
Let w = 210 + -210. Let f(k) be the second derivative of -3/2*k**3 - k - 1/4*k**4 - 3*k**2 + w. What is b in f(b) = 0?
-2, -1
Let v be 16/24 - 7/(-3). Factor 2*d**4 + 3*d**3 - v*d**2 + d - 3*d + d**4 - d.
3*d*(d - 1)*(d + 1)**2
Suppose -4*d + 2*d + 66 = 0. Let z be (-6)/(-33) + 126/d. Factor 3*h**2 - 4*h**2 + z - 2 - h.
-(h - 1)*(h + 2)
Suppose 11*n**3 - 4*n - 23*n**3 + 23*n**4 - 20*n**2 + 12*n**4 + n**4 = 0. What is n?
-1/3, 0, 1
Suppose -9*u + 61 - 7 = 0. Factor -u*i - 8*i + 9*i + 6 - i**2.
-(i - 1)*(i + 6)
Let n(l) be the third derivative of l**6/30 + 202*l**5/15 - 203*l**4/6 + 94*l**2 + 3*l. Factor n(z).
4*z*(z - 1)*(z + 203)
Let x(g) be the third derivative of -g**6/540 + g**5/90 + g**4/27 - 76*g**2. Factor x(h).
-2*h*(h - 4)*(h + 1)/9
Let c(u) = 2*u. Let a be c(3). Suppose -8 = -2*j + a*s - 5*s, -j - 14 = 4*s. Factor -23*k**2 - 3*k**3 + 14*k**j + 0*k**3.
-3*k**2*(k + 3)
Let z(r) be the first derivative of -r**6/240 + r**4/48 - r**2/16 + 11*r + 10. Let k(q) be the first derivative of z(q). Factor k(p).
-(p - 1)**2*(p + 1)**2/8
Let u be 10 - -76*13/(-104). Factor -w + 0 - u*w**2.
-w*(w + 2)/2
Let w(n) = -3*n**2 - 7*n + 2. Let o(y) = -8*y - 11*y - 14*y**2 - 14*y - 3*y + 10. Let m(s) = -3*o(s) + 16*w(s). Determine g so that m(g) = 0.
-1, 1/3
Factor -5*o**4 + 9*o**5 - 192*o + 18 - 32*o**3 - 3*o**4 - 22*o**3 + 2*o**4 + 108*o**2 + 117*o.
3*(o - 1)**3*(o + 3)*(3*o - 2)
Suppose 2*t - 4*z = 24, 0 = 2*t + 4*z + 1 + 15. Factor -4 + 3*i**t + 6*i**3 - 5*i - i - 1 + 2.
3*(i - 1)*(i + 1)*(2*i + 1)
Factor 63 - 113 + 58 + 4*q - 4*q**2.
-4*(q - 2)*(q + 1)
Let t = -173 - -128. Let q be -24*((-100)/t + -4). Factor -32/3*g - q*g**2 - 2/3.
-2*(8*g + 1)**2/3
Let v(m) be the first derivative of -m**6/10 - 3*m**5/20 + 10*m - 3. Let s(o) be the first derivative of v(o). Determine b so that s(b) = 0.
-1, 0
Let c(h) = -14*h**4 + 126*h**3 + 372*h**2 + 252*h + 4. Let f(k) = -10*k**4 + 127*k**3 + 373*k**2 + 251*k + 3. Let r(w) = 3*c(w) - 4*f(w). Factor r(x).
-2*x*(x + 1)*(x + 2)*(x + 62)
Let z(k) be the second derivative of -k**5/10 + 10*k**4/3 - 37*k**3/3 + 18*k**2 + k - 39. Suppose z(p) = 0. Calculate p.
1, 18
Let g = 6 - 2. Suppose 0*o + k + 5 = -g*o, 0 =