I want to get a test of linear trend from an ordered factor, but I don’t want all the extra polynomial trend tests that R spits out automatically (e.g. quadratic, cubic etc)

Here’s some toy data

d <- data.frame(f_ord = factor(x = rep(letters[1:5],each=5),
                               ordered = TRUE),
                f_nonOrd = factor(x = rep(letters[1:5],each=5),
                                  ordered = FALSE)
                score = as.vector(sapply(seq(0,20,5), function(i) rnorm(n=5,i,2))))

When we do a simple regression on this data with the ordered factor as the predictor

summary(lm(score ~ f, data = d))

# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)    
# (Intercept)   9.8472     0.4723  20.850 4.87e-15 ***
# f.L          16.0248     1.0561  15.174 1.95e-12 ***
# f.Q           1.5136     1.0561   1.433   0.1672    
# f.C          -0.5138     1.0561  -0.487   0.6319    
# f^4           1.9568     1.0561   1.853   0.0787 .

The output gives us polynomial trend tests all the way up to quarternary.

Is there any way either to

(1) Remove the higher-order trend tests from the ordered factor

(2) Specify a single set of contrast coefficients to the non-ordered factor

Any help much appreciated.